Which statement concerning the van der Waals constants a and b is true? (a) The magnitude of a relates to molecular volume, whereas b relates to attractions between molecules. (b) The magnitude of a relates to attractions between molecules, whereas b relates to molecular volume. (c) The magnitudes of a and b depend on pressure. (d) The magnitudes of a and b depend on temperature.

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Identify the purpose of the van der Waals equation, which is to account for the non-ideal behavior of real gases by introducing two constants, a and b.

Understand that the constant 'a' in the van der Waals equation corrects for the attractive forces between gas molecules, which are not present in an ideal gas.

Recognize that the constant 'b' accounts for the finite volume occupied by gas molecules, which is ignored in the ideal gas law.

Evaluate each statement: (a) incorrectly swaps the roles of a and b; (b) correctly assigns 'a' to attractions and 'b' to volume; (c) and (d) incorrectly suggest that a and b depend on pressure and temperature, which they do not.

Conclude that statement (b) is true: 'The magnitude of a relates to attractions between molecules, whereas b relates to molecular volume.'

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

van der Waals Equation

The van der Waals equation is an adjustment of the ideal gas law that accounts for the volume occupied by gas molecules and the attractive forces between them. It introduces two constants, 'a' and 'b', which correct for these non-ideal behaviors. The constant 'a' quantifies the strength of intermolecular attractions, while 'b' represents the volume occupied by the gas molecules themselves.

Constant 'a'

In the van der Waals equation, the constant 'a' is associated with the attractive forces between molecules. A larger value of 'a' indicates stronger intermolecular attractions, which can lead to deviations from ideal gas behavior, especially at high pressures and low temperatures. This constant is crucial for understanding how real gases behave compared to ideal gases.

Constant 'b'

The constant 'b' in the van der Waals equation represents the effective volume occupied by gas molecules, accounting for the finite size of the particles. It reflects the volume excluded from the available space for molecular motion due to the presence of the molecules themselves. A larger 'b' value indicates that the gas molecules occupy more space, which is significant in understanding the behavior of gases under various conditions.

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Calculate the pressure that CCl₄ will exert at 80 °C if 1.00 mol occupies 33.3 L, assuming that (a) CCl₄ obeys the ideal-gas equation (b) CCl₄ obeys the van der Waals equation. (Values for the van der Waals constants are given in Table 10.3.)

Textbook Question

A gas of unknown molecular mass was allowed to effuse through a small opening under constant-pressure conditions. It required 105 s for 1.0 L of the gas to effuse. Under identical experimental conditions it required 31 s for 1.0 L of O2 gas to effuse. Calculate the molar mass of the unknown gas. (Remember that the faster the rate of effusion, the shorter the time required for effusion of 1.0 L; in other words, rate is the amount that diffuses over the time it takes to diffuse.)

Textbook Question

The planet Jupiter has a surface temperature of 140 K and a mass 318 times that of Earth. Mercury (the planet) has a surface temperature between 600 K and 700 K and a mass 0.05 times that of Earth. On which planet is the atmosphere more likely to obey the ideal-gas law? Explain.

Textbook Question

(b) List two reasons why the gases deviate from ideal behavior.

Textbook Question

Based on their respective van der Waals constants( Table 10.3), is Ar or CO2 expected to behave more nearlylike an ideal gas at high pressures?