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. (b) How many grams of NaCl were used in the experiment, assuming complete reaction?

Verified step by step guidance

1. Identify the relevant chemical reaction: \(2 \text{NaCl} + 2 \text{H}_2\text{SO}_4 + \text{MnO}_2 \rightarrow \text{Na}_2\text{SO}_4 + \text{MnSO}_4 + 2 \text{H}_2\text{O} + \text{Cl}_2\).
2. Use the ideal gas law \(PV = nRT\) to find the moles of \(\text{Cl}_2\) gas produced. Remember to adjust the pressure to account for water vapor: \(P_{\text{dry}} = 755 \text{ mm Hg} - 28.7 \text{ mm Hg}\).
3. Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.
4. Calculate the moles of \(\text{Cl}_2\) using the ideal gas law with the adjusted pressure, volume, and temperature.
5. Use stoichiometry to convert moles of \(\text{Cl}_2\) to moles of \(\text{NaCl}\), and then convert moles of \(\text{NaCl}\) to grams using its molar mass.

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It allows us to determine the amount of substances consumed and produced in a reaction. In this case, understanding the stoichiometric relationships between NaCl and Cl2 is essential to calculate the mass of NaCl used.

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 crucial for determining the number of moles of Cl2 produced in the reaction, as it allows us to convert the measured volume and pressure of the gas into moles, which can then be related back to the mass of NaCl.

Partial Pressure

Partial pressure is the pressure exerted by a single component of a mixture of gases. In this scenario, the total pressure of the gas mixture includes the partial pressure of Cl2 and the water vapor. To find the pressure of Cl2 alone, we must subtract the partial pressure of water vapor from the total pressure, which is necessary for accurate calculations using the Ideal Gas Law.