A student proposed the following hypothesis regarding the behavior of gases: *Hypothesis*:… — ACT

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?

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

Answer

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}

84\text{ g/mol}

, the diffusion time increases from

12\text{ s}

55\text{ s}

, which supports this modification.

Step-by-Step Solution

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}

55\text{ s}

This establishes the relationship between molar mass and diffusion time.

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.

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.

Key Concept

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

Estimated Time:1m 0s

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