Question 1

Which of the following statements best explains why real gases deviate from ideal behavior at high pressures?

Accepted Answer

At high pressures, repulsive forces between gas molecules become significant, increasing the pressure above ideal predictions.

Question 2

Which modification does the van der Waals equation introduce to the ideal gas law to account for real gas behavior?

Accepted Answer

It subtracts a constant from the volume and adds a constant to the pressure to account for molecular volume and intermolecular forces.

Question 3

Given the van der Waals equation for one mole of gas: $$\left(P + \frac{a}{V^2$}\right)(V - b) = RT$$, what does the parameter $$a$$ physically represent?

Accepted Answer

The strength of attractive intermolecular forces.

Question 4

A real gas is found to have a compressibility factor $$Z \u003c 1 at $$low pressure. What does this indicate about the intermolecular forces present?

Accepted Answer

Attractive forces dominate, causing the pressure to be lower than predicted.

Question 5

Which equation of state provides the most accurate fit to experimental data for real gases, especially when many terms are included?

Accepted Answer

Virial equation of state

Question 6

Why do all gases, even ideal ones, have a compressibility factor $$Z \u003e 1 at $$very high pressures?

Accepted Answer

At high pressure, repulsive forces dominate, increasing the pressure above ideal predictions.

Question 7

Which of the following is NOT a characteristic of real gases?

Accepted Answer

They are accurately modeled by $$PV = nRT at $$all conditions.

Question 8

The Law of Corresponding States (LOC) is based on which critical property of substances?

Accepted Answer

The critical point, where there is no distinction between liquid and gas phases.

Question 9

If a gas is modeled using the van der Waals equation and the parameter $$b is $$increased, what is the expected effect on the molar volume at a given pressure and temperature?

Accepted Answer

The molar volume increases because $$b$$ accounts for the finite size of molecules.

Question 10

Which scenario would most likely require the use of a real gas equation of state rather than the ideal gas law?

Accepted Answer

A sample of carbon dioxide at 50 atm and 250 K.

Question 11

The virial equation of state is often written as $$\frac{PV}{RT} = 1 + \frac{B}{V} + \frac{C}{V^2$} + \ldots. $$What do the coefficients $$B$$ and $$C$$ physically represent?

Accepted Answer

They represent molecular pair and triplet interactions, respectively.

Question 12

A gas sample is found to condense at low temperature. Which property of real gases does this observation illustrate?

Accepted Answer

Presence of attractive intermolecular forces.

Question 13

Which of the following best describes the physical meaning of the compressibility factor $$Z$$?

Accepted Answer

It is a measure of how much a real gas deviates from ideal behavior, defined as $$Z = \frac{PV}{nRT}.$$

Question 14

Which of the following is a limitation of the van der Waals equation when modeling real gases?

Accepted Answer

It predicts non-physical behavior such as van der Waals loops.

Question 15

A chemist is studying a gas near its critical point. Which equation of state would best allow her to compare its behavior to other gases?

Accepted Answer

Law of Corresponding States using reduced variables

Question 16

Which of the following is true about the virial equation of state?

Accepted Answer

Its accuracy improves as more terms are added, but each successive term contributes less.

Question 17

If a real gas is found to have $$Z \u003e 1 at a $$certain pressure and temperature, which of the following is the most likely explanation?

Accepted Answer

Repulsive forces dominate, increasing the pressure above ideal predictions.

Question 18

Which of the following is a direct consequence of the Law of Corresponding States?

Accepted Answer

All gases obey the same equation of state when expressed in terms of reduced variables.

Question 19

A sample of hydrogen gas at low pressure is found to have $$Z \u003e 1. $$What does this indicate about the dominant intermolecular forces?

Accepted Answer

Repulsive forces dominate.

Question 20

Which of the following best describes the behavior of real gases at low temperature and high pressure?

Accepted Answer

They deviate significantly from ideal behavior due to non-negligible volume and intermolecular forces.

Properties of Real Gases: Equations of State and Critical Phenomena

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