Using the data in Appendix C and given the pressures listed, calculate K_p and ΔG for each of the following reactions:
(a) N₂(g) + 3 H₂(g) → 2 NH₃(g) P_N2 = 2.6 atm, P_H2 = 5.9 atm, P_NH3 = 1.2 atm
(b) 2 N₂H₄(g) + 2 NO₂(g) → 3 N₂(g) + 4 H₂O(g) P_N2H4 = P_NO2 = 5.0 × 10^-2 atm, P_N2 = 0.5 atm, P_H2O = 0.3 atm
(c) N₂H₄(g) → N₂(g) + 2 H₂(g) P_N2H4 = 0.5 atm, P_N2 = 1.5 atm, P_H2 = 2.5 atm

Verified step by step guidance

1. Step 1: The equilibrium constant for the reaction in terms of pressure, Kp, is given by the expression Kp = (P_N2 * (P_H2)^2) / P_N2H4. Here, P_N2, P_H2, and P_N2H4 are the partial pressures of N2, H2, and N2H4 respectively. Substitute the given values into this expression to calculate Kp.
2. Step 2: To calculate ΔG for the reaction, you need to use the formula ΔG = -RT ln(Kp), where R is the gas constant (0.0821 L atm / K mol for this equation), T is the temperature in Kelvin, and ln is the natural logarithm. However, the problem does not provide a temperature, so we cannot calculate a numerical value for ΔG. If a temperature were provided, you would substitute the values of R, T, and Kp into this equation to calculate ΔG.
3. Step 3: If the temperature is not given, you can use the standard Gibbs free energy change (ΔG°) and the equation ΔG = ΔG° + RT ln(Q) to find ΔG. Here, Q is the reaction quotient, which is equal to Kp at equilibrium. ΔG° can be calculated using the formula ΔG° = ΔG°_products - ΔG°_reactants, where ΔG°_products and ΔG°_reactants are the standard Gibbs free energy of formation of the products and reactants, respectively. These values can be found in Appendix C.
4. Step 4: Substitute the values of ΔG°_products and ΔG°_reactants into the equation ΔG° = ΔG°_products - ΔG°_reactants to calculate ΔG°.
5. Step 5: Finally, substitute the values of ΔG°, R, T, and Q into the equation ΔG = ΔG° + RT ln(Q) to calculate ΔG.

Key Concepts

Equilibrium Constant (Kp)

The equilibrium constant, Kp, is a dimensionless value that expresses the ratio of the partial pressures of the products to the reactants at equilibrium for a gas-phase reaction. It is calculated using the formula Kp = (P_products)^coefficients / (P_reactants)^coefficients. For the reaction N2H4(g) → N2(g) + 2 H2(g), Kp can be determined by substituting the given partial pressures into this equation.

Gibbs Free Energy (ΔG)

Gibbs free energy, ΔG, is a thermodynamic potential that indicates the spontaneity of a reaction at constant temperature and pressure. It is related to the equilibrium constant by the equation ΔG = -RT ln(Kp), where R is the universal gas constant and T is the temperature in Kelvin. A negative ΔG indicates that the reaction is spontaneous in the forward direction.

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 gases. In the context of the given reaction, the partial pressures of N2H4, N2, and H2 are essential for calculating Kp and ΔG, as they directly influence the equilibrium state of the reaction.