A What is the pressure predicted by the ideal gas law for...

A What is the pressure predicted by the ideal gas law for one mole of steam in $31.0 \mathrm{~L}$ at $100^{\circ} \mathrm{C}$ ? What is the pressure predicted by the van der Waals equation (Section $12-15)$ given that $a=5.464 \mathrm{~L}^{2} \cdot \mathrm{atm} / \mathrm{mol}^{2}$ and $\bar{b}=0.03049 \mathrm{~L} / \mathrm{mol}$ ? What is the percent difference between these values? Does steam deviate from ideality significantly at $100^{\circ} \mathrm{C}$ ? Why?

A What is the pressure predicted by the ideal gas law for one mole of steam in $31.0 \mathrm{~L}$ at $100^{\circ} \mathrm{C}$ ? What is the pressure predicted by the van der Waals equation (Section $12-15)$ given that $a=5.464 \mathrm{~L}^{2} \cdot \mathrm{atm} / \mathrm{mol}^{2}$ and $\bar{b}=0.03049 \mathrm{~L} / \mathrm{mol}$ ?
What is the percent difference between these values? Does steam deviate from ideality significantly at $100^{\circ} \mathrm{C}$ ? Why?

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Key Concepts

Ideal Gas Law

The ideal gas law is a fundamental equation in thermodynamics that relates pressure, volume, temperature, and the number of moles in a gas through the equation PV = nRT. It is based on the assumption that gas molecules do not attract or repel each other and that their volume is negligible compared to the volume of the container.

van der Waals Equation

The van der Waals equation is a modified version of the ideal gas law that accounts for the finite size of molecules and the intermolecular forces between them. This is achieved by introducing two correction factors: one (a) that adjusts for attractive forces and another (b) that corrects for the nonzero volume occupied by the gas molecules, leading to a more accurate description of real gas behavior.

Real Gas Behavior and Deviations from Ideality

Real gases deviate from ideal behavior when the conditions cause the assumptions of the ideal gas law to break down, such as at high pressures or low temperatures. By comparing predictions from the ideal gas law and the van der Waals equation, one can assess the significance of these deviations. A small percent difference suggests the gas behaves approximately ideally, indicating that molecular interactions and volume effects are minimal under those conditions.

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