Formulating and Modifying Hypotheses

37 questions

An environmental chemist studies the capture of carbon dioxide ( $CO_2$ ) by a newly synthesized metal-organic framework (MOF) at different temperatures. The chemist proposes the following hypothesis:

*Hypothesis*: As the temperature of the system increases, the amount of $CO_2$ gas adsorbed by the MOF at any given pressure will increase, because the increased kinetic energy of the gas molecules will enhance their interaction with the MOF's pore surface.

The chemist measures the mass of $CO_2$ adsorbed per gram of MOF ( $m_{ads}$ , in $mg/g$ ) at three different temperatures across a range of pressures, as shown in the table below:

Pressure (bar)	$m_{ads}$ at $273\text{ K}$ (mg/g)	$m_{ads}$ at $298\text{ K}$ (mg/g)	$m_{ads}$ at $323\text{ K}$ (mg/g)
1.0	120	85	50
3.0	210	150	95
5.0	260	190	120
7.0	290	215	140
10.0	320	240	160

Based on the experimental results, which of the following describes how the hypothesis should be modified?

The hypothesis should be modified to state that as temperature increases, the amount of

CO_2

adsorbed increases only at pressures below

5.0\text{ bar}

The hypothesis should be retained as originally proposed, because the increase in pressure leads to an increase in

m_{ads}

at all three temperatures tested.

The hypothesis should be modified to state that as temperature increases, the amount of

CO_2

adsorbed decreases, indicating that the adsorption process is weakened by higher thermal energy.

The hypothesis should be modified to state that at a pressure of

10.0\text{ bar}

, a temperature of

350\text{ K}

will result in a

m_{ads}

value greater than

320\text{ mg/g}

Show answer & explanation

Answer: The hypothesis should be modified to state that as temperature increases, the amount of $CO_2$ adsorbed decreases, indicating that the adsorption process is weakened by higher thermal energy.

Answer

The hypothesis should be modified to state that as temperature increases, the amount of

CO_2

adsorbed decreases, indicating that the adsorption process is weakened by higher thermal energy.

The correct answer states that the hypothesis should be modified to show that adsorption decreases as temperature increases. Comparing the columns at any given pressure (horizontal rows) reveals that

m_{ads}

consistently drops as temperature rises from

273\text{ K}

323\text{ K}

. For instance, at

1.0\text{ bar}

, the adsorption goes from

120\text{ mg/g}

85\text{ mg/g}

and then to

50\text{ mg/g}

. This inverse relationship directly refutes the chemist's proposal that higher temperatures would increase adsorption, requiring a complete reversal of the hypothesized trend.

Step-by-Step Solution

Identify the variable relationships in the hypothesis.

The hypothesis predicts a direct relationship: increasing temperature increases the mass of gas adsorbed (

m_{ads}

) at any constant pressure.

To evaluate the hypothesis, we must first define the expected trend it predicts.

Analyze the experimental data for temperature effects at a constant pressure.

At a constant pressure of

5.0\text{ bar}

m_{ads}

260\text{ mg/g}

273\text{ K}

190\text{ mg/g}

298\text{ K}

, and

120\text{ mg/g}

323\text{ K}

. This represents an inverse relationship.

Comparing values across a single row isolates the effect of temperature on adsorption while keeping pressure constant.

Determine the necessary modification to the hypothesis.

Since the actual trend is opposite to the prediction (adsorption decreases as temperature increases), the hypothesis must be modified to reflect this inverse relationship.

Scientific hypotheses must be updated or discarded when they are contradicted by empirical data.

Key Concept

Formulating and Modifying Hypotheses

Question 22Question →

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

*Hypothesis*: As the surrounding temperature increases, the chirping rate of crickets will decrease because lower temperatures stimulate metabolic activity.

The student measured the chirping rate of a group of crickets at different temperatures and recorded the results in the table below:

Temperature (°C)	Average chirps per minute
15	60
20	80
25	100
30	120

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

Modify the hypothesis to state that as the temperature increases, the average chirping rate remains constant.

Modify the hypothesis to state that as the temperature decreases, the average chirping rate increases.

Modify the hypothesis to state that as the temperature increases, the average chirping rate increases.

Modify the hypothesis to state that the average chirping rate is the independent variable that controls the temperature.

Show answer & explanation

Answer: Modify the hypothesis to state that as the temperature increases, the average chirping rate increases.

Answer

Modify the hypothesis to state that as the temperature increases, the average chirping rate increases.

The correct option states that the hypothesis should be modified to show that as temperature increases, the average chirping rate increases. This is supported by the data table: as the temperature rises from 15°C to 30°C, the average chirping rate steadily increases from 60 to 120 chirps per minute.

Step-by-Step Solution

Analyze the original hypothesis and compare it with the collected data.

The original hypothesis states that as temperature increases, chirping rate decreases. The data table shows that at 15°C, the chirping rate is 60; at 20°C, it is 80; at 25°C, it is 100; and at 30°C, it is 120.

To determine how to modify the hypothesis, we must first compare the initial prediction to the actual experimental observations.

Identify the relationship between temperature and chirping rate shown in the data.

Both temperature and average chirping rate increase together, showing a direct relationship.

This relationship directly contradicts the original hypothesis, which predicted an inverse relationship.

Formulate a modified hypothesis that accurately reflects the observed direct relationship.

The modified hypothesis must state that as temperature increases, the average chirping rate increases.

A scientific hypothesis must be revised or replaced when experimental evidence contradicts its predictions.

Key Concept

A hypothesis is a testable statement that must be modified or rejected if it is contradicted by experimental evidence. When data shows that a dependent variable increases as the independent variable increases, the hypothesis must reflect this direct relationship.

Estimated Time:1m 0s

Question 23Question →

A student investigates the rate of an enzyme-catalyzed reaction. The student proposed the following hypothesis:

*Hypothesis*: The rate of the reaction is directly proportional to the enzyme concentration at all temperatures, meaning that doubling the enzyme concentration will double the reaction rate regardless of the temperature.

To test this hypothesis, the student measured the reaction rate (in $\mu\text{mol/min}$ ) at enzyme concentrations of $1.0\text{ g/L}$ and $2.0\text{ g/L}$ across four different temperatures. The results are shown in the table below:

Temperature ( $^\circ\text{C}$ )	Reaction rate at $1.0\text{ g/L}$ enzyme ( $\mu\text{mol/min}$ )	Reaction rate at $2.0\text{ g/L}$ enzyme ( $\mu\text{mol/min}$ )
$15$	$12.4$	$24.8$
$25$	$22.1$	$44.2$
$35$	$31.5$	$63.0$
$45$	$10.2$	$12.1$

Which of the following statements best explains whether the data support the student's hypothesis, and how the hypothesis should be modified?

The data do not support the hypothesis, because doubling the enzyme concentration did not double the reaction rate at

45^\circ\text{C}

; the hypothesis should be modified to state that the direct proportion only holds below the temperature at which the enzyme denatures.

The data support the hypothesis, because the reaction rate increased when the enzyme concentration was increased from

1.0\text{ g/L}

2.0\text{ g/L}

at all four tested temperatures.

The data do not support the hypothesis, because the reaction rates at

15^\circ\text{C}

25^\circ\text{C}

, and

35^\circ\text{C}

show that the reaction rate is inversely proportional to the enzyme concentration.

The data support the hypothesis, because doubling the enzyme concentration resulted in an approximate doubling of the reaction rate when averaged across all four temperatures.

Show answer & explanation

Answer: The data do not support the hypothesis, because doubling the enzyme concentration did not double the reaction rate at $45^\circ\text{C}$ ; the hypothesis should be modified to state that the direct proportion only holds below the temperature at which the enzyme denatures.

Answer

The data do not support the hypothesis, because doubling the enzyme concentration did not double the reaction rate at

45^\circ\text{C}

; the hypothesis should be modified to state that the direct proportion only holds below the temperature at which the enzyme denatures.

The correct answer is that the data do not support the hypothesis because doubling the enzyme concentration did not double the reaction rate at

45^\circ\text{C}

. The hypothesis must be modified to state that the direct proportion only holds below the temperature at which the enzyme denatures. This is supported by the data: at

15^\circ\text{C}

25^\circ\text{C}

, and

35^\circ\text{C}

, the rate doubled exactly, but at

45^\circ\text{C}

, the rate only increased slightly (from

10.2

12.1

). This deviation indicates the hypothesis is incorrect as written and requires a temperature limit.

Step-by-Step Solution

Identify the core prediction made by the student's hypothesis.

The hypothesis predicts that doubling the enzyme concentration will double the reaction rate at all temperatures.

This establishes the mathematical relationship that must be tested against the experimental data.

Analyze the experimental data for each temperature to determine if the rate doubles when enzyme concentration increases from

1.0\text{ g/L}

2.0\text{ g/L}

15^\circ\text{C}

12.4 \times 2 = 24.8

(doubled). At

25^\circ\text{C}

22.1 \times 2 = 44.2

(doubled). At

35^\circ\text{C}

31.5 \times 2 = 63.0

(doubled). At

45^\circ\text{C}

10.2 \times 2 = 20.4

, but the actual rate at

2.0\text{ g/L}

is only

12.1

(not doubled).

Checking each individual temperature test condition determines if the hypothesis holds under all circumstances.

Determine if the hypothesis is supported and how it should be modified.

Since the rate did not double at

45^\circ\text{C}

, the hypothesis is not supported. It must be modified to include a temperature limitation, recognizing that the direct proportion fails at higher temperatures (such as

45^\circ\text{C}

) where enzymes typically undergo thermal denaturation.

A scientific hypothesis must be revised or restricted when experimental evidence contradicts its predictions.

Key Concept

Evaluating and modifying a scientific hypothesis based on experimental results that contradict the initial prediction.

Question 24Question →

A geologist conducted an experiment to test the following hypothesis:

*Hypothesis*: Basalt rocks subjected to freeze-thaw cycles will experience a greater percentage loss in mass when saturated with water of lower salinity, because lower salinity water expands more upon freezing, exerting greater pressure within rock pores.

Identical basalt rock samples of the same initial mass were saturated with water of three different salinity levels: $0\text{ g/L}$ (freshwater), $15\text{ g/L}$ (brackish water), and $35\text{ g/L}$ (ocean water). The samples were then subjected to $50$ freeze-thaw cycles between $-10^\circ\text{C}$ and $20^\circ\text{C}$ . The average percentage loss in mass for each group of samples was calculated and recorded in the table below:

Water salinity ( $\text{g/L}$ )	Average mass loss (\%)
$0$	$4.8$
$15$	$3.2$
$35$	$1.5$

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

Yes, because the average mass loss increased as the salinity of the water increased from

0\text{ g/L}

35\text{ g/L}

Yes, because the average mass loss was greatest for the basalt samples saturated with the lowest salinity water (

0\text{ g/L}

No, because the average mass loss was lowest for the basalt samples saturated with the lowest salinity water (

0\text{ g/L}

No, because the average mass loss decreased as the salinity of the water decreased from

35\text{ g/L}

0\text{ g/L}

Show answer & explanation

Answer: Yes, because the average mass loss was greatest for the basalt samples saturated with the lowest salinity water ( $0\text{ g/L}$ ).

Answer

The results support the hypothesis because the average mass loss was greatest for the basalt samples saturated with the lowest salinity water (

0\text{ g/L}

The geologist's hypothesis predicts that basalt rocks saturated with water of lower salinity will experience a greater percentage mass loss. According to the table, the basalt samples saturated with water at

0\text{ g/L}

salinity (the lowest salinity tested) had an average mass loss of

4.8\%

, which is the highest mass loss recorded. As salinity increases to

15\text{ g/L}

and then

35\text{ g/L}

, the mass loss decreases to

3.2\%

and

1.5\%

, respectively. This trend demonstrates that lower salinity corresponds to greater mass loss, thereby supporting the geologist's hypothesis.

Step-by-Step Solution

Identify the geologist's hypothesis.

The hypothesis predicts that lower salinity water leads to a greater percentage mass loss in basalt rocks during freeze-thaw cycles.

This establishes the expected relationship between salinity (independent variable) and mass loss (dependent variable).

Analyze the experimental data in the table.

0\text{ g/L}

salinity, mass loss is

4.8\%

. At

15\text{ g/L}

, mass loss is

3.2\%

. At

35\text{ g/L}

, mass loss is

1.5\%

This identifies the actual relationship between water salinity and average mass loss.

Compare the data trend to the hypothesis.

As salinity decreases (from

35\text{ g/L}

0\text{ g/L}

), the average mass loss increases (from

1.5\%

4.8\%

, with the lowest salinity yielding the greatest loss). This matches the hypothesis.

This determines whether the experimental results support or refute the geologist's hypothesis.

Key Concept

Evaluating a hypothesis against experimental data

Estimated Time:1m 15s

Question 25Question →

An experiment is conducted to study how the concentration of dissolved oxygen in an aquarium affects the respiration rate of a specific fish species. A researcher predicts that if the dissolved oxygen concentration increases, the respiration rate (measured in gill flares per minute) of the fish will decrease. The table below displays the results:

Dissolved Oxygen ( $mg/L$ )	Respiration Rate (gill flares/min)
$4.0$	$82$
$6.0$	$68$
$8.0$	$54$
$10.0$	$41$

Based on the table, does the experimental data support the researcher's prediction?

No, because as the dissolved oxygen concentration increased, the respiration rate decreased.

No, because as the dissolved oxygen concentration increased, the respiration rate increased.

Yes, because as the dissolved oxygen concentration increased, the respiration rate decreased.

Yes, because as the dissolved oxygen concentration increased, the respiration rate increased.

Show answer & explanation

Answer: Yes, because as the dissolved oxygen concentration increased, the respiration rate decreased.

Answer

Yes, because as the dissolved oxygen concentration increased, the respiration rate decreased.

The correct option states that the data supports the prediction because as the dissolved oxygen concentration increased, the respiration rate decreased. This matches the researcher's prediction that respiration rate would decrease as dissolved oxygen concentration increased.

Step-by-Step Solution

Identify the researcher's prediction.

The researcher predicted that as dissolved oxygen concentration increases, the respiration rate will decrease.

To evaluate the hypothesis, we first need to know what trend is being predicted.

Analyze the trend in the data table.

As the dissolved oxygen concentration increases from

4.0\text{ mg/L}

10.0\text{ mg/L}

, the respiration rate decreases from

82

41\text{ gill flares/min}

To see if the prediction is correct, we must determine the actual relationship shown by the data.

Compare the predicted trend with the actual trend.

The predicted trend (increase in oxygen leads to decrease in respiration) matches the actual trend (as oxygen increases, respiration decreases). Therefore, the data supports the prediction.

This comparison allows us to make the final determination.

Key Concept

Evaluating a hypothesis using experimental data

Estimated Time:45s

Question 26Question →

A student hypothesized that as the concentration of dissolved carbon dioxide ( $\text{CO}_2$ ) in water increases, the pH of the solution will increase. To test this, the student bubbled different volumes of $\text{CO}_2$ gas into 100 mL samples of distilled water at $25^\circ\text{C}$ and measured the pH of each sample. The results are shown in the table below:

Sample	Volume of $\text{CO}_2$ bubbled (mL)	pH of solution
1	0	7.0
2	10	6.2
3	20	5.8
4	30	5.5
5	40	5.3

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

Modify the hypothesis to state that as the concentration of dissolved

\text{CO}_2

increases, the pH of the solution decreases.

Modify the hypothesis to state that as the concentration of dissolved

\text{CO}_2

increases, the pH of the solution remains constant.

Modify the hypothesis to state that as the concentration of dissolved

\text{CO}_2

decreases, the pH of the solution decreases.

Modify the hypothesis to state that there is no relationship between the concentration of dissolved

\text{CO}_2

and the pH of the solution.

Show answer & explanation

Answer: Modify the hypothesis to state that as the concentration of dissolved $\text{CO}_2$ increases, the pH of the solution decreases.

Answer

Modify the hypothesis to state that as the concentration of dissolved carbon dioxide increases, the pH of the solution decreases.

The correct answer is correct because the experimental data in the table demonstrate a clear trend: as the volume of carbon dioxide bubbled into the water increases from 0 mL to 40 mL, the pH of the solution decreases from 7.0 to 5.3. Since bubbling carbon dioxide increases the dissolved concentration of the gas, the student must modify the hypothesis to reflect this inverse relationship.

Step-by-Step Solution

Analyze the student's initial hypothesis regarding the relationship between carbon dioxide concentration and pH.

The initial hypothesis states that an increase in dissolved carbon dioxide concentration will cause the pH of the solution to increase.

Establishing the initial prediction allows for a direct comparison with the collected data to see if a modification is necessary.

Examine the experimental data in the table to determine the actual relationship between the independent variable (volume of bubbled carbon dioxide) and the dependent variable (pH).

As the volume of bubbled carbon dioxide increases from 0 mL to 40 mL, the measured pH of the solution decreases from 7.0 to 5.3.

Determining the observed relationship from the data provides the basis for correcting the hypothesis.

Compare the initial hypothesis to the observed trend and formulate the correct modification.

The hypothesis predicted a direct relationship (pH increases as concentration increases), but the data show an inverse relationship (pH decreases as concentration increases). Thus, the student should modify the hypothesis to state that increasing dissolved carbon dioxide concentration decreases the pH.

A scientific hypothesis must be modified to align with the empirical evidence obtained from the experiment.

Key Concept

Formulating and Modifying Hypotheses

Estimated Time:1m 0s

Question 27Question →

A student proposed the following hypothesis regarding planetary atmospheres:

*Hypothesis*: The rate of atmospheric escape of a gas from a planet's atmosphere is determined solely by the planet's surface temperature, such that planets with higher surface temperatures will experience higher rates of escape for all gases, regardless of the gravity of the planet or the molar mass of the gas.

To test this hypothesis, scientists measured the escape rates of helium ( $He$ , molar mass $\approx 4\text{ g/mol}$ ) and xenon ( $Xe$ , molar mass $\approx 131\text{ g/mol}$ ) from three different planets. The surface temperature, surface gravity (measured in units of $g$ , where $1\text{ }g = 9.8\text{ m/s}^2$ ), and escape rates of the gases are shown in the table below:

Planet	Surface Temperature ( $K$ )	Surface Gravity ( $g$ )	Helium ( $He$ ) Escape Rate (kg/s)	Xenon ( $Xe$ ) Escape Rate (kg/s)
Planet X	$300$	$0.40$	$1.2 \times 10^3$	$0.0$
Planet Y	$500$	$0.90$	$4.5 \times 10^2$	$0.0$
Planet Z	$500$	$0.40$	$8.8 \times 10^4$	$1.1 \times 10^1$

Based on these results, which of the following modifications to the student's hypothesis is best supported by the data?

The escape rate of a gas is determined solely by the planet's surface gravity, because planets with higher surface gravity always experience higher escape rates of all gases.

The hypothesis should be retained without modification because Planet Z has the highest surface temperature and also exhibits the highest escape rates for both gases.

The escape rate of a gas depends on both the planet's surface gravity and the molar mass of the gas, with lower surface gravity and lower molar mass leading to higher escape rates.

The escape rate of a gas is inversely proportional to temperature and directly proportional to molar mass, meaning heavier gases escape faster from colder planets.

Show answer & explanation

Answer: The escape rate of a gas depends on both the planet's surface gravity and the molar mass of the gas, with lower surface gravity and lower molar mass leading to higher escape rates.

Answer

The escape rate of a gas depends on both the planet's surface gravity and the molar mass of the gas, with lower surface gravity and lower molar mass leading to higher escape rates.

The correct option correctly states that the escape rate depends on both surface gravity and molar mass, with lower gravity and lower molar mass promoting higher escape rates. This is supported by comparing Planet X and Planet Y, where the higher gravity of Planet Y results in a lower helium escape rate despite its higher temperature, and by comparing the escape rates of Helium and Xenon on Planet Z, where the lighter gas (Helium) escapes at a much faster rate.

Step-by-Step Solution

Analyze the student's initial hypothesis.

The hypothesis claims that atmospheric escape rate depends solely on surface temperature, and is independent of gravity or molar mass.

To evaluate or modify a hypothesis, we must first understand its core assumptions.

Compare the Helium escape rates of Planet X and Planet Y to test if temperature is the sole factor.

Planet Y has a higher temperature (

500\text{ K}

) than Planet X (

300\text{ K}

), but a lower Helium escape rate (

4.5 \times 10^2\text{ kg/s}

vs.

1.2 \times 10^3\text{ kg/s}

). This difference corresponds to Planet Y's higher surface gravity (

0.90\text{ }g

vs.

0.40\text{ }g

This demonstrates that surface gravity is a confounding factor that must be included in the hypothesis, and that higher gravity decreases the escape rate.

Compare the escape rates of Helium and Xenon on Planet Z to evaluate the effect of molar mass.

On Planet Z, Helium (molar mass

\approx 4\text{ g/mol}

) has a much higher escape rate (

8.8 \times 10^4\text{ kg/s}

) than Xenon (molar mass

\approx 131\text{ g/mol}

, escape rate

1.1 \times 10^1\text{ kg/s}

This shows that the molar mass of the gas also affects the escape rate, with lighter gases escaping more readily, which invalidates the claim that escape rate is independent of molar mass.

Synthesize these findings to identify the correct modification.

The hypothesis must be modified to include both surface gravity (inversely related to escape rate) and gas molar mass (inversely related to escape rate).

This directly addresses all the contradictions found between the original hypothesis and the experimental data.

Key Concept

Evaluating and modifying a hypothesis based on multi-variable experimental data.

Estimated Time:2m 30s

Question 28Question →

A student proposed the following hypothesis regarding liquid evaporation:

*Hypothesis*: The rate of evaporation of a liquid is directly proportional to its boiling point because liquids with stronger intermolecular forces evaporate more rapidly at a constant temperature of $25^\circ\text{C}$ .

To test this hypothesis, the student placed equal volumes of three different liquids in identical open beakers. The beakers were kept in a temperature-controlled room at $25^\circ\text{C}$ and $1\text{ atm}$ of pressure. The volume of liquid remaining in each beaker was measured over a $24$ -hour period to determine the average evaporation rate. The boiling points and measured evaporation rates are shown in the table below.

Liquid	Boiling Point ( $^\circ\text{C}$ )	Average Evaporation Rate (mL/hr)
Acetone	$56$	$4.2$
Ethanol	$78$	$1.8$
Water	$100$	$0.5$

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

The hypothesis should be modified to state that the rate of evaporation is inversely related to the boiling point of the liquid, because the liquid with the highest boiling point had the slowest evaporation rate.

The hypothesis should be modified to state that the rate of evaporation is directly proportional to the boiling point of the liquid, because the liquid with the lowest boiling point had the slowest evaporation rate.

The hypothesis should be modified to state that the rate of evaporation is independent of the boiling point, because all three liquids evaporated at the same rate.

The hypothesis should be modified to state that the rate of evaporation is inversely related to the boiling point of the liquid, because acetone evaporated more slowly than water.

Show answer & explanation

Answer: The hypothesis should be modified to state that the rate of evaporation is inversely related to the boiling point of the liquid, because the liquid with the highest boiling point had the slowest evaporation rate.

Answer

The experimental results show an inverse relationship between a liquid's boiling point and its evaporation rate: as the boiling point increases from

56^\circ\text{C}

100^\circ\text{C}

, the evaporation rate decreases from

4.2\text{ mL/hr}

0.5\text{ mL/hr}

. This contradicts the student's original hypothesis of a direct relationship. Therefore, the hypothesis must be modified to state that the rate of evaporation is inversely related to the boiling point, which is supported by the fact that water has the highest boiling point and the slowest evaporation rate.

Step-by-Step Solution

Analyze the student's original hypothesis and identify what it predicts.

The hypothesis predicts a direct relationship: higher boiling point leads to a faster evaporation rate.

Understanding the hypothesis is necessary to determine if the experimental data supports or refutes it.

Examine the relationship between boiling point and evaporation rate in the provided data table.

As the boiling point increases from

56^\circ\text{C}

78^\circ\text{C}

100^\circ\text{C}

, the evaporation rate decreases from

4.2\text{ mL/hr}

1.8\text{ mL/hr}

0.5\text{ mL/hr}

This step determines the actual trend shown by the empirical data.

Compare the data trend with the original hypothesis to formulate a modified hypothesis.

Because the evaporation rate decreases as the boiling point increases, the relationship is inverse, not direct. Water (highest boiling point) has the slowest evaporation rate, so the hypothesis must be modified to state that the evaporation rate is inversely related to the boiling point.

This allows selecting the statement that correctly describes the necessary modification and aligns with the data.

Key Concept

Evaluating and modifying a hypothesis based on experimental trends in data

Estimated Time:1m 30s

Question 29Question →

A student proposed the following hypothesis regarding electromagnetism:

*Hypothesis*: The magnetic field strength of an electromagnet, as measured by the number of steel paperclips it can lift, is directly proportional to the number of wire coils wrapped around its core.

To test this hypothesis, the student wrapped varying numbers of wire coils around an iron nail core, connected the coils to a constant power source, and recorded the average number of paperclips lifted over $5$ trials. The results are shown in the table below:

Number of wire coils	Average number of paperclips lifted
$10$	$4$
$20$	$8$
$30$	$12$
$40$	$13$
$50$	$13$

Which of the following modifications to the hypothesis is best supported by the experimental results?

The hypothesis is fully supported and requires no modification because the average number of paperclips lifted increases at a constant rate from

10

coils to

50

coils.

The hypothesis should be modified to state that the magnetic field strength decreases once the number of coils exceeds

30

coils.

The magnetic field strength is directly proportional to the number of coils only up to

30

coils, after which additional coils do not further increase the strength.

The hypothesis should be modified to state that the magnetic field strength is inversely proportional to the number of coils across all tested values.

Show answer & explanation

Answer: The magnetic field strength is directly proportional to the number of coils only up to $30$ coils, after which additional coils do not further increase the strength.

Answer

The magnetic field strength is directly proportional to the number of coils only up to

30

coils, after which additional coils do not further increase the strength.

The correct answer is correct because the ratio of paperclips to coils is constant at

0.4

from

10

30

coils, confirming a direct proportion in this range. However, at

40

and

50

coils, the number of paperclips lifted plateaus at

13

, indicating that wrapping more than

30

coils does not produce a proportional increase in magnetic strength.

Step-by-Step Solution

Analyze the student's initial hypothesis.

The hypothesis states that the number of paperclips lifted (representing magnetic field strength) is directly proportional to the number of wire coils. Mathematically, this means the ratio of paperclips to coils should remain constant.

Establishing the mathematical definition of direct proportionality allows us to test it against the data.

Calculate the ratio of paperclips lifted to wire coils for each data point in the table.

For

10

coils,

\frac{4}{10} = 0.4

. For

20

coils,

\frac{8}{20} = 0.4

. For

30

coils,

\frac{12}{30} = 0.4

. For

40

coils,

\frac{13}{40} = 0.325

. For

50

coils,

\frac{13}{50} = 0.26

Comparing these ratios identifies where the linear relationship holds and where it breaks down.

Identify the trend and determine how to modify the hypothesis.

The ratio is constant at

0.4

up to

30

coils, but it decreases at

40

and

50

coils as the average number of paperclips lifted plateaus at

13

. Thus, the direct proportionality is valid only up to

30

coils, and the hypothesis must be restricted to this range.

A modified scientific hypothesis must align with all observed experimental facts.

Key Concept

Formulating and Modifying Hypotheses

Question 30Question →

A student proposes the following hypothesis regarding the thermal stability of Group 2 metal carbonates:

*Hypothesis*: The decomposition temperature of a Group 2 metal carbonate is directly proportional to the charge density of its metal cation. Because charge density decreases as ionic radius increases, metal carbonates with larger metal cations will decompose at lower temperatures.

A chemist conducts an experiment to test this hypothesis by measuring the decomposition temperature ( $T_d$ , the temperature at which the carbonate decomposes into a metal oxide and carbon dioxide) of four Group 2 metal carbonates. The results are shown in Table 1.

### Table 1

Metal Carbonate	Metal Cation	Cation Ionic Radius ( $\text{pm}$ )	Decomposition Temperature ( $^\circ\text{C}$ )
$\text{MgCO}_3$	$\text{Mg}^{2+}$	72	350
$\text{CaCO}_3$	$\text{Ca}^{2+}$	100	825
$\text{SrCO}_3$	$\text{Sr}^{2+}$	118	1,100
$\text{BaCO}_3$	$\text{Ba}^{2+}$	135	1,360

Based on Table 1, is the student's hypothesis supported by the experimental results, and how should the hypothesis be modified?

Yes; the data show that as the ionic radius of the metal cation increases, the decomposition temperature also increases.

No; the hypothesis should be modified to state that as the ionic radius of the metal cation increases, the decomposition temperature increases.

No; the hypothesis should be modified to state that the decomposition temperature of a Group 2 metal carbonate is independent of the metal cation's ionic radius.

Yes; the data show that

\text{MgCO}_3

, which contains the metal cation with the highest charge density, decomposes at the lowest temperature.

Show answer & explanation

Answer: No; the hypothesis should be modified to state that as the ionic radius of the metal cation increases, the decomposition temperature increases.

Answer

The student's hypothesis is not supported because the experimental data show that as the ionic radius of the metal cation increases, the decomposition temperature increases. Therefore, the hypothesis should be modified to state that as the ionic radius of the metal cation increases, the decomposition temperature increases.

The experimental results show that as the ionic radius increases, the decomposition temperature increases. This trend is the opposite of the student's prediction that larger cations would decompose at lower temperatures. Thus, the hypothesis is not supported and must be modified to state that as the ionic radius of the metal cation increases, the decomposition temperature increases.

Step-by-Step Solution

Determine the prediction made by the student's hypothesis.

The student predicted that since charge density decreases as ionic radius increases, larger metal cations would lead to lower decomposition temperatures (an inverse relationship between ionic radius and decomposition temperature).

To evaluate a hypothesis, we must first clearly define the relationship it predicts.

Analyze the experimental data in Table 1 to identify the actual trend.

As the ionic radius of the cation increases from

72\text{ pm}

(

\text{Mg}^{2+}

) to

135\text{ pm}

(

\text{Ba}^{2+}

), the decomposition temperature increases from

350\ ^\circ\text{C}

1,360\ ^\circ\text{C}

(a direct relationship).

This establishes the empirical relationship demonstrated by the experiment.

Compare the predicted trend with the observed trend.

The observed direct relationship is the opposite of the predicted inverse relationship, meaning the hypothesis is not supported.

Comparing predictions with actual data determines whether the hypothesis is supported or refuted.

Formulate the correct modification to the hypothesis.

The hypothesis should be modified to state that as the ionic radius of the metal cation increases, the decomposition temperature increases.

Modifying a refuted hypothesis requires aligning it with the experimental evidence.

Key Concept

Evaluating and modifying a hypothesis based on empirical data trends

Question 31Question →

A student conducted an experiment to investigate the effect of light wavelength on the rate of photosynthesis in *Elodea* plants. The student formulated the following hypothesis:

*Hypothesis:* The rate of photosynthesis, as measured by the volume of oxygen ( $O_2$ ) gas produced per hour, increases continuously as the wavelength of light increases from $400\text{ nm}$ to $700\text{ nm}$ .

The student exposed identical *Elodea* plants to different wavelengths of light for 1 hour each, keeping all other environmental variables constant. The results are shown in the table below:

Wavelength	Volume of $O_2$ produced
$400\text{ nm}$	$1.2\text{ mL}$
$450\text{ nm}$	$4.5\text{ mL}$
$550\text{ nm}$	$0.3\text{ mL}$
$650\text{ nm}$	$5.8\text{ mL}$
$700\text{ nm}$	$1.0\text{ mL}$

Based on the results of the experiment, does the data support the student's hypothesis, and how should the hypothesis be modified?

Yes; the data show that the overall rate of photosynthesis increases continuously from

400\text{ nm}

700\text{ nm}

No; the rate of photosynthesis does not increase continuously, so the hypothesis should be modified to state that photosynthesis peaks under blue (

450\text{ nm}

) and red (

650\text{ nm}

) light.

Yes; the rate of photosynthesis is highest at

650\text{ nm}

, which is greater than the rate at any lower wavelength tested.

No; the rate of photosynthesis decreases continuously, so the hypothesis should be modified to state that the rate is inversely proportional to wavelength.

Show answer & explanation

Answer: No; the rate of photosynthesis does not increase continuously, so the hypothesis should be modified to state that photosynthesis peaks under blue ( $450\text{ nm}$ ) and red ( $650\text{ nm}$ ) light.

Answer

No; the rate of photosynthesis does not increase continuously, so the hypothesis should be modified to state that photosynthesis peaks under blue (

450\text{ nm}

) and red (

650\text{ nm}

) light.

The correct answer is correct because the experimental results show that oxygen production does not increase continuously. Instead, it rises and falls, reaching local maxima at

450\text{ nm}

and

650\text{ nm}

, and a minimum at

550\text{ nm}

. Therefore, the hypothesis is unsupported and must be modified to state that photosynthesis is most efficient (peaks) at specific wavelengths corresponding to blue and red light.

Step-by-Step Solution

Analyze the student's hypothesis.

The hypothesis predicts a continuous, monotonic increase in oxygen production as wavelength increases from

400\text{ nm}

700\text{ nm}

Understanding the prediction is necessary to evaluate it against the experimental data.

Examine the trend in the data table.

The volume of oxygen increases from

1.2\text{ mL}

(at

400\text{ nm}

) to

4.5\text{ mL}

(at

450\text{ nm}

), drops to

0.3\text{ mL}

(at

550\text{ nm}

), increases to

5.8\text{ mL}

(at

650\text{ nm}

), and drops again to

1.0\text{ mL}

(at

700\text{ nm}

This determines whether the actual rate of photosynthesis increases continuously.

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

Because the trend shows peaks at

450\text{ nm}

and

650\text{ nm}

rather than a continuous increase, the hypothesis is not supported and should be modified to describe these dual peaks.

Formulating a modified hypothesis must accurately represent the observed experimental results.

Key Concept

Formulating and Modifying Hypotheses

Estimated Time:1m 30s

Question 32Question →

A student proposed the following hypothesis regarding the corrosion of iron:

*Hypothesis*: The mass of rust that forms on an iron nail submerged in a sodium chloride ( $NaCl$ ) solution for 7 days will increase continuously as the concentration of $NaCl$ in the solution increases from 0% to 10%.

To test this hypothesis, the student submerged identical iron nails in 5 different $NaCl$ solutions for 7 days and recorded the mass of the rust that formed on each nail. The results are shown in the table below:

$NaCl$ concentration (% by mass)	Mass of rust formed (mg)
0%	1.2
1%	3.5
3%	5.8
5%	4.2
10%	2.1

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

The student should modify the hypothesis to state that the mass of rust formed increases with

NaCl

concentration up to approximately 3%, but decreases at higher concentrations.

The student should modify the hypothesis to state that the mass of rust formed is inversely proportional to the

NaCl

concentration across all tested levels.

The student should modify the hypothesis to state that the mass of rust formed remains constant at all

NaCl

concentrations greater than 3%.

The student should retain the hypothesis without modification because the nail in the 10% solution produced more rust than the nail in the 0% solution.

Show answer & explanation

Answer: The student should modify the hypothesis to state that the mass of rust formed increases with $NaCl$ concentration up to approximately 3%, but decreases at higher concentrations.

Answer

The student should modify the hypothesis to state that the mass of rust formed increases with

NaCl

concentration up to approximately 3%, but decreases at higher concentrations.

The correct option accurately reflects the empirical data, which shows a rise in rust mass up to 3%

NaCl

concentration followed by a decline at higher concentrations. This requires a modification of the hypothesis from a continuous increase to a peaked relationship.

Step-by-Step Solution

Analyze the original hypothesis to identify the predicted trend.

The original hypothesis predicts that the mass of rust will continuously increase as the

NaCl

concentration increases from 0% to 10%.

This establishes the baseline expectation that must be compared against the actual data.

Examine the experimental data in the table to determine the actual trend.

As the concentration increases from 0% to 3%, the mass of rust increases from 1.2 mg to 5.8 mg. However, as the concentration increases further from 3% to 10%, the mass of rust decreases from 5.8 mg to 2.1 mg.

This identifies the pattern of the empirical evidence.

Compare the actual trend to the original hypothesis and determine the necessary modification.

Since the mass does not increase continuously but rather peaks at 3% and then decreases, the hypothesis must be modified to reflect this non-linear relationship (increasing up to a point, then decreasing).

This directly matches the learning objective of modifying a hypothesis based on new experimental data.

Key Concept

Formulating and Modifying Hypotheses

Question 33Question →

An environmental scientist investigated the relationship between water temperature and the concentration of dissolved oxygen (DO) at saturation. The scientist hypothesized that as water temperature increases, the concentration of DO at saturation also increases because higher temperatures increase the solubility of gases in water. To test this hypothesis, the scientist measured the DO concentration at saturation in water samples at five different temperatures. The results are presented in the table below.

Water Temperature ( $^\circ\text{C}$ )	Dissolved Oxygen Concentration ( $\text{mg/L}$ )
$5$	$12.8$
$15$	$10.1$
$25$	$8.3$
$35$	$6.9$
$45$	$5.9$

Based on these results, does the data support the scientist's hypothesis, and how should the hypothesis be revised?

No; the revised hypothesis should state that as water temperature increases, the concentration of dissolved oxygen at saturation decreases.

Yes; the revised hypothesis should state that as water temperature increases, the concentration of dissolved oxygen at saturation increases.

No; the revised hypothesis should state that changing the concentration of dissolved oxygen at saturation causes the water temperature to decrease.

No; the revised hypothesis should state that the concentration of dissolved oxygen at saturation remains constant regardless of water temperature.

Show answer & explanation

Answer: No; the revised hypothesis should state that as water temperature increases, the concentration of dissolved oxygen at saturation decreases.

Answer

No; the revised hypothesis should state that as water temperature increases, the concentration of dissolved oxygen at saturation decreases.

The scientist's hypothesis predicted that as temperature increases, the concentration of dissolved oxygen at saturation would also increase. However, the experimental results show that as the temperature increases from

5^\circ\text{C}

45^\circ\text{C}

, the concentration of dissolved oxygen decreases from

12.8\text{ mg/L}

5.9\text{ mg/L}

. Because the results show the opposite of the predicted trend, the hypothesis is not supported, and the revised hypothesis must state that as water temperature increases, the concentration of dissolved oxygen at saturation decreases.

Step-by-Step Solution

Identify the scientist's original hypothesis and its predicted outcome.

The original hypothesis predicts that an increase in water temperature results in an increase in dissolved oxygen (DO) concentration (a direct relationship).

Establishing the initial prediction allows direct comparison with the actual experimental data.

Analyze the trend shown in the experimental data table.

As the temperature increases from

5^\circ\text{C}

45^\circ\text{C}

, the DO concentration steadily decreases from

12.8\text{ mg/L}

5.9\text{ mg/L}

(an inverse relationship).

Determining the actual mathematical relationship between the variables reveals if the initial prediction was correct.

Determine if the hypothesis is supported and formulate the necessary revision.

The data contradicts the hypothesis, meaning it is not supported (No). The hypothesis must be revised to reflect the inverse trend: as water temperature increases, DO concentration at saturation decreases.

Hypotheses must be modified to align with experimental findings when those findings refute the initial prediction.

Key Concept

Formulating and Modifying Hypotheses

Estimated Time:1m 30s

Question 34Question →

A student proposed the following hypothesis regarding electrical circuits:

*Hypothesis*: As the cross-sectional area of a metal wire increases, its electrical resistance will increase because a larger wire contains more atoms that collide with and resist the flow of electrons.

To test this hypothesis, the student measured the electrical resistance of four copper wires, each $10\text{ m}$ long but with different diameters, at a constant temperature of $20^\circ\text{C}$ . The results are shown in the table below:

Wire	Diameter ( $\text{mm}$ )	Cross-sectional area ( $\text{mm}^2$ )	Resistance ( $\Omega$ )
1	0.5	0.20	4.00
2	1.0	0.79	1.00
3	1.5	1.77	0.44
4	2.0	3.14	0.25

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

The student should modify the hypothesis to state that as the cross-sectional area of a wire increases, its electrical resistance decreases.

The student should modify the hypothesis to state that the electrical resistance of a wire is independent of its cross-sectional area.

The student should keep the hypothesis as written because the wire with the largest cross-sectional area (

3.14\text{ mm}^2

) had the lowest resistance (

0.25\ \Omega

The student should modify the hypothesis to state that as the diameter of a wire decreases, its electrical resistance decreases.

Show answer & explanation

Answer: The student should modify the hypothesis to state that as the cross-sectional area of a wire increases, its electrical resistance decreases.

Answer

The student should modify the hypothesis to state that as the cross-sectional area of a wire increases, its electrical resistance decreases.

The correct answer states that the hypothesis should be modified to show that as the cross-sectional area of a wire increases, its electrical resistance decreases. The table shows that as the cross-sectional area increases from

0.20\text{ mm}^2

3.14\text{ mm}^2

, the resistance decreases from

4.00\ \Omega

0.25\ \Omega

. Since the initial hypothesis predicted that resistance would increase as cross-sectional area increases, the experimental results contradict the hypothesis. Therefore, the hypothesis must be modified to reflect this inverse relationship.

Step-by-Step Solution

Analyze the student's initial hypothesis.

The initial hypothesis states that larger cross-sectional area leads to higher resistance (a direct relationship).

To evaluate the hypothesis, we must first define the expected relationship between the variables.

Examine the experimental data in the table to determine the actual relationship between cross-sectional area and resistance.

As the cross-sectional area increases from

0.20\text{ mm}^2

3.14\text{ mm}^2

, the resistance decreases from

4.00\ \Omega

0.25\ \Omega

Comparing the independent variable (cross-sectional area) with the dependent variable (resistance) reveals the empirical trend.

Compare the empirical trend with the initial hypothesis and select the correct modification.

The empirical trend is inverse (area increases, resistance decreases), which contradicts the hypothesized direct relationship. Therefore, the hypothesis must be modified to state that resistance decreases as cross-sectional area increases.

A scientific hypothesis must be modified when experimental evidence consistently contradicts its predictions.

Key Concept

Evaluating and modifying a hypothesis based on conflicting experimental data.

Estimated Time:1m 30s

Question 35Question →

To study thermal expansion in solids, a researcher proposed that the coefficient of linear expansion ( $\alpha$ ) of a metal rod depends on its starting length. Specifically, the researcher hypothesized that longer rods of the same metal would exhibit a larger value of $\alpha$ when subjected to the same temperature change.

To test this hypothesis, the researcher measured the physical expansion of three copper rods under identical heating conditions. The results of the measurements and the calculated values of $\alpha$ are recorded in the table below.

Copper Rod	Initial Length ( $L_0$ , $\text{m}$ )	Temperature Increase ( $\Delta T$ , $^\circ\text{C}$ )	Expansion ( $\Delta L$ , $\text{mm}$ )	Coefficient of Linear Expansion ( $\alpha$ , $10^{-6}\text{ }^\circ\text{C}^{-1}$ )
Rod A	1.0	50	0.85	17
Rod B	2.0	50	1.70	17
Rod C	3.0	50	2.55	17

Based on the results of the experiment, does the data support the researcher's hypothesis, and how should the hypothesis be modified?

Yes; the data show that the total expansion of the rod increases from

0.85\text{ mm}

2.55\text{ mm}

as the initial length increases.

Yes; the data show that the coefficient of linear expansion increases proportionally with the initial length of the copper rod.

No; the data show that the coefficient of linear expansion decreases as the initial length of the rod increases.

No; the data show that the coefficient of linear expansion remains constant at

17 \times 10^{-6}\text{ }^\circ\text{C}^{-1}

regardless of the rod's initial length.

Show answer & explanation

Answer: No; the data show that the coefficient of linear expansion remains constant at $17 \times 10^{-6}\text{ }^\circ\text{C}^{-1}$ regardless of the rod's initial length.

Answer

The experimental data does not support the hypothesis because the coefficient of linear expansion remains constant at

17 \times 10^{-6}\text{ }^\circ\text{C}^{-1}

for all initial lengths, meaning the hypothesis should be modified to state that the coefficient of linear expansion is independent of the initial length of the rod.

The correct option accurately states that the hypothesis is not supported because the coefficient of linear expansion (

\alpha

) remains constant at

17 \times 10^{-6}\text{ }^\circ\text{C}^{-1}

for all three rods, regardless of their initial length. A scientific hypothesis must be rejected or modified when the measured property does not change in the predicted direction.

Step-by-Step Solution

Identify the core assertion of the researcher's hypothesis.

The hypothesis predicts that as the initial length (

L_0

) of a metal rod increases, the coefficient of linear expansion (

\alpha

) of that metal will also increase.

Understanding the hypothesis defines the independent variable (initial length) and the dependent variable (coefficient of linear expansion) that must be compared using the data.

Analyze the data table to observe how the coefficient of linear expansion (

\alpha

) behaves as the initial length increases.

As the initial length increases from

1.0\text{ m}

2.0\text{ m}

and then

3.0\text{ m}

, the calculated coefficient of linear expansion (

\alpha

) remains constant at

17 \times 10^{-6}\text{ }^\circ\text{C}^{-1}

Evaluating the trend of the target variable (

\alpha

) against the independent variable (

L_0

) determines whether the hypothesis is supported or refuted.

Determine the proper modification of the hypothesis based on the constant values of

\alpha

Since

\alpha

did not increase, the hypothesis is refuted. The modified hypothesis must reflect that the coefficient of linear expansion remains constant and is independent of the initial length of the rod.

Comparing the empirical data directly to the proposed hypothesis allows the researcher to correctly modify it to align with the experimental results.

Key Concept

Formulating and Modifying Hypotheses

Estimated Time:1m 15s

Question 36Question →

A student proposed the following hypothesis regarding soil drainage:

*Hypothesis*: Soil permeability (the rate at which water flows through soil) is determined by the average particle size of the soil, such that soils with larger average particle sizes will always have higher water flow rates, regardless of the compaction level of the soil.

To test this hypothesis, the student measured the water flow rate, in milliliters per minute ( $\text{mL/min}$ ), through three different soil samples under both uncompacted and compacted conditions. The results are shown in the table below.

Soil Sample	Average Particle Size ( $\text{mm}$ )	Flow Rate - Uncompacted ( $\text{mL/min}$ )	Flow Rate - Compacted ( $\text{mL/min}$ )
X	$0.1$	$15$	$3$
Y	$0.5$	$45$	$12$
Z	$2.0$	$120$	$8$

Based on these results, do the data support the student's hypothesis?

Yes; under both uncompacted and compacted conditions, the flow rate increased as the average particle size increased from Soil X to Soil Z.

Yes; the flow rate of each soil sample was higher under uncompacted conditions than under compacted conditions.

No; under compacted conditions, Soil Z had a lower flow rate than Soil Y, even though Soil Z has a larger average particle size.

No; under uncompacted conditions, Soil Y had a higher flow rate than Soil X, which contradicts the hypothesis.

Show answer & explanation

Answer: No; under compacted conditions, Soil Z had a lower flow rate than Soil Y, even though Soil Z has a larger average particle size.

Answer

No; under compacted conditions, Soil Z had a lower flow rate than Soil Y, even though Soil Z has a larger average particle size.

The correct answer is the option stating that under compacted conditions, Soil Z had a lower flow rate than Soil Y, even though Soil Z has a larger average particle size. The student's hypothesis states that soils with larger average particle sizes will always have higher flow rates, regardless of compaction level. However, the data show that in compacted conditions, Soil Z (average particle size

2.0\text{ mm}

) has a water flow rate of

8\text{ mL/min}

, which is lower than that of Soil Y (average particle size

0.5\text{ mm}

, flow rate

12\text{ mL/min}

). This direct contradiction means the hypothesis is not supported by the data.

Step-by-Step Solution

Identify the student's hypothesis and the conditions it applies to.

The hypothesis asserts that soils with larger average particle sizes will always have higher flow rates, regardless of the compaction level.

This establishes the rule that the experimental data must satisfy in order to support the hypothesis.

Examine the data for both uncompacted and compacted conditions.

In uncompacted conditions, flow rates increase as particle size increases (

15 < 45 < 120\text{ mL/min}

). In compacted conditions, the flow rate increases from Soil X (

3\text{ mL/min}

) to Soil Y (

12\text{ mL/min}

), but decreases for Soil Z (

8\text{ mL/min}

), which has the largest particle size.

Evaluating each set of conditions separately is required because the hypothesis states the relationship must hold true regardless of compaction level.

Compare the behavior under compacted conditions to the hypothesis.

Under compacted conditions, Soil Z (particle size

2.0\text{ mm}

) has a lower flow rate than Soil Y (particle size

0.5\text{ mm}

), showing that a larger particle size does not always lead to a higher flow rate.

A single contradiction is sufficient to refute the student's hypothesis.

Key Concept

Formulating and Modifying Hypotheses based on experimental results and identifying counterexamples.

Question 37Question →

A student proposed the following hypothesis regarding the decomposition of hydrogen peroxide ( $H_2O_2$ ) in the presence of the catalyst catalase:

*Hypothesis*: The rate of $H_2O_2$ decomposition increases linearly as the concentration of catalase increases, because more catalyst molecules are available to speed up the reaction.

To test this hypothesis, the student measured the rate of oxygen ( $O_2$ ) gas production (in mL/min) at various catalase concentrations (in percent, $\%$ ) while keeping the substrate concentration and temperature constant. The results are shown in the table below:

Catalase concentration ( $\%$ )	$O_2$ production rate (mL/min)
0.0	0.0
1.0	5.4
2.0	10.8
3.0	16.2
4.0	16.3
5.0	16.3

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

The hypothesis should be modified to state that the reaction rate is inversely proportional to catalase concentration at all tested concentrations.

The hypothesis should be modified to state that the reaction rate increases continuously without limit as catalase concentration increases.

The hypothesis should be modified to state that the reaction rate increases linearly with catalase concentration up to a threshold, above which the rate remains constant.

The hypothesis should be modified to state that the reaction rate decreases once the catalase concentration exceeds 3.0\%.

Show answer & explanation

Answer: The hypothesis should be modified to state that the reaction rate increases linearly with catalase concentration up to a threshold, above which the rate remains constant.

Answer

The hypothesis should be modified to state that the reaction rate increases linearly with catalase concentration up to a threshold, above which the rate remains constant.

The experimental results demonstrate a linear relationship between catalase concentration and oxygen production rate from 0.0\% to 3.0\%, with the rate increasing by exactly 5.4 mL/min for each 1.0\% increase in concentration. However, at concentrations of 4.0\% and 5.0\%, the rate levels off and remains nearly constant at 16.3 mL/min. The correct option reflects this transition by stating that the rate increases linearly up to a threshold (around 3.0\%), after which it remains constant.

Step-by-Step Solution

Analyze the student's initial hypothesis.

The initial hypothesis predicts a linear, unlimited increase in the reaction rate as the catalase concentration increases.

To evaluate a hypothesis, we must first identify its specific predictions.

Examine the relationship between catalase concentration and oxygen production rate in the data table.

From 0.0\% to 3.0\% catalase, the rate increases linearly by 5.4 mL/min for every 1.0\% increase in catalase concentration (

0.0 \rightarrow 5.4 \rightarrow 10.8 \rightarrow 16.2

This step determines the range over which the original hypothesis holds true.

Analyze the trend in the data table above the 3.0\% catalase concentration.

At 4.0\% and 5.0\% catalase, the rate remains constant at approximately 16.3 mL/min.

Identifying where the data deviates from the predicted trend shows how the hypothesis must be modified.

Synthesize the two trends to modify the hypothesis.

The rate increases linearly up to 3.0\% (a threshold) and then plateaus, meaning the hypothesis must be modified to include this threshold and constant behavior.

This produces the final modified hypothesis that is fully supported by all experimental data.

Key Concept

Modifying a hypothesis to align with data that shows a transition from a linear increase to a plateau (saturation effect).

Estimated Time:1m 30s

PreviousPage 2 / 2

Formulating and Modifying Hypotheses

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