Why do real gases deviate from ideal gas behavior at high pressures?

Real gases deviate from ideality at high pressures because gas particle density increases, making the combined volume of particles significant relative to container volume. Additionally, intermolecular attractive forces become more pronounced when particles are closer together. These factors violate kinetic molecular theory assumptions that particles occupy negligible volume and exert no attractive forces on each other.

What does the volume correction factor nb represent in the van der Waals equation?

The volume correction factor nb accounts for the actual volume occupied by gas molecules themselves. At high pressures, the combined molecular volume becomes significant and must be subtracted from the container volume to determine the volume available for particle movement. The constant b is gas-specific and experimentally determined, with units of L/mol.

How do intermolecular forces affect gas pressure in real gases?

Intermolecular attractive forces reduce the pressure exerted by real gases compared to ideal gases. When particles interact, they spend more time with neighboring molecules and less time colliding with container walls, decreasing collision frequency. The van der Waals equation corrects for this using the term an²/V², where a represents the strength of intermolecular attraction for a specific gas.

Under what conditions does the van der Waals equation reduce to the ideal gas law?

The van der Waals equation reduces to the ideal gas law PV = nRT when volume is relatively large and the number of moles is relatively small, corresponding to low-pressure conditions. Under these circumstances, both correction terms become negligible: molecular volume is insignificant relative to container volume, and particles are too far apart for intermolecular forces to matter.

Why is the PV/RT ratio used to identify non-ideal gas behavior?

For one mole of an ideal gas, the ratio PV/RT equals one regardless of pressure. When this ratio deviates from one, it indicates non-ideal behavior. At low pressures, real gases approach this ideal value, but as pressure increases, the ratio diverges significantly, with different gases showing different deviations based on their molecular properties.

How does temperature affect the significance of intermolecular forces in real gases?

At high temperatures, gas particles possess high kinetic energy relative to intermolecular attractive forces, allowing them to overcome attractions and move quickly. At lower temperatures, particles move more slowly and have lower kinetic energy, making intermolecular forces more significant. This is why deviations from ideal behavior are more pronounced at low temperatures and high pressures.

What are the constants a and b in the van der Waals equation, and what do they represent?

The constant a represents the strength of intermolecular attractive forces for a specific gas, with units of L²·atm/mol². The constant b represents the size of gas molecules and the volume they occupy, with units of L/mol. Both are experimentally determined values that vary for different gases and are essential for correcting real gas behavior.

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Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

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Ideal gases follow the relation PV over nRT equals one. Recall Boyle’s law, which states that when the amount and temperature of a gas are held constant, increasing the pressure will invariably decrease the volume to maintain a constant ratio.

But when that ratio is plotted as a function of pressure for one mole of several real gases, it equals the ideal value “one” only at low pressures. As the pressure increases, the curves deviate significantly from ideality.

At low pressures, the combined volume of gas particles is negligible relative to the container volume — like a pea inside a basketball. Therefore, the volume available to ideal gas particles equals the total container volume.

At higher pressures, the gas density is much greater. Thus, the combined volume of the gas particles becomes significant — like a pea inside a ping-pong ball.

Therefore, the assumption of the kinetic molecular theory that gas particles occupy negligible volume is invalid at high pressures.

The volume occupied by a real gas is greater than the volume available to its particles, which is the volume it would occupy in an ideal case, by nb, where b is an experimentally determined constant that depends on the gas and has units of L/mol.

Deducting nb adjusts the volume of a real gas downward to that available to its particles, which is equivalent to the ideal volume.

Another assumption of the kinetic molecular theory — that intermolecular forces between gas molecules are negligible — is valid only under high-temperature and low-pressure conditions.

Typically, gases exert very weak attractive forces. Under low-pressure conditions, the gas particles are separated by large distances and, therefore, do not perceive the attractive forces of other particles.

Similarly, under high-temperature conditions, the particles have high kinetic energies relative to the attractive forces and move very quickly. When particles collide, they bounce off each other because the high kinetic energy overcomes the small attractive forces.

However, when the gas is at higher pressures, the particle density is greater. The particles are, therefore, separated by shorter distances, and the likelihood that they will interact thereby increases. The attractive forces between the particles accordingly become more significant at high pressures.

This is more evident as the temperature is lowered. The kinetic energy of the particles decreases, and they move more slowly. When intermolecular attraction becomes significant, particles are increasingly likely to ‘stick’ to each other upon colliding.

As gas particles spend more time interacting with neighboring particles, the frequency of collisions with the container surface decreases.

Consequently, the pressure exerted by a real gas is lower than that of an ideal gas by an²/V². Here, a is an experimentally determined constant that depends on the gas and has units of L²·atm/mol², and V is the real volume.

Adding this term adjusts the real pressure upward to that exerted by an ideal gas. The modified equation with the pressure and volume correction factors is called the van der Waals equation for non-ideal or real gases.

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Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical…