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

Verified step by step guidance

1. insert step 1> Identify the van der Waals equation, which is an adjustment of the ideal gas law to account for the volume occupied by gas molecules and the intermolecular forces between them. The equation is: \( \left( P + \frac{an^2}{V^2} \right)(V - nb) = nRT \), where \( a \) and \( b \) are the van der Waals constants.
2. insert step 2> Understand that the constant \( a \) accounts for the attractive forces between molecules. A smaller \( a \) value indicates weaker intermolecular forces, making the gas behave more ideally.
3. insert step 3> Recognize that the constant \( b \) accounts for the volume occupied by the gas molecules themselves. A smaller \( b \) value suggests that the gas molecules occupy less volume, making the gas behave more ideally.
4. insert step 4> Compare the van der Waals constants \( a \) and \( b \) for Ar and CO2 from Table 10.3. Determine which gas has smaller values for both constants, as this gas will behave more like an ideal gas at high pressures.
5. insert step 5> Conclude which gas, Ar or CO2, is expected to behave more nearly like an ideal gas at high pressures based on the comparison of their van der Waals constants.

Key Concepts

Ideal Gas Law

The Ideal Gas Law describes the behavior of ideal gases through the equation PV=nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. Ideal gases are assumed to have no intermolecular forces and occupy no volume, making them behave predictably under various conditions. Understanding this law is crucial for comparing real gases to ideal behavior, especially at high pressures.

Van der Waals Equation

The Van der Waals equation modifies the Ideal Gas Law to account for the volume occupied by gas molecules and the attractive forces between them. It introduces two constants, a and b, which are specific to each gas and reflect the strength of intermolecular forces and the size of the molecules, respectively. This equation helps predict how real gases deviate from ideal behavior, particularly under high pressure and low temperature.

Intermolecular Forces

Intermolecular forces are the attractive or repulsive forces between molecules that influence their physical properties and behavior. In the context of gases, stronger intermolecular forces can lead to greater deviations from ideal gas behavior, especially at high pressures where molecules are closer together. Understanding these forces is essential for predicting whether a gas like Ar or CO2 will behave more ideally under specific conditions.