A student hypothesized that the solubility of carbon dioxide (CO_2) in water is directly p… — ACT

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?

A
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.
B
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.Answer
D
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.

Answer

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.

Step-by-Step Solution

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}

40^\circ\text{C}

, the

CO_2

solubility decreases from

2.4\text{ g/kg}

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.

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.

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.

Key Concept

Formulating and Modifying Hypotheses

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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