A student proposed the following hypothesis: *Hypothesis*: As the temperature of water inc… — ACT

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?

A
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.
B
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.Answer
D
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.

Answer

Modify the hypothesis to state that as temperature increases from

0^\circ\text{C}

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

0^\circ\text{C}

0.99997 \text{ g/cm}^3

4^\circ\text{C}

before decreasing. Similarly, for the

10\text{ ppt}

sample, the density increases from

1.00802 \text{ g/cm}^3

0^\circ\text{C}

1.00808 \text{ g/cm}^3

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.

Step-by-Step Solution

Examine the density values of both the

0\text{ ppt}

and

10\text{ ppt}

salinity samples as temperature increases from

0^\circ\text{C}

10^\circ\text{C}

For both samples, density increases to a peak value (

0.99997 \text{ g/cm}^3

4^\circ\text{C}

and

1.00808 \text{ g/cm}^3

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.

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.

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.

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.

Key Concept

Formulating and Modifying Hypotheses

Estimated Time:2m 0s

Question

Answer

Step-by-Step Solution

Key Concept

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