The normal boiling points of \(\mathrm{CO}\) and \(\mathrm{SO}_{2}\) are \(-192^{\circ} \mathrm{C}\) and \(-10^{\circ} \mathrm{C}\), respectively. (a) At \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\), which gas would you expect to have a molar volume closest to the ideal value? (b) If you wanted to reduce the deviation from ideal gas behavior, in what direction would you change the temperature? The pressure?

In order to perform this analysis, we need to understand the ideal gas behavior. The Ideal Gas Law is given by: PV = nRT Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

(a) To determine which gas performs better at 25°C and 1 atm, we will compare their molar volumes to see which is closest to the ideal value. For an ideal gas, V = nRT/P Since we are comparing the molar volumes, we will use 1 mole for each gas. Therefore, n = 1: V = (1 mol)R(25+273.15 K)/1 atm Using the value of R in L atm / (mol K), R = 0.0821 V = (1 mol)(0.0821 L atm/(mol K))(298.15 K)/1 atm ≈ 24.5 L/mol A gas that behaves most like an ideal gas will have the closest molar volume to 24.5 L/mol. At a higher temperature, both gases will have a molar volume closer to the ideal value, while at a lower temperature, the molar volume deviates more. Since CO has a lower boiling point, it is farther from the ideal situation. On the other hand, SO2, with a higher boiling point, has a molar volume closer to the ideal value. Therefore, at 25°C and 1 atm, SO2 would have a molar volume closer to the ideal value.

(b) To reduce the deviation from the ideal gas behavior, we need to analyze how changes in temperature and pressure affect the deviation. 1. Temperature: As the temperature increases, the kinetic energy of the gas molecules increases, which makes the gas behave more like an ideal gas. Therefore, to reduce deviation, increase the temperature. 2. Pressure: Lower pressures result in a larger volume, which allows gas molecules to move more freely. This leads to a gas behaving more like an ideal gas. Therefore, to reduce deviation, decrease the pressure.