Real Gases and Deviations from Ideal Gas Behavior

Gases

Deviations from Ideal Gas Behavior

The behavior of real gases often deviates from the predictions of the Ideal Gas Law, especially under certain conditions. Understanding these deviations is crucial for accurately describing and predicting the properties of gases in real-world scenarios.

• Ideal Gas Law: Assumes that gas particles have negligible volume and experience no intermolecular forces. The law is expressed as:

$PV = nRT$

• Kinetic Molecular Theory (KMT): Provides the foundation for the Ideal Gas Law, based on the assumptions that gas particles are in constant, random motion, have negligible volume, and do not attract or repel each other.

• Limitations: At high pressures and low temperatures, the assumptions of KMT break down, leading to observable deviations from ideal behavior.

Volume Correction: Finite Size of Gas Particles

In reality, gas particles occupy a finite volume. At high pressures, the volume of the particles becomes significant compared to the volume of the container.

• Corrected Volume: The actual free volume available for particle movement is less than the container volume.

• Van der Waals Equation (Volume Correction):

$[V - nb]$

• b: Van der Waals constant for the size of gas particles (L/mol).

• n: Number of moles of gas.

The corrected equation for the volume term is:

$P(V - nb) = nRT$

Pressure Correction: Intermolecular Forces

Gas particles experience intermolecular attractions, which reduce the frequency and force of collisions with the container walls, thus lowering the observed pressure.

• Corrected Pressure: The measured pressure is less than the ideal pressure due to these attractive forces.

• Van der Waals Equation (Pressure Correction):

$P_{real} = P_{ideal} - a\left(\frac{n}{V}\right)^2$

• a: Van der Waals constant for intermolecular attraction (L2·atm/mol2).

The full Van der Waals equation, accounting for both corrections, is:

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

Van der Waals Constants

The constants a and b are unique to each gas and reflect the strength of intermolecular forces and the size of the gas particles, respectively.

Substance	a (L2·atm/mol2)	b (L/mol)
He	0.034	0.0237
Ne	0.213	0.0171
Ar	1.34	0.0322
H2	0.244	0.0266
N2	1.39	0.0391
O2	1.36	0.0318
CO2	3.59	0.0427
CH4	2.25	0.0428
NH3	4.17	0.0371
H2O	5.46	0.0305
CCl4	20.4	0.1383

Additional info: Table values are representative; refer to your textbook for a complete list.

Conditions Favoring Ideal vs. Real Gas Behavior

• Ideal Gas Behavior: Favored at low pressures (large volume) and high temperatures (high kinetic energy), where particle volume and intermolecular forces are negligible.

• Real Gas Behavior: Observed at high pressures (particles are closer together) and low temperatures (intermolecular attractions are significant).

Example: At high pressure, the volume correction becomes important because the finite size of particles reduces the free space available. At low temperature, the pressure correction is significant due to increased intermolecular attractions.

Identifying Gases Prone to Ideal or Real Behavior

• Most Ideal: Gases with small, nonpolar molecules and weak intermolecular forces (e.g., He, H2).

• Most Real: Gases with strong intermolecular forces or larger molecular size (e.g., H2O, NH3).

Example Questions:

• Which of the following gases is more likely to exhibit ideal gas behavior: H2, Cl2, or CO2? Answer: H2 (small, nonpolar, weak intermolecular forces).

• Which gas is more likely to exhibit real gas behavior, CH4 or H2O? Answer: H2O (strong hydrogen bonding).

Worked Example: Calculating Pressure for Real vs. Ideal Gas

A sample of 1.000 mol of CO2 is confined to a 1.000 L container at 300.0 K. Calculate the pressure using both the ideal and van der Waals equations.

• Ideal Gas Law:

$P = \frac{nRT}{V} = 7.470\ \text{atm}$

• Van der Waals Equation:

$P = \frac{nRT}{V - nb} - a\left(\frac{n}{V}\right)^2 = 7.189\ \text{atm}$

Additional info: The van der Waals equation yields a lower pressure due to corrections for intermolecular attractions and finite particle volume.