The graph below shows the change in pressure as the temperature increases for a 1-mol sample of a gas confined to a 1-L container. The four plots correspond to an ideal gas and three real gases: CO2, N2, and Cl2. (b) Use the van der Waals constants in Table 10.3 to match the labels in the plot (A, B, and C) with the respective gases 1CO2, N2, and Cl22.

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Identify the van der Waals equation: \( \left( P + \frac{an^2}{V^2} \right)(V-nb) = nRT \), where \( a \) and \( b \) are van der Waals constants.

Understand that the constant \( a \) accounts for intermolecular forces, and \( b \) accounts for the volume occupied by gas molecules.

Compare the van der Waals constants for CO2, N2, and Cl2 from Table 10.3. Note that a higher \( a \) value indicates stronger intermolecular forces, and a higher \( b \) value indicates larger molecular size.

Analyze the graph: At high temperatures, the behavior of real gases approaches that of an ideal gas. At lower temperatures, deviations occur due to intermolecular forces and molecular size.

Match the plots (A, B, C) with the gases by considering the extent of deviation from ideal behavior, using the van der Waals constants to determine which gas corresponds to each plot.

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주요 개념

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Ideal Gas Law

The Ideal Gas Law describes the relationship between pressure, volume, temperature, and the number of moles of a gas, expressed as PV = nRT. This law assumes that gas particles do not interact and occupy no volume, making it a useful approximation for many gases under standard conditions. Understanding this law is crucial for analyzing the behavior of gases in the context of temperature and pressure changes.

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 is expressed as (P + a(n/V)²)(V - nb) = nRT, where 'a' and 'b' are constants specific to each gas. This equation is essential for understanding the behavior of real gases, especially at high pressures and low temperatures, where deviations from ideal behavior occur.

Real Gases vs. Ideal Gases

Real gases deviate from ideal behavior due to intermolecular forces and the finite volume of gas particles. Factors such as temperature and pressure can influence these deviations, making it important to use models like the Van der Waals equation for accurate predictions. Recognizing the differences between real and ideal gases helps in interpreting experimental data and understanding the behavior of gases in various conditions.