A mixture of CH4 and H2O is passed over a nickel catalyst at 1000 K. The emerging gas is collected in a 5.00-L flask and is found to contain 8.62 g of CO, 2.60 g of H2, 43.0 g of CH4, and 48.4 g of H2O. Assuming that equilibrium has been reached, calculate Kc and Kp for the reaction CH4(g) + H2O(g) ⇌ CO(g) + 3H2(g).

Verified step by step guidance

1. Step 1: Calculate the number of moles of each gas using their given masses and molar masses. Use the formula: \( n = \frac{\text{mass}}{\text{molar mass}} \).
2. Step 2: Determine the equilibrium concentrations of each gas by dividing the number of moles by the volume of the flask (5.00 L).
3. Step 3: Write the expression for the equilibrium constant \( K_c \) for the reaction: \( K_c = \frac{[\text{CO}][\text{H}_2]^3}{[\text{CH}_4][\text{H}_2O]} \). Substitute the equilibrium concentrations into this expression.
4. Step 4: Use the relationship between \( K_c \) and \( K_p \) to find \( K_p \). The formula is \( K_p = K_c(RT)^{\Delta n} \), where \( \Delta n \) is the change in moles of gas (products - reactants), \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), and \( T \) is the temperature in Kelvin.
5. Step 5: Calculate \( \Delta n \) for the reaction, which is the difference in moles of gaseous products and reactants. Substitute \( \Delta n \), \( R \), and \( T \) into the \( K_p \) formula to find \( K_p \).

Key Concepts

Equilibrium Constant (Kc and Kp)

The equilibrium constant (Kc) is a ratio of the concentrations of products to reactants at equilibrium, raised to the power of their coefficients in the balanced equation. Kp is similar but uses partial pressures instead of concentrations. For the reaction CH4(g) + H2O(g) ⇌ CO(g) + 3H2(g), Kc and Kp can be calculated using the molar concentrations or partial pressures of the gases involved, reflecting the extent of the reaction at equilibrium.

Stoichiometry

Stoichiometry involves the quantitative relationships between the amounts of reactants and products in a chemical reaction. In this case, the stoichiometric coefficients from the balanced equation indicate that one mole of CH4 reacts with one mole of H2O to produce one mole of CO and three moles of H2. Understanding stoichiometry is essential for calculating the concentrations or partial pressures needed to determine Kc and Kp.

Gas Laws and Molar Volume

Gas laws describe the behavior of gases under various conditions of temperature and pressure. The ideal gas law (PV=nRT) relates pressure (P), volume (V), number of moles (n), the ideal gas constant (R), and temperature (T). In this problem, the volume of the gas collected (5.00 L) and the mass of each component allow for the calculation of moles, which are necessary for determining concentrations or partial pressures for the equilibrium constant calculations.