Q: Which of the following is the correct expression for the relative error when comparing the ideal gas law and van der Waals equation pressures?

$$\text{Relative Error} = \frac{|p_{\text{vdW}} - p_{\text{ideal}}|}{|p_{\text{ideal}}|} \times 100$$

Question 1

Which of the following assumptions is NOT made in the kinetic-molecular theory of ideal gases?

Accepted Answer

Gas molecules exert attractive and repulsive forces on each other.

Question 2

The van der Waals equation for real gases introduces two parameters, $$a$$ and $$b. $$What do these parameters account for?

Accepted Answer

$$a$$ corrects for intermolecular attractions, $$b$$ corrects for molecular volume.

Question 3

Given the van der Waals equation for one mole of gas: $$\left(p + \frac{a}{V^2$}\right)(V - b) = RT$$, what would happen to the calculated pressure if the attractive forces between molecules (parameter $$a) $$were ignored?

Accepted Answer

The calculated pressure would be higher than the real pressure.

Question 4

A sample of 1.0 mol of H$$_2S $$gas is confined at 500 K in a 0.150 dm$$^3$$ container. Given $$a = 4.484$$ atm dm$$^6$$ mol$$^{-2}$$, $$b = 0.0434 dm$^3$$ mol$$^{-1}$$, and $$R = 0.08206 L $$atm K$$^{-1}$$ mol$$^{-1}$$, which equation would you use to calculate the real pressure?

Accepted Answer

$$\left(p + \frac{a}{V^2$}\right)(V - b) = RT$$

Question 5

Which of the following best explains why the pressure of a real gas is lower than that predicted by the ideal gas law at moderate pressures?

Accepted Answer

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

Question 6

Which of the following is the correct expression for the relative error when comparing the ideal gas law and van der Waals equation pressures?

Accepted Answer

$$	ext{Relative Error} = \frac{|p_{	ext{vdW}} - p_{	ext{ideal}}|}{|p_{	ext{ideal}}|} 	imes 100$$

Question 7

Why does liquid nitrogen rapidly expand when boiling water is added to it?

Accepted Answer

The temperature difference causes the liquid nitrogen to vaporize, expanding its volume by about 700 times.

Question 8

Which of the following statements about the van der Waals parameters is TRUE?

Accepted Answer

The parameter $$a is $$larger for gases with stronger intermolecular attractions.

Question 9

A gas is compressed to a very small volume at constant temperature. Which van der Waals parameter becomes most significant in this scenario?

Accepted Answer

Parameter $$b$$, which accounts for the finite volume of gas molecules.

Question 10

Which of the following best describes the critical point of a substance?

Accepted Answer

The temperature and pressure above which the gas and liquid phases are indistinguishable.

Question 11

Which real-world application requires accurate modeling of real gas behavior rather than assuming ideal gas behavior?

Accepted Answer

Designing industrial chemical reactors operating at high pressures.

Question 12

Which intermolecular force is NOT typically considered in the van der Waals equation?

Accepted Answer

Ionic bonding.

Question 13

If the compressibility factor $$Z$$ for a gas is less than 1, what does this indicate about the behavior of the gas?

Accepted Answer

Attractive forces dominate, causing the gas to be more compressible than predicted by the ideal gas law.

Question 14

Which of the following is a direct consequence of the first law of thermodynamics?

Accepted Answer

The internal energy of a system changes as heat is added or work is done.

Question 15

A gas sample is cooled at constant pressure until it condenses. Which statement best explains this phenomenon?

Accepted Answer

At lower temperatures, intermolecular attractions become significant enough to bring molecules together into a liquid.

Question 16

Which of the following equations best represents the ideal gas law?

Accepted Answer

$$pV = nRT$$

Question 17

Which scenario would result in the largest deviation from ideal gas behavior?

Accepted Answer

High pressure and low temperature.

Question 18

Which of the following best describes the principle of corresponding states?

Accepted Answer

All gases, when compared at the same reduced temperature and pressure, have approximately the same compressibility factor.

Question 19

Which of the following is a reason why the van der Waals equation is considered empirical?

Accepted Answer

The parameters $$a$$ and $$b$$ are determined experimentally for each gas.

Question 20

A gas is found to have a van der Waals $$a$$ parameter much larger than another gas. What does this suggest about the gas?

Accepted Answer

It has stronger intermolecular attractions.

Real Gases and the van der Waals Equation: Mini-Textbook Study Notes

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