Formulating and Modifying Hypotheses Alıştırma Soruları — ACT

Soru 1Soru →

Researchers studied the effect of dissolved organic carbon (DOC) on the photochemical degradation rate of Pollutant X in water samples exposed to constant UV light. Two initial hypotheses were proposed:

* Hypothesis 1: DOC acts as a photosensitizer, so increasing DOC concentration will continuously increase the degradation rate of Pollutant X.
* Hypothesis 2: DOC acts as a light attenuator (blocking UV light), so increasing DOC concentration will continuously decrease the degradation rate of Pollutant X.

The degradation rate of Pollutant X was measured at various DOC concentrations, and the results are recorded in the table below:

DOC Concentration ( $\text{mg/L}$ )	Degradation Rate (\%\text{ per hour})
$0$	$5.2$
$2$	$8.4$
$4$	$11.1$
$8$	$9.5$
$12$	$6.8$
$16$	$4.3$

Based on these results, which of the following modified hypotheses best describes the relationship between DOC concentration and the degradation rate of Pollutant X?

DOC acts as a light attenuator across all tested concentrations, meaning the degradation rate of Pollutant X decreased continuously as DOC concentration increased from

0\text{ mg/L}

to

16\text{ mg/L}

.

DOC has no effect on the degradation rate of Pollutant X, meaning the rate remains constant at approximately

11.1\%\text{ per hour}

regardless of changes in DOC concentration.

DOC increases the degradation rate of Pollutant X at low concentrations (up to

4\text{ mg/L}

) by acting as a photosensitizer, but decreases the rate at higher concentrations (above

4\text{ mg/L}

) due to light attenuation.

DOC acts as a photosensitizer across all concentrations, meaning the degradation rate of Pollutant X will continuously increase as the DOC concentration is raised beyond

4\text{ mg/L}

.

Cevabı ve açıklamayı göster

Cevap: DOC increases the degradation rate of Pollutant X at low concentrations (up to $4\text{ mg/L}$ ) by acting as a photosensitizer, but decreases the rate at higher concentrations (above $4\text{ mg/L}$ ) due to light attenuation.

Cevap

Dissolved organic carbon (DOC) increases the degradation rate of Pollutant X at low concentrations (up to

4\text{ mg/L}

) by acting as a photosensitizer, but decreases the rate at higher concentrations (above

4\text{ mg/L}

) due to light attenuation.

The correct hypothesis must account for the biphasic trend observed in the data. The degradation rate of Pollutant X rises from

5.2\%\text{ per hour}

to

11.1\%\text{ per hour}

as the dissolved organic carbon (DOC) concentration increases from

0\text{ mg/L}

to

4\text{ mg/L}

, supporting the photosensitizer role (Hypothesis 1). However, as the DOC concentration increases further from

4\text{ mg/L}

to

16\text{ mg/L}

, the degradation rate steadily decreases to

4.3\%\text{ per hour}

, which supports the light attenuator role (Hypothesis 2). Combining these two effects into a single modified hypothesis correctly explains the entire range of data.

Adım Adım Çözüm

1

Analyze the trend in the degradation rate of Pollutant X as the DOC concentration increases from

0\text{ mg/L}

to

4\text{ mg/L}

.

The degradation rate increases from

5.2\%\text{ per hour}

to

11.1\%\text{ per hour}

.

To determine if the initial phase of the reaction supports the photosensitizer hypothesis.

2

Analyze the trend in the degradation rate as the DOC concentration increases from

4\text{ mg/L}

to

16\text{ mg/L}

.

The degradation rate decreases from

11.1\%\text{ per hour}

to

4.3\%\text{ per hour}

.

To determine if the subsequent phase of the reaction supports the light attenuator hypothesis.

3

Synthesize these observations to evaluate the proposed hypotheses and formulate a modified hypothesis.

A modified hypothesis must state that DOC acts as a photosensitizer at low concentrations but as a light attenuator at high concentrations, matching both trends.

To find the option that correctly describes this dual behavior across the entire range.

Anahtar Kavram

Evaluating and modifying scientific hypotheses based on experimental data that exhibit non-linear or multi-phase relationships.

Tahmini Süre:2m 0s

Soru 2Soru →

A plant physiologist formulated the following hypothesis:

*Hypothesis*: Under constant high-light conditions, the rate of transpiration in a particular plant species is determined solely by stomatal conductance. Consequently, any environmental change that reduces stomatal conductance will result in a proportionally identical decrease in the transpiration rate.

To test this hypothesis, the physiologist placed several plants in a controlled chamber under constant high-light conditions. Stomatal conductance and transpiration rate were measured at various relative humidity (RH) levels. Measurements taken at $80\%$ RH served as the baseline ( $100\%$ ). The results are shown in the table below:

Relative Humidity (RH)	Stomatal Conductance (% of baseline)	Transpiration Rate (% of baseline)
$80\%$ (Baseline)	$100\%$	$100\%$
$60\%$	$75\%$	$120\%$
$40\%$	$50\%$	$135\%$
$20\%$	$25\%$	$140\%$

Which of the following modifications to the physiologist's hypothesis is most consistent with these results?

The rate of transpiration is independent of stomatal conductance, and is instead determined solely by the relative humidity, which shares a direct, positive relationship with the transpiration rate.

The rate of transpiration is determined by multiple interacting factors; a decrease in relative humidity increases the evaporative gradient between the leaf interior and the air, which can increase transpiration even as stomatal conductance decreases.

The rate of transpiration is determined solely by stomatal conductance, but the decrease in relative humidity caused an increase in the leaf's internal water vapor concentration that kept stomatal conductance high.

The original hypothesis remains valid because the transpiration rate would begin to decrease proportionally once stomatal conductance falls below a threshold of

25\%

of the baseline.

Cevabı ve açıklamayı göster

Cevap: The rate of transpiration is determined by multiple interacting factors; a decrease in relative humidity increases the evaporative gradient between the leaf interior and the air, which can increase transpiration even as stomatal conductance decreases.

Cevap

The rate of transpiration is determined by multiple interacting factors; a decrease in relative humidity increases the evaporative gradient between the leaf interior and the air, which can increase transpiration even as stomatal conductance decreases.

The correct option correctly identifies that transpiration is influenced by multiple factors, including the evaporative gradient between the leaf interior and the ambient air. As relative humidity decreases, this gradient becomes steeper, driving more water to evaporate from the leaf. This evaporative demand can override the effect of stomatal closure, explaining why the transpiration rate increases even as stomatal conductance decreases from

100\%

to

25\%

.

Adım Adım Çözüm

1

Analyze the original hypothesis to identify the predicted relationship between stomatal conductance and transpiration rate.

The hypothesis predicts that transpiration is solely determined by stomatal conductance in a 1:1 proportional relationship, meaning any decrease in conductance must yield an identical percentage decrease in transpiration.

To evaluate a hypothesis, you must first clarify its specific, testable predictions.

2

Compare the predicted relationship with the actual data shown in the table.

As relative humidity decreases, stomatal conductance decreases (from

100\%

to

25\%

), but transpiration rate increases (from

100\%

to

140\%

).

Comparing actual data against predictions reveals whether the hypothesis is supported or refuted.

3

Formulate a modified hypothesis that explains why transpiration rate increases despite the reduction in stomatal conductance.

Transpiration must be controlled by multiple factors. The reduction in relative humidity increases the evaporative demand (driving force) on the leaf, which overrides the limiting effect of the closing stomates.

A modified hypothesis must reconcile the conflicting variables to account for the physical trends in the data.

Anahtar Kavram

Formulating and Modifying Hypotheses

Tahmini Süre:1m 30s

Soru 3Soru →

A student hypothesized that as the temperature of water increases, the maximum mass of sugar that can dissolve in $100\text{ mL}$ of water decreases. To test this, the student measured the maximum mass of sugar dissolved at various temperatures and recorded the results in the table below:

Temperature ( $^\circ\text{C}$ )	Maximum mass of sugar dissolved ( $\text{g}$ )
$20$	$204$
$40$	$238$
$60$	$287$
$80$	$362$

Based on these results, how should the student modify their hypothesis?

The student should modify the hypothesis to state that as the temperature of water increases, the maximum mass of sugar that can dissolve increases.

The student should modify the hypothesis to state that as the temperature of water increases, the maximum mass of sugar that can dissolve remains the same.

The student should modify the hypothesis to state that as the temperature of water decreases, the maximum mass of sugar that can dissolve increases.

The student should modify the hypothesis to state that the maximum mass of sugar that can dissolve is independent of water temperature.

Cevabı ve açıklamayı göster

Cevap: The student should modify the hypothesis to state that as the temperature of water increases, the maximum mass of sugar that can dissolve increases.

Cevap

The student should modify the hypothesis to state that as the temperature of water increases, the maximum mass of sugar that can dissolve increases.

The correct answer is correct because the experimental data directly contradicts the original hypothesis. As the independent variable (temperature) increases from

20^\circ\text{C}

to

80^\circ\text{C}

, the dependent variable (maximum mass of sugar dissolved) increases from

204\text{ g}

to

362\text{ g}

. Therefore, the student should modify the hypothesis to state that as the temperature of water increases, the maximum mass of sugar that can dissolve increases.

Adım Adım Çözüm

1

Analyze the student's original hypothesis and compare it to the independent variable (temperature) and dependent variable (maximum mass of sugar dissolved) in the table.

The student predicted a negative relationship: higher temperatures would lead to a lower mass of dissolved sugar.

To determine how to modify the hypothesis, we must first establish what the student originally expected.

2

Identify the trend in the data table as temperature increases from

20^\circ\text{C}

to

80^\circ\text{C}

.

At

20^\circ\text{C}

, the mass is

204\text{ g}

. At

40^\circ\text{C}

, it is

238\text{ g}

. At

60^\circ\text{C}

, it is

287\text{ g}

. At

80^\circ\text{C}

, it is

362\text{ g}

. As temperature increases, the dissolved mass increases.

Comparing the data points allows us to see if the dependent variable increases or decreases with the independent variable.

3

Compare the observed trend with the original hypothesis to formulate the modified hypothesis.

The actual trend (solubility increases with temperature) is the opposite of the original hypothesis. Therefore, the student should modify the hypothesis to state that solubility increases as temperature increases.

A modified hypothesis must align with the actual experimental evidence gathered.

Anahtar Kavram

Formulating and Modifying Hypotheses

Tahmini Süre:45s

Soru 4Soru →

A student performed an experiment to study the reaction between magnesium metal and hydrochloric acid ( $HCl$ ). The student hypothesized that as the concentration of $HCl$ increases, the reaction time will decrease at a constant rate. The student measured the time required for a $1.0\text{ g}$ pellet of magnesium to completely dissolve in $50\text{ mL}$ of $HCl$ at $25^\circ\text{C}$ using different concentrations of the acid. The results are shown in the table below.

$HCl$ Concentration (M)	Reaction Time (s)
0.5	120
1.0	60
1.5	40
2.0	30

Do the results of the experiment support the student's hypothesis?

No; although the reaction time decreased as the concentration of

HCl

increased, the rate of decrease was not constant.

Yes; as the concentration of

HCl

increased, the reaction time decreased by a constant

60\text{ s}

for every

0.5\text{ M}

increase.

Yes; the reaction time decreased by exactly

20\text{ s}

for each

0.5\text{ M}

increase in concentration.

No; as the concentration of

HCl

increased, the reaction time increased rather than decreased.

Cevabı ve açıklamayı göster

Cevap: No; although the reaction time decreased as the concentration of $HCl$ increased, the rate of decrease was not constant.

Cevap

No; although the reaction time decreased as the concentration of

HCl

increased, the rate of decrease was not constant.

The correct answer is correct because the student's hypothesis predicted that the reaction time would decrease at a constant rate. While the reaction time did decrease as the concentration of

HCl

increased, the rate of decrease was not constant: the time decreased by

60\text{ s}

(from

120\text{ s}

to

60\text{ s}

) when concentration increased from

0.5\text{ M}

to

1.0\text{ M}

, but only decreased by

20\text{ s}

(from

60\text{ s}

to

40\text{ s}

) when concentration increased from

1.0\text{ M}

to

1.5\text{ M}

. Because the rate of decrease varies, the hypothesis of a constant rate of decrease is not supported.

Adım Adım Çözüm

1

Identify the student's hypothesis regarding the relationship between

HCl

concentration and reaction time.

The hypothesis states that as concentration increases, reaction time will decrease at a constant rate.

This establishes the criteria required to support the hypothesis.

2

Analyze the trend in the data table to determine if reaction time decreases as concentration increases.

As concentration increases from

0.5\text{ M}

to

2.0\text{ M}

, reaction time decreases from

120\text{ s}

to

30\text{ s}

.

This checks the first part of the hypothesis (decreasing trend).

3

Calculate the change in reaction time for equal increments of concentration to determine if the rate of decrease is constant.

For each

0.5\text{ M}

increase, the reaction time changes by

-60\text{ s}

, then

-20\text{ s}

, and finally

-10\text{ s}

. The rate of decrease is not constant.

This tests the second part of the hypothesis (constant rate) to draw the final conclusion.

Anahtar Kavram

Evaluating a hypothesis by comparing its predictions (specifically, a constant rate of change) against quantitative experimental results.

Soru 5Soru →

Two students propose competing hypotheses regarding the rate of oxygen ( $O_2$ ) gas production during the catalytic decomposition of hydrogen peroxide ( $H_2O_2$ ) by a yeast suspension.

Student 1 Hypothesizes: The rate of $O_2$ production is directly proportional to the initial concentration of $H_2O_2$ because a higher concentration of reactant increases the frequency of collisions.

Student 2 Hypothesizes: The rate of $O_2$ production is limited by the number of active enzyme sites on the yeast cells. Once all active sites are saturated, the rate will reach a maximum value ( $V_{max}$ ) and remain constant, regardless of further increases in $H_2O_2$ concentration.

The students perform five trials measuring the volume of $O_2$ gas produced in the first 60 seconds under various initial conditions. The results are shown in the table below:

Trial	Initial $H_2O_2$ concentration (M)	Yeast suspension volume (mL)	Volume of $O_2$ produced in 60 s (mL)
1	0.5	2.0	15.0
2	1.0	2.0	30.0
3	2.0	2.0	45.0
4	3.0	2.0	45.0
5	2.0	4.0	90.0

Based on these results, which of the following statements best describes how one of the hypotheses should be modified to align with the experimental data?

Student 2's hypothesis is supported by the data, but it must be modified to state that the value of

V_{max}

is directly proportional to the volume of the yeast suspension.

Student 1's hypothesis is supported by the data, but it must be modified to state that the rate of

O_2

production decreases at yeast suspension volumes greater than 2.0 mL.

Student 2's hypothesis is refuted by the data, and it must be modified to state that yeast concentration has no effect on the maximum rate of reaction.

Student 1's hypothesis is supported across all trials, and it must be modified to state that doubling the concentration of

H_2O_2

always results in a 1.5-fold increase in the volume of

O_2

produced.

Cevabı ve açıklamayı göster

Cevap: Student 2's hypothesis is supported by the data, but it must be modified to state that the value of $V_{max}$ is directly proportional to the volume of the yeast suspension.

Cevap

Student 2's hypothesis is supported by the data, but it must be modified to state that the value of

V_{max}

is directly proportional to the volume of the yeast suspension.

The correct answer is the option stating that Student 2's hypothesis is supported but must be modified to show that the maximum rate is directly proportional to the volume of the yeast suspension. Trials 3 and 4 show that once a concentration of

2.0\text{ M}

is reached, further increases in

H_2O_2

do not increase the volume of

O_2

produced, confirming the saturation model. Trial 5 shows that doubling the yeast volume at this saturation level doubles the total

O_2

produced, confirming that

V_{max}

is directly proportional to the amount of catalyst.

Adım Adım Çözüm

1

Analyze Trials 3 and 4 to evaluate the effect of reactant concentration at high levels.

In Trials 3 and 4, the initial concentration of

H_2O_2

increases from

2.0\text{ M}

to

3.0\text{ M}

while yeast volume remains constant at

2.0\text{ mL}

. The volume of

O_2

produced remains constant at

45.0\text{ mL}

.

This identifies that the reaction rate has reached a plateau, which supports the active-site saturation hypothesis of Student 2.

2

Analyze Trial 5 relative to Trial 3 to determine the effect of catalyst volume.

In Trial 5, the yeast suspension volume is doubled to

4.0\text{ mL}

while keeping

H_2O_2

at

2.0\text{ M}

. The volume of

O_2

produced doubles from

45.0\text{ mL}

to

90.0\text{ mL}

.

This determines how the maximum rate (

V_{max}

) responds to an increase in enzyme concentration.

3

Synthesize the findings to modify the appropriate hypothesis.

Since

V_{max}

scales linearly with the yeast volume (from

45.0\text{ mL}

to

90.0\text{ mL}

when yeast volume doubles), Student 2's hypothesis must be modified to reflect that the maximum rate is directly proportional to catalyst volume.

This completes the formulation and modification of the hypothesis based on the entire dataset.

Anahtar Kavram

Formulating and Modifying Hypotheses

Tahmini Süre:1m 30s

Soru 6Soru →

A student investigates how the surface roughness of a ramp affects the distance a wooden block travels after sliding down. The student proposes the following hypothesis: 'A block will travel a shorter distance on smoother surfaces because smooth surfaces offer less frictional resistance.'

The student collects the following data:

Surface	Relative Roughness	Sliding Distance (cm)
Sandpaper	High	12
Unfinished wood	Medium	28
Polished plastic	Low	65

Based on these results, which of the following represents the most accurate modification to the student's hypothesis?

The block will travel a longer distance on smoother surfaces because smooth surfaces offer less frictional resistance.

The block will travel a shorter distance on smoother surfaces because smooth surfaces offer more frictional resistance.

The block will travel a longer distance on rougher surfaces because rougher surfaces offer less frictional resistance.

The surface roughness of the ramp does not affect the sliding distance of the block.

Cevabı ve açıklamayı göster

Cevap: The block will travel a longer distance on smoother surfaces because smooth surfaces offer less frictional resistance.

Cevap

The block will travel a longer distance on smoother surfaces because smooth surfaces offer less frictional resistance.

The correct answer is that the block will travel a longer distance on smoother surfaces because smooth surfaces offer less frictional resistance. According to the data, the polished plastic surface (low roughness) resulted in a sliding distance of 65 cm, which is much greater than the 12 cm distance on sandpaper (high roughness). This confirms that decreasing roughness increases the distance traveled, so the hypothesis must be modified to reflect this positive relationship between smoothness and distance.

Adım Adım Çözüm

1

Analyze the student's initial hypothesis.

The student hypothesized that a block travels a shorter distance on smoother surfaces due to less friction.

To evaluate the hypothesis, we must first identify its specific claim about the relationship between surface smoothness and distance.

2

Examine the experimental data in the table.

As surface roughness decreases from sandpaper (high) to polished plastic (low), the sliding distance increases from 12 cm to 65 cm.

Comparing the relative roughness to the measured sliding distance shows how the dependent variable responds to changes in the independent variable.

3

Compare the data trend with the initial hypothesis.

The data contradicts the initial hypothesis because the block traveled further on the smoother surface, not shorter.

Determining whether the data supports or refutes the hypothesis is necessary to formulate the correct modification.

4

Modify the hypothesis to align with the data.

The modified hypothesis must state that the block travels a longer distance on smoother surfaces because less friction allows for more motion.

A valid scientific hypothesis must accurately reflect the empirical trends observed in the experimental results.

Anahtar Kavram

Formulating and Modifying Hypotheses

Soru 7Soru →

A student hypothesized that under constant light and temperature, the rate of transpiration in bean plants increases as the relative humidity of the surrounding air increases. To test this hypothesis, the student measured the transpiration rates of several identical bean plants at different relative humidity levels. The results are shown in the table below:

Relative Humidity (%)	Transpiration Rate ( $mg/dm^2/hr$ )
30	15.2
50	10.4
70	5.8
90	1.3

Based on these results, how should the student modify their hypothesis to accurately reflect the relationship between relative humidity and transpiration rate?

The student should hypothesize that the transpiration rate increases as relative humidity increases, because a lower relative humidity slows the rate of evaporation from the leaves.

The student should hypothesize that the transpiration rate remains constant at all relative humidity levels, because relative humidity has no effect on transpiration.

The student should hypothesize that the transpiration rate decreases as relative humidity increases, because a higher humidity decreases the water vapor concentration gradient between the leaf interior and the air.

The student should hypothesize that the transpiration rate decreases as relative humidity increases, because a higher relative humidity increases the rate of water absorption by the leaves from the air.

Cevabı ve açıklamayı göster

Cevap: The student should hypothesize that the transpiration rate decreases as relative humidity increases, because a higher humidity decreases the water vapor concentration gradient between the leaf interior and the air.

Cevap

The student should hypothesize that the transpiration rate decreases as relative humidity increases, because a higher humidity decreases the water vapor concentration gradient between the leaf interior and the air.

The correct option states that the transpiration rate decreases as relative humidity increases, which matches the trend in the data. It also provides the correct scientific explanation: higher humidity reduces the water vapor concentration gradient between the leaf's wet interior and the air, reducing the rate of diffusion.

Adım Adım Çözüm

1

Analyze the experimental data in the table to determine the relationship between the independent variable (relative humidity) and the dependent variable (transpiration rate).

As relative humidity increases from 30% to 90%, the transpiration rate decreases from 15.2 mg/dm^2/hr to 1.3 mg/dm^2/hr.

This establishes the empirical trend that refutes the student's initial hypothesis of a positive correlation.

2

Identify which proposed hypothesis modifications align with the observed inverse relationship.

The modifications stating that transpiration rate decreases as relative humidity increases align with the trend.

This eliminates hypotheses predicting increasing or constant trends.

3

Evaluate the scientific reasoning behind the remaining options to select the correct physical/biological mechanism.

A higher humidity reduces the concentration gradient of water vapor between the humid interior of the leaf and the outside air, which reduces the evaporation/transpiration rate.

The correct hypothesis must couple the correct trend with scientifically sound reasoning.

Anahtar Kavram

Formulating and Modifying Hypotheses

Soru 8Soru →

A student hypothesized that the solubility of carbon dioxide ( $CO_2$ ) in water is directly proportional to the water temperature because higher temperatures increase the kinetic energy of the gas molecules, allowing them to interact more with water molecules and remain dissolved. The student measured the solubility of $CO_2$ in water at a constant pressure of $1.0\text{ atm}$ across several temperatures and recorded the data in the table below:

Temperature ( $^\circ\text{C}$ )	$CO_2$ Solubility ( $g/kg\text{ of }H_2O$ )
10	2.4
20	1.7
30	1.3
40	1.0

Based on the results in the table, which of the following modifications to the student's hypothesis and explanation is most appropriate?

The student should retain the hypothesis because the solubility of

CO_2

increases with temperature as gas molecules gain kinetic energy and bind more tightly to water molecules.

The student should modify the hypothesis to state that

CO_2

solubility is inversely proportional to water temperature, because at higher temperatures, gas molecules lose kinetic energy and settle at the bottom of the container.

The student should modify the hypothesis to state that

CO_2

solubility is inversely proportional to water temperature, because the increased kinetic energy of the gas molecules at higher temperatures allows them to overcome intermolecular forces and escape the solution.

The student should retain the hypothesis because the decrease in solubility from

2.4\text{ g/kg}

to

1.0\text{ g/kg}

as temperature rises demonstrates a direct relationship between temperature and solubility.

Cevabı ve açıklamayı göster

Cevap: The student should modify the hypothesis to state that $CO_2$ solubility is inversely proportional to water temperature, because the increased kinetic energy of the gas molecules at higher temperatures allows them to overcome intermolecular forces and escape the solution.

Cevap

The student should modify the hypothesis to state that

CO_2

solubility is inversely proportional to water temperature, because the increased kinetic energy of the gas molecules at higher temperatures allows them to overcome intermolecular forces and escape the solution.

The correct answer correctly identifies that the data shows an inverse relationship between temperature and

CO_2

solubility (solubility decreases as temperature increases). It also provides the correct scientific explanation: higher temperatures increase the kinetic energy of the dissolved gas molecules, enabling them to break intermolecular bonds with the solvent and escape as gas.

Adım Adım Çözüm

1

Analyze the solubility data in the table to determine the relationship between water temperature and

CO_2

solubility.

As the water temperature increases from

10^\circ\text{C}

to

40^\circ\text{C}

, the

CO_2

solubility decreases from

2.4\text{ g/kg}

to

1.0\text{ g/kg}

. This indicates an inverse relationship, contradicting the student's hypothesis of a direct relationship.

Evaluating the data trend is necessary to see if the hypothesis is supported or refuted.

2

Assess the physical reasoning of the student's hypothesis regarding kinetic energy.

Higher temperatures do increase the kinetic energy of gas molecules. However, higher kinetic energy makes gas molecules more active, enabling them to break intermolecular bonds with the solvent and escape into the gas phase, which explains the decreased solubility.

Understanding the correct physical mechanism explains why the relationship is inverse rather than direct.

3

Identify the option that correctly describes the necessary modification (inverse relationship) and the accurate physical reasoning.

The option suggesting that solubility is inversely proportional because higher kinetic energy allows gas molecules to escape the solution is the correct choice.

Matching both the data trend and the correct scientific explanation leads to the correct answer.

Anahtar Kavram

Formulating and Modifying Hypotheses

Soru 9Soru →

A student hypothesized that planets located farther from the Sun have shorter orbital periods. The student gathered average orbital data for four planets:

Planet	Average Distance from Sun (AU)	Orbital Period (years)
Mercury	0.39	0.24
Venus	0.72	0.62
Earth	1.00	1.00
Mars	1.52	1.88

Based on these data, how should the student modify their hypothesis?

Modify the hypothesis to state that planets farther from the Sun have longer orbital periods, because orbital period increases as distance increases.

Keep the hypothesis as is, because Mars is farther from the Sun and has the longest orbital period.

Modify the hypothesis to state that distance from the Sun has no effect on a planet's orbital period.

Modify the hypothesis to state that as distance increases, orbital period decreases at a constant rate.

Cevabı ve açıklamayı göster

Cevap: Modify the hypothesis to state that planets farther from the Sun have longer orbital periods, because orbital period increases as distance increases.

Cevap

Modify the hypothesis to state that planets farther from the Sun have longer orbital periods, because orbital period increases as distance increases.

The correct answer is correct because the data in the table shows that as distance from the Sun increases (from

0.39\text{ AU}

to

1.52\text{ AU}

), the orbital period also increases (from

0.24\text{ years}

to

1.88\text{ years}

). Therefore, the student must modify the hypothesis to reflect this direct relationship.

Adım Adım Çözüm

1

Analyze the student's original hypothesis.

The original hypothesis states that planets farther from the Sun have shorter orbital periods.

To evaluate a hypothesis, we must first understand the relationship it proposes (farther distance

\rightarrow

shorter period).

2

Examine the data table to identify the actual relationship.

As distance increases from

0.39\text{ AU}

to

1.52\text{ AU}

, the orbital period increases from

0.24\text{ years}

to

1.88\text{ years}

.

This establishes the empirical relationship shown by the experimental data (larger distance

\rightarrow

longer period).

3

Compare the data trend with the original hypothesis to determine the necessary modification.

The data contradicts the original hypothesis, showing a direct relationship instead of an inverse one. Thus, the hypothesis must be modified to state that planets farther from the Sun have longer orbital periods.

Hypotheses must be updated to align with observed scientific evidence.

Anahtar Kavram

Formulating and Modifying Hypotheses

Tahmini Süre:45s

Soru 10Soru →

A student investigates how the temperature of carbonic acid ( $H_2CO_3$ ) affects the chemical weathering of basalt. The student hypothesizes that as the temperature of the acid solution increases, the rate of chemical weathering (measured as the mass of basalt dissolved over a 24-hour period) will increase. The student performs four trials, starting with a $50.0\text{ g}$ sample of basalt in each trial, while keeping the acid volume and concentration constant. The results are shown in the table below:

Trial	Temperature (°C)	Final mass of basalt (g)
1	15	48.5
2	25	46.8
3	35	45.2
4	45	43.7

Based on the student's hypothesis, if a fifth trial were conducted at $55^\circ\text{C}$ under the same conditions, what would be the predicted final mass of the basalt sample?

Between

43.7\text{ g}

and

45.2\text{ g}

Less than

43.7\text{ g}

Exactly

48.5\text{ g}

Greater than

50.0\text{ g}

Cevabı ve açıklamayı göster

Cevap: Less than $43.7\text{ g}$

Cevap

Less than

43.7\text{ g}

According to the student's hypothesis, as temperature increases, the rate of weathering increases, meaning more basalt dissolves over 24 hours. Because the initial mass of basalt is constant at

50.0\text{ g}

, a higher dissolution rate results in a lower final mass of basalt. Since

55^\circ\text{C}

is higher than the maximum tested temperature of

45^\circ\text{C}

, the final mass at

55^\circ\text{C}

must be less than the final mass measured at

45^\circ\text{C}

(

43.7\text{ g}

). Therefore, the predicted final mass is less than

43.7\text{ g}

.

Adım Adım Çözüm

1

Analyze the student's hypothesis.

The hypothesis states that as temperature increases, the rate of chemical weathering (mass of basalt dissolved) increases.

This establishes the direct relationship between temperature and dissolution rate.

2

Relate dissolution rate to the final mass of basalt.

Since each trial begins with

50.0\text{ g}

of basalt, a higher dissolution rate (more basalt dissolved) will result in a lower remaining final mass.

This translates the hypothesis about dissolution rate into a prediction about the measured variable (final mass).

3

Predict the final mass at

55^\circ\text{C}

relative to the existing data points.

A temperature of

55^\circ\text{C}

is higher than the highest tested temperature of

45^\circ\text{C}

(which had a final mass of

43.7\text{ g}

). According to the hypothesis, more dissolution must occur at

55^\circ\text{C}

than at

45^\circ\text{C}

, so the final mass must be less than

43.7\text{ g}

.

This applies the relationship to the target temperature value to find the correct range.

Anahtar Kavram

Formulating and testing predictions based on a scientific hypothesis.

Tahmini Süre:1m 0s

Soru 11Soru →

A student hypothesized that as the concentration of salt ( $\text{NaCl}$ ) dissolved in water increases, the boiling point of the water decreases. To test this, the student added different masses of $\text{NaCl}$ to $100\text{ mL}$ of pure water and recorded the boiling point of each solution. The results are shown in the table below:

Trial	Mass of $\text{NaCl}$ added ( $\text{g}$ )	Boiling point ( $^\circ\text{C}$ )
1	0	100.0
2	5	100.5
3	10	101.0
4	15	101.5

Based on these results, how should the student modify their hypothesis?

Modify the hypothesis to state that the boiling point of the water remains constant regardless of the concentration of

\text{NaCl}

.

Modify the hypothesis to state that as the concentration of

\text{NaCl}

increases, the boiling point of the water increases.

Modify the hypothesis to state that as the concentration of

\text{NaCl}

increases, the boiling point of the water decreases.

Modify the hypothesis to state that as the concentration of

\text{NaCl}

increases, the boiling point of the water decreases by

0.5^\circ\text{C}

for every

5\text{ g}

of

\text{NaCl}

added.

Cevabı ve açıklamayı göster

Cevap: Modify the hypothesis to state that as the concentration of $\text{NaCl}$ increases, the boiling point of the water increases.

Cevap

Modify the hypothesis to state that as the concentration of

\text{NaCl}

increases, the boiling point of the water increases.

The experimental data show that as the mass of dissolved salt increases, the boiling point of the water increases from

100.0^\circ\text{C}

to

101.5^\circ\text{C}

. This contradicts the student's initial hypothesis that the boiling point would decrease. Therefore, the hypothesis must be modified to state that the boiling point increases as the salt concentration increases.

Adım Adım Çözüm

1

Analyze the student's initial hypothesis.

The student proposed that increasing salt concentration decreases the boiling point of water.

Understanding the starting hypothesis is necessary to determine how it should be modified.

2

Examine the experimental data in the table.

As the mass of salt increases from

0\text{ g}

to

15\text{ g}

, the boiling point increases from

100.0^\circ\text{C}

to

101.5^\circ\text{C}

.

Analyzing the empirical data reveals the actual relationship between the variables.

3

Compare the observed data trend with the initial hypothesis and modify it accordingly.

The data shows that the boiling point increases rather than decreases. The hypothesis must be modified to reflect this direct relationship.

A scientific hypothesis must be revised when experimental evidence contradicts its initial prediction.

Anahtar Kavram

Formulating and Modifying Hypotheses

Tahmini Süre:45s

Soru 12Soru →

A student proposed the following hypothesis:
*Hypothesis*: As the temperature of water increases from $0^\circ\text{C}$ to $10^\circ\text{C}$ , the density of the water will decrease continuously, and this density decrease will be more pronounced in water with higher salinity.

To test this hypothesis, the student measured the density of freshwater ( $0\text{ ppt}$ salinity) and saline water ( $10\text{ ppt}$ salinity) at different temperatures. The results are shown in the table below.

Temperature ( $^\circ\text{C}$ )	Density at $0\text{ ppt}$ salinity ( $\text{g/cm}^3$ )	Density at $10\text{ ppt}$ salinity ( $\text{g/cm}^3$ )
$0$	$0.99984$	$1.00802$
$2$	$0.99994$	$1.00808$
$4$	$0.99997$	$1.00806$
$6$	$0.99994$	$1.00800$
$8$	$0.99985$	$1.00790$
$10$	$0.99970$	$1.00776$

Based on these results, how should the student modify the hypothesis regarding the relationship between temperature, salinity, and density?

Retain the hypothesis as proposed, because the density of both water samples at

10^\circ\text{C}

is lower than their density at

0^\circ\text{C}

, and the overall decrease in density is greater for the sample with higher salinity.

Modify the hypothesis to state that density decreases continuously for the sample with

0\text{ ppt}

salinity but first increases and then decreases for the sample with

10\text{ ppt}

salinity.

Modify the hypothesis to state that as temperature increases from

0^\circ\text{C}

to

10^\circ\text{C}

, density first increases and then decreases, and that the temperature at which maximum density occurs is lower for water with higher salinity.

Modify the hypothesis to state that as temperature increases from

0^\circ\text{C}

to

10^\circ\text{C}

, density first decreases and then increases, and that the temperature at which minimum density occurs is higher for water with higher salinity.

Cevabı ve açıklamayı göster

Cevap: Modify the hypothesis to state that as temperature increases from $0^\circ\text{C}$ to $10^\circ\text{C}$ , density first increases and then decreases, and that the temperature at which maximum density occurs is lower for water with higher salinity.

Cevap

Modify the hypothesis to state that as temperature increases from

0^\circ\text{C}

to

10^\circ\text{C}

, density first increases and then decreases, and that the temperature at which maximum density occurs is lower for water with higher salinity.

The correct answer states that density first increases and then decreases, and that the temperature of maximum density is lower for water with higher salinity. This is supported by the data because for the

0\text{ ppt}

sample, the density increases from

0.99984 \text{ g/cm}^3

at

0^\circ\text{C}

to

0.99997 \text{ g/cm}^3

at

4^\circ\text{C}

before decreasing. Similarly, for the

10\text{ ppt}

sample, the density increases from

1.00802 \text{ g/cm}^3

at

0^\circ\text{C}

to

1.00808 \text{ g/cm}^3

at

2^\circ\text{C}

before decreasing. Comparing these peak temperatures (

2^\circ\text{C} < 4^\circ\text{C}

) confirms that the temperature of maximum density decreases with higher salinity.

Adım Adım Çözüm

1

Examine the density values of both the

0\text{ ppt}

and

10\text{ ppt}

salinity samples as temperature increases from

0^\circ\text{C}

to

10^\circ\text{C}

.

For both samples, density increases to a peak value (

0.99997 \text{ g/cm}^3

at

4^\circ\text{C}

and

1.00808 \text{ g/cm}^3

at

2^\circ\text{C}

, respectively) and then decreases as temperature continues to rise to

10^\circ\text{C}

.

To evaluate whether the proposed hypothesis of a 'continuous decrease' matches the observed trend.

2

Determine the temperature of maximum density for each salinity concentration.

The

0\text{ ppt}

sample reaches its maximum density at

4^\circ\text{C}

, whereas the

10\text{ ppt}

sample reaches its maximum density at

2^\circ\text{C}

.

To identify the exact points of peak density and check if salinity shifts this temperature.

3

Compare the peak density temperatures between the two salinity groups (

0\text{ ppt}

and

10\text{ ppt}

).

The peak temperature for the higher salinity sample (

2^\circ\text{C}

) is lower than that of the lower salinity sample (

4^\circ\text{C}

).

To determine how salinity alters the temperature of maximum density.

4

Synthesize these observations to formulate a modified hypothesis.

A modified hypothesis must state that density first increases and then decreases, and that the temperature of maximum density decreases as salinity increases.

To construct a new hypothesis that is fully supported by the experimental data.

Anahtar Kavram

Formulating and Modifying Hypotheses

Tahmini Süre:2m 0s

Soru 13Soru →

A group of students studied the decomposition of sodium bicarbonate ( $NaHCO_3$ ) in aqueous solution. They proposed a hypothesis: *The rate of $NaHCO_3$ decomposition increases as the initial concentration of $NaHCO_3$ increases because a higher concentration of reactant particles leads to more frequent collisions.*

To test this, they performed two experiments. In Experiment 1, they measured the volume of carbon dioxide ( $CO_2$ ) gas produced over $10\text{ min}$ at a constant temperature of $25^\circ\text{C}$ using different initial concentrations of $NaHCO_3$ ( $0.1\text{ M}$ , $0.2\text{ M}$ , and $0.3\text{ M}$ ). In Experiment 2, they repeated the trials at a constant temperature of $50^\circ\text{C}$ . The results are shown in the table:

Trial	Temperature ( $^\circ\text{C}$ )	Initial $NaHCO_3$ Concentration ( $\text{M}$ )	Total $CO_2$ Produced in $10\text{ min}$ ( $\text{mL}$ )
1	25	0.1	12.4
2	25	0.2	12.5
3	25	0.3	12.3
4	50	0.1	24.8
5	50	0.2	25.1
6	50	0.3	24.9

Which of the following statements best describes how the students should modify their hypothesis?

The students should retain their original hypothesis because the total volume of

CO_2

gas produced increased when the temperature was raised from

25^\circ\text{C}

to

50^\circ\text{C}

.

The students should modify their hypothesis to state that the rate of

NaHCO_3

decomposition is independent of the initial

NaHCO_3

concentration but increases as temperature increases.

The students should modify their hypothesis to state that the rate of

NaHCO_3

decomposition increases as the initial

NaHCO_3

concentration increases, but only at a constant temperature of

50^\circ\text{C}

.

The students should modify their hypothesis to state that the rate of

NaHCO_3

decomposition decreases as the initial

NaHCO_3

concentration increases at higher temperatures.

Cevabı ve açıklamayı göster

Cevap: The students should modify their hypothesis to state that the rate of $NaHCO_3$ decomposition is independent of the initial $NaHCO_3$ concentration but increases as temperature increases.

Cevap

The students should modify their hypothesis to state that the rate of

NaHCO_3

decomposition is independent of the initial

NaHCO_3

concentration but increases as temperature increases.

The experimental results demonstrate that changing the initial concentration of

NaHCO_3

from

0.1\text{ M}

to

0.3\text{ M}

has negligible effect on the volume of gas produced (remaining at approximately

12.4\text{ mL}

at

25^\circ\text{C}

and

25.0\text{ mL}

at

50^\circ\text{C}

). However, increasing the temperature from

25^\circ\text{C}

to

50^\circ\text{C}

significantly increases the rate of decomposition, doubling the gas output. Therefore, the hypothesis must be modified to state that the rate is independent of the initial concentration but increases with temperature.

Adım Adım Çözüm

1

Analyze the effect of changing the initial

NaHCO_3

concentration at a constant temperature.

At

25^\circ\text{C}

(Trials 1-3), the

CO_2

volumes are

12.4\text{ mL}

,

12.5\text{ mL}

, and

12.3\text{ mL}

. At

50^\circ\text{C}

(Trials 4-6), the volumes are

24.8\text{ mL}

,

25.1\text{ mL}

, and

24.9\text{ mL}

.

To determine whether the data supports the students' hypothesis that a higher concentration increases the reaction rate.

2

Determine if there is a relationship between concentration and the rate of decomposition based on the step 1 results.

The volume of

CO_2

produced remains approximately constant regardless of the initial concentration, meaning concentration does not affect the rate.

To evaluate the validity of the original hypothesis.

3

Analyze the effect of temperature changes on the volume of gas produced at the same concentrations.

Comparing Trial 1 to Trial 4 (both

0.1\text{ M}

), the volume increases from

12.4\text{ mL}

to

24.8\text{ mL}

. Similar increases occur for other concentrations when temperature is raised.

To identify which variable (temperature) actually influences the rate of reaction.

4

Synthesize a modified hypothesis that aligns with both findings.

The modified hypothesis should state that the rate of decomposition is independent of the initial

NaHCO_3

concentration but increases as temperature increases.

To construct a hypothesis that accurately accounts for all observed trends in the experimental data.

Anahtar Kavram

Formulating and Modifying Hypotheses

Tahmini Süre:1m 30s

Soru 14Soru →

A student investigates the corrosion of iron in various acidic solutions. The student hypothesizes that the rate of corrosion, measured by the mass loss of an iron nail after $48\text{ hours}$ , increases linearly as the pH of the solution decreases from $7.0$ to $2.0$ . The student places identical iron nails in solutions of varying pH and records the mass loss in the table below:

pH of solution	Mass loss of iron nail (\text{mg})
$7.0$	$0.8$
$6.0$	$1.6$
$5.0$	$2.4$
$4.0$	$3.2$
$3.0$	$3.8$
$2.0$	$4.0$

Based on these results, which of the following statements best describes how the student should modify their hypothesis?

The rate of corrosion increases linearly as pH decreases from

7.0

to

4.0

, but the rate of increase begins to level off at a pH below

4.0

.

The rate of corrosion increases by a constant value of

0.8\text{ mg}

for every

1.0\text{ unit}

decrease in pH across the entire range of

7.0

to

2.0

.

The rate of corrosion decreases as the pH of the solution decreases from

7.0

to

4.0

, then increases at lower pH values.

The rate of corrosion remains constant at all pH values below

5.0

.

Cevabı ve açıklamayı göster

Cevap: The rate of corrosion increases linearly as pH decreases from $7.0$ to $4.0$ , but the rate of increase begins to level off at a pH below $4.0$ .

Cevap

The rate of corrosion increases linearly as pH decreases from 7.0 to 4.0, but the rate of increase begins to level off at a pH below 4.0.

The correct option correctly identifies that from pH 7.0 to 4.0, the mass loss increases by exactly 0.8 mg for each 1.0-unit decrease in pH, showing a linear relationship. Below pH 4.0, the mass loss increases by 0.6 mg (from pH 4.0 to 3.0) and then by 0.2 mg (from pH 3.0 to 2.0), which shows that the rate of increase is leveling off.

Adım Adım Çözüm

1

Analyze the student's initial hypothesis and the trend in the data.

The hypothesis predicts a constant, linear increase in mass loss (corrosion rate) as pH decreases from

7.0

to

2.0

. The data shows that as pH decreases from

7.0

to

4.0

, the mass loss increases by a constant

0.8\text{ mg}

per

1.0

pH unit (

0.8 \rightarrow 1.6 \rightarrow 2.4 \rightarrow 3.2

).

Establishing the baseline relationship helps identify where the data aligns with or deviates from the linear prediction.

2

Examine the data for pH values below

4.0

to determine if the linear trend continues.

From pH

4.0

to

3.0

, the mass loss increases by

0.6\text{ mg}

(

3.2 \rightarrow 3.8\text{ mg}

). From pH

3.0

to

2.0

, the mass loss increases by only

0.2\text{ mg}

(

3.8 \rightarrow 4.0\text{ mg}

).

Calculating the rate of change at lower pH values reveals whether the relationship remains strictly linear.

3

Formulate a modified hypothesis that accurately describes the entire dataset.

The rate of corrosion increases linearly as pH decreases from

7.0

to

4.0

, but the rate of increase begins to level off (increase by smaller amounts) at pH values below

4.0

.

A modified hypothesis must reflect both the initial linear range and the subsequent non-linear leveling off shown in the data.

Anahtar Kavram

Formulating and Modifying Hypotheses

Tahmini Süre:1m 30s

Soru 15Soru →

A student hypothesizes that as the angle of an inclined plane increases, the time it takes for a block to slide down the plane will decrease. The student conducts an experiment and measures the slide times at angles of $15^\circ$ , $30^\circ$ , and $45^\circ$ . If the student's hypothesis is correct, which of the following predictions is most likely true for the slide time of the block at an angle of $60^\circ$ ?

The slide time at

60^\circ

will be greater than the slide time at

45^\circ

.

The slide time at

60^\circ

will be less than the slide time at

45^\circ

.

The slide time at

60^\circ

will be equal to the slide time at

45^\circ

.

The slide time at

60^\circ

will be greater than the slide time at

15^\circ

.

Cevabı ve açıklamayı göster

Cevap: The slide time at $60^\circ$ will be less than the slide time at $45^\circ$ .

Cevap

The slide time at

60^\circ

will be less than the slide time at

45^\circ

.

The student's hypothesis proposes that slide time decreases as the angle of inclination increases. Since

60^\circ

is greater than the largest tested angle of

45^\circ

, the slide time at

60^\circ

must be less than the slide time at

45^\circ

to remain consistent with the hypothesis.

Adım Adım Çözüm

1

Identify the relationship proposed by the student's hypothesis.

The hypothesis states that as the angle of an inclined plane increases, the slide time decreases.

This establishes that there is an inverse relationship between the angle and the time taken.

2

Compare the test angle to the previously measured angles.

The target angle is

60^\circ

, which is greater than the previous angles of

15^\circ

,

30^\circ

, and

45^\circ

.

This determines how the independent variable is being modified relative to the existing data.

3

Apply the hypothesized relationship to make a prediction.

Since

60^\circ

is a larger angle than

45^\circ

, the slide time must be shorter than the slide time measured at

45^\circ

.

An increase in angle must result in a decrease in slide time to support the hypothesis.

Anahtar Kavram

Formulating predictions that align with a proposed hypothesis.

Tahmini Süre:45s

Soru 16Soru →

A student proposes the following hypothesis:

*Hypothesis*: Plants grown under blue light will grow taller than plants grown under green light or red light.

To test this hypothesis, the student grows $3$ identical pea plants under different wavelengths of light for $14$ days, keeping all other variables constant. The heights of the plants at the end of the experiment are shown in the table below:

Light Color	Final Plant Height ( $\text{cm}$ )
Blue	$12$
Green	$8$
Red	$15$

Based on these results, which of the following statements best describes how the student should modify the hypothesis?

Modify the hypothesis to state that plants grown under red light will grow taller than plants grown under blue light or green light.

Modify the hypothesis to state that plants grown under green light will grow taller than plants grown under blue light or red light.

Modify the hypothesis to state that plants grown under blue light and green light will grow to the same height.

Retain the hypothesis as originally proposed because the plant grown under blue light grew taller than the plant grown under green light.

Cevabı ve açıklamayı göster

Cevap: Modify the hypothesis to state that plants grown under red light will grow taller than plants grown under blue light or green light.

Cevap

Modify the hypothesis to state that plants grown under red light will grow taller than plants grown under blue light or green light.

The experimental results demonstrate that the plant grown under red light achieved the greatest height (

15\text{ cm}

), followed by the plant grown under blue light (

12\text{ cm}

), and the plant grown under green light (

8\text{ cm}

). Because the original hypothesis predicted that blue light would yield the tallest plants, the finding that red light resulted in the tallest plants contradicts the prediction. Therefore, the hypothesis must be modified to reflect that red light produces the greatest height.

Adım Adım Çözüm

1

Analyze the student's original hypothesis.

The hypothesis predicts that blue light results in the greatest plant height compared to green or red light.

To evaluate the hypothesis, we must first understand what it predicts.

2

Examine the experimental results in the table.

The final heights are: Red =

15\text{ cm}

, Blue =

12\text{ cm}

, Green =

8\text{ cm}

.

This provides the actual data to compare against the prediction.

3

Compare the data to the hypothesis and determine the correct modification.

Since red light resulted in the tallest growth (

15\text{ cm}

, which is greater than blue light's

12\text{ cm}

), the original hypothesis is incorrect. The hypothesis should be modified to state that red light leads to the tallest growth.

A scientific hypothesis must be updated when experimental evidence contradicts its initial prediction.

Anahtar Kavram

Evaluating and modifying a hypothesis based on experimental evidence.

Soru 17Soru →

Geophysicists study the rheology of magma to predict volcanic eruption styles. A volcanologist formulated a hypothesis regarding the combined effects of pressure ( $P$ ) and water content ( $W$ ) on the viscosity ( $\eta$ ) of rhyolitic magma at a constant temperature of $1000^\circ\text{C}$ :

*Hypothesis*: Increasing $W$ decreases $\eta$ by disrupting silicate network bonds. However, because higher $P$ compresses the melt and opposes this bond disruption, the viscosity-reducing effect of adding water (defined as the factor by which $\eta$ decreases when $W$ is increased from $0.1\text{ wt}\%$ to $3.0\text{ wt}\%$ ) will become weaker as $P$ increases.

To test this hypothesis, the volcanologist measured the viscosity of rhyolitic magma samples at $1000^\circ\text{C}$ under different combinations of $P$ and $W$ . The results are shown in the table below:

Trial	Pressure ( $P$ , $\text{MPa}$ )	Water content ( $W$ , $\text{wt}\%$ )	Viscosity ( $\eta$ , $\text{Pa}\cdot\text{s}$ )
1	50	0.1	$1.0 \times 10^8$
2	50	1.0	$5.0 \times 10^5$
3	50	3.0	$2.0 \times 10^3$
4	150	0.1	$8.0 \times 10^7$
5	150	1.0	$1.0 \times 10^5$
6	150	3.0	$9.0 \times 10^2$
7	300	0.1	$5.0 \times 10^7$
8	300	1.0	$3.0 \times 10^4$
9	300	3.0	$4.0 \times 10^2$

Which of the following statements best describes how the volcanologist should modify the hypothesis in light of these results?

Modify the hypothesis to state that the viscosity-reducing effect of water becomes stronger as pressure increases, because the factor by which viscosity decreases when water is added increases as pressure increases.

Modify the hypothesis to state that the viscosity-reducing effect of water becomes weaker as pressure increases, because the absolute decrease in viscosity when water is added is smallest at

300\text{ MPa}

.

Retain the hypothesis because at each pressure, increasing the water content from

0.1\text{ wt}\%

to

3.0\text{ wt}\%

decreases the magma viscosity.

Modify the hypothesis to state that increasing pressure increases magma viscosity, because compaction at higher pressures prevents water from effectively lubricating the silicate network.

Cevabı ve açıklamayı göster

Cevap: Modify the hypothesis to state that the viscosity-reducing effect of water becomes stronger as pressure increases, because the factor by which viscosity decreases when water is added increases as pressure increases.

Cevap

Modify the hypothesis to state that the viscosity-reducing effect of water becomes stronger as pressure increases, because the factor by which viscosity decreases when water is added increases as pressure increases.

The correct option correctly identifies that the volcanologist's hypothesis must be modified to state that the viscosity-reducing effect of water becomes stronger at higher pressures. The hypothesis defines the effect as the factor by which viscosity decreases when water is increased from

0.1\text{ wt}\%

to

3.0\text{ wt}\%

. Calculating this factor (viscosity at

0.1\text{ wt}\%

divided by viscosity at

3.0\text{ wt}\%

) yields

50,000

at

50\text{ MPa}

, approximately

88,889

at

150\text{ MPa}

, and

125,000

at

300\text{ MPa}

. Since this factor increases with pressure, the effect becomes stronger, contradicting the hypothesis that it would become weaker.

Adım Adım Çözüm

1

Identify the definition of the viscosity-reducing effect in the hypothesis.

The effect is defined as the factor (ratio) by which viscosity decreases when water content increases from

0.1\text{ wt}\%

to

3.0\text{ wt}\%

.

This sets the criteria for evaluating the strength of the water's effect.

2

Calculate the reduction factor at each pressure level using the formula:

\text{Factor} = \frac{\eta_{\text{at } 0.1\%}}{\eta_{\text{at } 3.0\%}}

.

At

50\text{ MPa}

:

\frac{1.0 \times 10^8}{2.0 \times 10^3} = 50,000

. At

150\text{ MPa}

:

\frac{8.0 \times 10^7}{9.0 \times 10^2} \approx 88,889

. At

300\text{ MPa}

:

\frac{5.0 \times 10^7}{4.0 \times 10^2} = 125,000

.

This quantifies the strength of the viscosity-reducing effect of water at each pressure.

3

Compare the calculated factors across different pressures to see if they increase or decrease.

As pressure increases from

50\text{ MPa}

to

300\text{ MPa}

, the factor of decrease increases from

50,000

to

125,000

.

This allows us to determine the trend in the viscosity-reducing effect as pressure increases.

4

Evaluate the hypothesis against this trend and determine the modification.

The hypothesis predicted the effect would become weaker (factor would decrease), but the data shows it becomes stronger (factor increases). Therefore, the hypothesis must be modified to state the effect becomes stronger as pressure increases.

This directly answers the question.

Anahtar Kavram

Evaluating and modifying a hypothesis based on experimental results by analyzing relative rates of change in a controlled experiment.

Tahmini Süre:2m 0s

Soru 18Soru →

A student proposed the following hypothesis regarding the growth of a bacterial biofilm in a flow chamber:

*Hypothesis*: The biofilm growth rate ( $G$ , in $\mu\text{m/day}$ ) is directly proportional to the bulk nutrient concentration ( $C$ , in $\text{mg/L}$ ) across all concentrations, and the rate of decrease in $G$ per unit increase in fluid shear stress ( $\tau$ , in $\text{Pa}$ ) is constant.

To test this hypothesis, the student conducted two experiments. In Experiment 1, the student varied $C$ while maintaining a constant $\tau$ of $0.10\text{ Pa}$ . In Experiment 2, the student varied $\tau$ while maintaining a constant $C$ of $10.0\text{ mg/L}$ . The results are shown in the tables below.

**Experiment 1 ( $\tau = 0.10\text{ Pa}$ )**

Bulk Nutrient Concentration ( $C$ , mg/L)	Biofilm Growth Rate ( $G$ , $\mu\text{m/day}$ )
2.0	0.5
4.0	1.0
8.0	2.0
16.0	2.0

**Experiment 2 ( $C = 10.0\text{ mg/L}$ )**

Fluid Shear Stress ( $\tau$ , Pa)	Biofilm Growth Rate ( $G$ , $\mu\text{m/day}$ )
0.05	2.4
0.10	2.0
0.20	1.5
0.40	1.0

Based on the results of Experiments 1 and 2, which of the following statements describes how the student should modify the hypothesis?

Biofilm growth rate (

G

) is directly proportional to bulk nutrient concentration (

C

) across all concentrations; and the rate of decrease in

G

per unit increase in shear stress (

\tau

) increases as

\tau

increases.

Biofilm growth rate (

G

) is directly proportional to bulk nutrient concentration (

C

) only up to a threshold concentration, after which

G

becomes independent of

C

; and the rate of decrease in

G

per unit increase in shear stress (

\tau

) decreases as

\tau

increases.

Biofilm growth rate (

G

) is independent of bulk nutrient concentration (

C

) at low concentrations but becomes directly proportional at high concentrations; and the rate of decrease in

G

per unit increase in shear stress (

\tau

) remains constant.

Biofilm growth rate (

G

) is directly proportional to bulk nutrient concentration (

C

) only up to a threshold concentration, after which

G

becomes independent of

C

; and biofilm growth rate (

G

) increases as shear stress (

\tau

) increases.

Cevabı ve açıklamayı göster

Cevap: Biofilm growth rate ( $G$ ) is directly proportional to bulk nutrient concentration ( $C$ ) only up to a threshold concentration, after which $G$ becomes independent of $C$ ; and the rate of decrease in $G$ per unit increase in shear stress ( $\tau$ ) decreases as $\tau$ increases.

Cevap

Biofilm growth rate (

G

) is directly proportional to bulk nutrient concentration (

C

) only up to a threshold concentration, after which

G

becomes independent of

C

; and the rate of decrease in

G

per unit increase in shear stress (

\tau

) decreases as

\tau

increases.

The correct option states that the growth rate is directly proportional to the nutrient concentration up to a threshold, and that the rate of decrease per unit increase in shear stress decreases as shear stress increases. This is supported by Experiment 1, which shows a linear increase in growth rate from

0.5

to

2.0\text{ }\mu\text{m/day}

as nutrient concentration increases from

2.0

to

8.0\text{ mg/L}

, followed by a constant growth rate of

2.0\text{ }\mu\text{m/day}

at higher concentrations. Furthermore, Experiment 2 demonstrates that as shear stress increases, the growth rate decreases at a declining rate: the average rate of change decreases in magnitude from

-8.0

to

-5.0

, and then to

-2.5\text{ }\mu\text{m}/(\text{day}\cdot\text{Pa})

across successive intervals.

Adım Adım Çözüm

1

Analyze Experiment 1 to determine the relationship between nutrient concentration (

C

) and growth rate (

G

).

G

increases linearly with

C

from

0.5

to

2.0\text{ }\mu\text{m/day}

as

C

goes from

2.0

to

8.0\text{ mg/L}

. However, at

16.0\text{ mg/L}

,

G

remains at

2.0\text{ }\mu\text{m/day}

, indicating that the relationship is directly proportional only up to a threshold concentration of

8.0\text{ mg/L}

.

This establishes how the first part of the hypothesis should be modified to account for nutrient saturation.

2

Analyze Experiment 2 to determine the general trend between shear stress (

\tau

) and growth rate (

G

).

As

\tau

increases from

0.05

to

0.40\text{ Pa}

,

G

decreases from

2.4

to

1.0\text{ }\mu\text{m/day}

, confirming that growth rate decreases as shear stress increases.

This rule-out step eliminates any modifications suggesting a positive relationship between growth rate and shear stress.

3

Calculate the rate of change (slope) of

G

with respect to

\tau

over successive intervals to test the linearity of the decrease.

From

0.05\text{ Pa}

to

0.10\text{ Pa}

, the rate of change is

\frac{2.0 - 2.4}{0.10 - 0.05} = -8.0\text{ }\mu\text{m}/(\text{day}\cdot\text{Pa})

. From

0.10\text{ Pa}

to

0.20\text{ Pa}

, it is

\frac{1.5 - 2.0}{0.20 - 0.10} = -5.0\text{ }\mu\text{m}/(\text{day}\cdot\text{Pa})

. From

0.20\text{ Pa}

to

0.40\text{ Pa}

, it is

\frac{1.0 - 1.5}{0.40 - 0.20} = -2.5\text{ }\mu\text{m}/(\text{day}\cdot\text{Pa})

.

Calculating the rates of change over different intervals evaluates whether the rate of decrease is constant, increasing, or decreasing.

4

Compare the calculated slopes to evaluate how the rate of decrease changes.

The magnitude of the rate of decrease (slopes of

-8.0

,

-5.0

, and

-2.5

) becomes smaller as shear stress increases. This means the rate of decrease in growth rate per unit increase in shear stress decreases.

This determines the correct modification for the second part of the hypothesis.

Anahtar Kavram

Evaluating and modifying a hypothesis based on experimental results showing non-linear relationships and saturation thresholds.

Tahmini Süre:3m 0s

Soru 19Soru →

A student proposed the following hypothesis regarding the behavior of gases:

*Hypothesis*: Under identical temperature and pressure conditions, gases with a larger molar mass will diffuse through a porous membrane at a faster rate than gases with a smaller molar mass.

To test this hypothesis, the student measured the diffusion time (the time required for a $1.0\text{ L}$ sample of gas to pass completely through a membrane) for four different gases. The results are shown in the table below:

Gas	Molar mass ( $\text{g/mol}$ )	Diffusion time ( $\text{s}$ )
Helium ( $\text{He}$ )	$4$	$12$
Neon ( $\text{Ne}$ )	$20$	$27$
Argon ( $\text{Ar}$ )	$40$	$38$
Krypton ( $\text{Kr}$ )	$84$	$55$

Based on these results, how should the student modify the hypothesis to accurately reflect the relationship between a gas's molar mass and its rate of diffusion?

The student should modify the hypothesis to state that as molar mass increases, the rate of diffusion increases, because the diffusion time decreases.

The student should retain the hypothesis because an increase in molar mass results in an increase in diffusion time, which represents an increase in the rate of diffusion.

The student should modify the hypothesis to state that as molar mass increases, the rate of diffusion decreases, because the diffusion time increases.

The student should retain the hypothesis because the gas with the largest molar mass had the shortest diffusion time, indicating the fastest rate of diffusion.

Cevabı ve açıklamayı göster

Cevap: The student should modify the hypothesis to state that as molar mass increases, the rate of diffusion decreases, because the diffusion time increases.

Cevap

The student should modify the hypothesis to state that as molar mass increases, the rate of diffusion decreases, because the diffusion time increases.

The correct option states that the student should modify the hypothesis to show that as molar mass increases, the rate of diffusion decreases, because the diffusion time increases. A longer diffusion time means the gas takes more time to pass through the membrane, indicating a slower rate of movement. The data shows that as molar mass increases from

4\text{ g/mol}

to

84\text{ g/mol}

, the diffusion time increases from

12\text{ s}

to

55\text{ s}

, which supports this modification.

Adım Adım Çözüm

1

Identify the independent variable (molar mass) and the dependent variable (diffusion time) from the data table, and determine their trend.

As the molar mass increases from

4\text{ g/mol}

(Helium) to

84\text{ g/mol}

(Krypton), the diffusion time increases from

12\text{ s}

to

55\text{ s}

.

This establishes the relationship between molar mass and diffusion time.

2

Relate the measured variable (diffusion time) to the concept in the hypothesis (rate of diffusion).

Since rate is inversely proportional to time, a longer diffusion time indicates a slower rate of diffusion.

To evaluate the hypothesis about the rate of diffusion, the student must translate diffusion times into diffusion rates.

3

Compare the trend in the rate of diffusion with the original hypothesis to decide how to modify it.

The original hypothesis states that larger molar mass leads to a faster diffusion rate, but the data shows that larger molar mass leads to a slower diffusion rate (longer time). Therefore, the student must modify the hypothesis to state that rate of diffusion decreases as molar mass increases.

This selects the option that correctly modifies the hypothesis according to the data.

Anahtar Kavram

Formulating and modifying hypotheses based on experimental observations and the relationships between measured variables.

Tahmini Süre:1m 0s

Soru 20Soru →

A biology lab group investigated how wind speed affects the rate of water loss in *Phaseolus vulgaris* (common bean) plants. The group initially hypothesized that transpiration rates would increase continuously and linearly across all wind speeds due to the constant removal of the boundary layer of water vapor.

They recorded the transpiration rates at different wind speeds in a wind tunnel and compiled the data in the table below:

Wind Speed ( $\text{m/s}$ )	Transpiration Rate ( $\text{mg}\cdot\text{dm}^{-2}\cdot\text{min}^{-1}$ )
$0.0$	$1.8$
$1.0$	$3.5$
$2.0$	$5.2$
$3.0$	$6.8$
$4.0$	$7.0$
$5.0$	$6.9$

Based on the results in the table, which of the following statements represents the most accurate modification of the group's initial hypothesis?

The transpiration rate is completely unaffected by wind speed and remains constant across all tested speeds.

The transpiration rate decreases continuously as wind speed increases because the wind cools the leaf surface.

The transpiration rate increases with wind speed up to a threshold of approximately

3.0\text{ m/s}

, after which it plateaus and remains relatively constant.

The transpiration rate increases linearly and continuously across all wind speeds, with no upper limit.

Cevabı ve açıklamayı göster

Cevap: The transpiration rate increases with wind speed up to a threshold of approximately $3.0\text{ m/s}$ , after which it plateaus and remains relatively constant.

Cevap

The transpiration rate increases with wind speed up to a threshold of approximately

3.0\text{ m/s}

, after which it plateaus and remains relatively constant.

The correct option correctly describes the two distinct phases of the data trend: a steady rise in the transpiration rate up to about

3.0\text{ m/s}

, followed by a plateau where the rate remains constant. This modification reflects the physical limits of the system, such as stomatal closure in high winds, which prevent a continuous linear increase.

Adım Adım Çözüm

1

Analyze the change in transpiration rate values as wind speed increases from

0.0\text{ m/s}

to

3.0\text{ m/s}

.

The rate increases steadily from

1.8

to

6.8\text{ mg}\cdot\text{dm}^{-2}\cdot\text{min}^{-1}

.

This establishes that there is an initial positive relationship between wind speed and transpiration rate, supporting the direction of the initial hypothesis in this range.

2

Analyze the transpiration rate values as wind speed increases further from

3.0\text{ m/s}

to

5.0\text{ m/s}

.

The rate changes minimally from

6.8

to

7.0

and then slightly drops to

6.9\text{ mg}\cdot\text{dm}^{-2}\cdot\text{min}^{-1}

.

This shows that the rate levels off and no longer increases, indicating a threshold effect or plateau.

3

Combine these observations to formulate a modified hypothesis that matches the overall data trend.

The rate increases initially but plateaus after a threshold of approximately

3.0\text{ m/s}

.

A modified hypothesis must reflect both trends observed in the experimental data to be scientifically valid.

Anahtar Kavram

Formulating and Modifying Hypotheses

Tahmini Süre:1m 30s

Formulating and Modifying Hypotheses

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