Chlorine gas was first prepared in 1774 by the oxidation of NaCl with MnO₂: 2 NaCl(s) + 2 H₂SO₄(l) + MnO₂(s) → Na₂SO₄(s) + MnSO₄(s) + 2 H₂O(g) + Cl₂(g) Assume that the gas produced is saturated with water vapor at a partial pressure of 28.7 mm Hg and that it has a volume of 0.597 L at 27 °C and 755 mm Hg pressure. (a) What is the mole fraction of Cl₂ in the gas?

Verified step by step guidance

1. Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. This is necessary for calculations involving gases which require absolute temperature in Kelvin.
2. Calculate the total pressure of the dry gas by subtracting the partial pressure of the water vapor from the total pressure of the gas mixture.
3. Use the ideal gas law, PV = nRT, to find the number of moles of dry gas. Here, P is the pressure of the dry gas, V is the volume, R is the ideal gas constant (0.0821 L atm K^-1 mol^-1), and T is the temperature in Kelvin.
4. Calculate the partial pressure of Cl₂ by subtracting the partial pressure of water vapor from the total pressure of the gas mixture.
5. Determine the mole fraction of Cl₂ by dividing the partial pressure of Cl₂ by the total pressure of the dry gas.

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the behavior of gases under various conditions. In this question, it helps determine the number of moles of Cl2 and water vapor present in the gas mixture.

Partial Pressure

Partial pressure is the pressure exerted by a single component of a gas mixture. According to Dalton's Law, the total pressure of a gas mixture is the sum of the partial pressures of its individual components. Understanding partial pressure is crucial for calculating the mole fraction of Cl2, as it allows us to separate the contributions of Cl2 and water vapor to the total pressure.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture, defined as the ratio of the number of moles of that component to the total number of moles in the mixture. It is a dimensionless quantity that provides insight into the composition of gas mixtures. In this problem, calculating the mole fraction of Cl2 requires knowing the moles of Cl2 and the total moles of gas present, including water vapor.