Problem 93 - Chemistry: The Central Science

Question

Based on their respective van der Waals constants (Table 10.3), is Ar or \(\mathrm{CO}_{2}\) expected to behave more nearly like an ideal gas at high pressures? Explain.

Step-by-Step Solution

Answer

Ar is expected to behave more nearly like an ideal gas at high pressures compared to CO2, because its van der Waals constants, \( a_{Ar} = 1.34 L^2atm/mol^2 \) and \( b_{Ar} = 0.032 L/mol \), are lower than those of CO2, \( a_{CO2} = 3.59 L^2atm/mol^2 \) and \( b_{CO2} = 0.042 L/mol \). Lower van der Waals constants indicate less deviation from ideal gas behavior.

Step 1: Find the van der Waals constants of Ar and CO2

To compare Ar and CO2, first, we need to check their van der Waals constants, which can be found in Table 10.3 (provided in the question). The constants (a) and (b) give information about the intermolecular forces and the size of the molecules, respectively. The numerical values for the constants are: For Ar: \( a = 1.34 L^2 atm/mol^2 \) \( b = 0.032 L/mol \) For CO2: \( a = 3.59 L^2 atm/mol^2 \) \( b = 0.042 L/mol \)

Step 2: Compare the van der Waals constants

The values of the van der Waals constants indicate how much the gas deviates from ideal behavior. The higher the value of a and b, the greater the deviation from the ideal gas law. In this case, we can compare the constants directly: For Ar, \( a_{Ar} = 1.34 L^2atm/mol^2 \) and \( b_{Ar} = 0.032 L/mol \) For CO2, \( a_{CO2} = 3.59 L^2atm/mol^2 \) and \( b_{CO2} = 0.042 L/mol \) \( a_{Ar} < a_{CO2} \) and \( b_{Ar} < b_{CO2} \)

Step 3: Determine which gas behaves more like the ideal gas at high pressures

Since van der Waals constants are lower for Ar than for CO2, Ar deviates less from the ideal gas behavior. Thus, at high pressures, Ar is expected to behave more nearly like an ideal gas compared to CO2.