A 125.4 g quantity of water and an equal molar amount of carbon monoxide were placed in an empty 10.0-L vessel, and the mixture was heated to 700 K. At equilibrium, the partial pressure of CO was 9.80 atm. The reaction is CO(g) + H2O(g) ⇌ CO2(g) + H2(g). (a) What is the value of Kp at 700 K? (b) An additional 31.4 g of water was added to the reaction vessel, and a new state of equilibrium was achieved. What are the equilibrium partial pressures of each gas in the mixture? What is the concentration of H2 in molecules/cm³?

Verified step by step guidance

1. Step 1: Calculate the initial moles of water and carbon monoxide. Use the molar mass of water (18.02 g/mol) to find the moles of water: moles of H2O = 125.4 g / 18.02 g/mol. Since the moles of CO are equal, they are the same as the moles of H2O.
2. Step 2: Determine the initial partial pressures of CO and H2O. Use the ideal gas law, PV = nRT, to find the initial partial pressures. Assume the initial volume is 10.0 L and the temperature is 700 K. Use R = 0.0821 L·atm/mol·K.
3. Step 3: Set up an ICE (Initial, Change, Equilibrium) table for the reaction CO(g) + H2O(g) ⇌ CO2(g) + H2(g). Use the given equilibrium partial pressure of CO (9.80 atm) to find the changes in pressure and calculate the equilibrium partial pressures of all gases.
4. Step 4: Calculate the equilibrium constant Kp using the expression Kp = (P_CO2 * P_H2) / (P_CO * P_H2O), where P represents the partial pressures of the gases at equilibrium.
5. Step 5: For the new equilibrium after adding 31.4 g of water, recalculate the moles of water and adjust the initial conditions in the ICE table. Solve for the new equilibrium partial pressures and use the ideal gas law to find the concentration of H2 in molecules/cm³.

Key Concepts

Equilibrium Constant (Kp)

The equilibrium constant, Kp, is a numerical value that expresses the ratio of the partial pressures of the products to the partial pressures of the reactants at equilibrium, each raised to the power of their respective coefficients in the balanced chemical equation. For the reaction CO(g) + H2O(g) ⇌ CO2(g) + H2(g), Kp can be calculated using the formula Kp = (P_CO2 * P_H2) / (P_CO * P_H2O). Understanding Kp is essential for predicting the direction of the reaction and the concentrations of the gases at equilibrium.

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 each individual gas. In this question, the partial pressures of CO, H2O, CO2, and H2 at equilibrium are crucial for calculating Kp and determining the new equilibrium state after adding more water.

Molarity and Concentration

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. In this context, after determining the equilibrium partial pressures, converting these values to concentrations in molecules per cm³ involves using Avogadro's number (6.022 x 10²³ molecules/mol) and the ideal gas law. Understanding how to relate partial pressures to molarity is key for solving the final part of the question regarding the concentration of H2.