Question 1

Which assumption of the Kinetic Molecular Theory is most violated at high pressures?

Accepted Answer

Gas particles have negligible volume compared to the container.

Question 2

Which correction does the van der Waals equation make to the Ideal Gas Law to account for the finite size of gas molecules?

Accepted Answer

It subtracts $nb$ from the volume: $V_{corrected} = V - nb$.

Question 3

A sample of $1.00$ mol of $CO_2$ is confined in a $1.00$ L container at $300$ K. Using the van der Waals constants $a = 3.59$ and $b = 0.0427$, which equation would you use to calculate the real pressure?

Accepted Answer

$P = \frac{nRT}{V-nb} - a\left(\frac{n}{V}\right)^2$

Question 4

Why does $H_2$ exhibit more ideal gas behavior than $CO_2$?

Accepted Answer

$H_2$ is smaller and has weaker intermolecular forces.

Question 5

Under which conditions do gases most deviate from ideal behavior?

Accepted Answer

High pressure and low temperature.

Question 6

Which van der Waals constant ($a$ or $b$) is most directly related to the strength of intermolecular forces?

Accepted Answer

$a$

Question 7

If a gas has a large $b$ value in the van der Waals equation, what does this indicate about its molecules?

Accepted Answer

The molecules occupy a large volume.

Question 8

Which of the following gases is most likely to require a pressure correction at low temperatures?

Accepted Answer

$H_2O$

Question 9

A real gas exerts less pressure than predicted by the Ideal Gas Law. What is the most likely cause?

Accepted Answer

Attractive intermolecular forces reduce the force of collisions with the container walls.

Question 10

Which of the following best explains why the volume correction ($V-nb$) is necessary in the van der Waals equation?

Accepted Answer

Gas molecules occupy space and cannot be compressed into zero volume.

Question 11

Given the van der Waals constants for $NH_3$ ($a = 4.17$, $b = 0.0371$) and $He$ ($a = 0.0341$, $b = 0.0237$), which gas is more likely to deviate from ideal behavior and why?

Accepted Answer

$NH_3$, because it has a much larger $a$ value indicating stronger intermolecular forces.

Question 12

Which of the following scenarios would most likely require the use of the van der Waals equation instead of the Ideal Gas Law?

Accepted Answer

A gas sample at very high pressure and low temperature.

Question 13

If the van der Waals constant $a$ for $CO_2$ is $3.59$, what does this value represent?

Accepted Answer

The magnitude of intermolecular attractions between $CO_2$ molecules.

Question 14

Which gas is most likely to behave ideally: $H_2$, $Cl_2$, or $CO_2$? Why?

Accepted Answer

$H_2$, because it is small and nonpolar with weak intermolecular forces.

Question 15

Which gas is more likely to exhibit real gas behavior: $CH_4$ or $H_2O$? Why?

Accepted Answer

$H_2O$, because it has strong intermolecular forces.

Question 16

A hospital stores $O_2$ gas in high-pressure tanks. Why must engineers use the van der Waals equation rather than the Ideal Gas Law to calculate the pressure inside these tanks?

Accepted Answer

At high pressures, the volume of $O_2$ molecules and intermolecular attractions become significant.

Question 17

Which of the following is a direct consequence of attractive intermolecular forces in a real gas?

Accepted Answer

The measured pressure is lower than predicted by the Ideal Gas Law.

Question 18

A sample of $1.00$ mol of $CO_2$ at $300$ K in a $1.00$ L container has a pressure of $7.47$ atm by the Ideal Gas Law. Using the van der Waals equation, the pressure is $7.19$ atm. What accounts for the difference?

Accepted Answer

Intermolecular attractions reduce the pressure exerted by the gas.

Real Gases and Deviations from Ideal Gas Behavior

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