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Multiple Choice
For the reaction A(g) ⇌ B(g) with ΔG° = 31.5 kJ at 298K, if the initial concentration of A is 0.100 M, what is the equilibrium concentration of B?
A
0.050 M
B
0.100 M
C
0.0001 M
D
0.200 M
Verified step by step guidance
1
Understand that the reaction A(g) ⇌ B(g) is at equilibrium, and we need to find the equilibrium concentration of B given ΔG° and the initial concentration of A.
Use the relationship between the standard Gibbs free energy change (ΔG°) and the equilibrium constant (K) given by the equation: ΔG° = -RT ln(K), where R is the universal gas constant (8.314 J/mol·K) and T is the temperature in Kelvin (298 K).
Rearrange the equation to solve for the equilibrium constant (K): K = e^(-ΔG° / RT). Substitute the given values (ΔG° = 31.5 kJ = 31500 J, R = 8.314 J/mol·K, T = 298 K) into the equation to calculate K.
Set up the expression for the equilibrium constant K in terms of the concentrations of A and B: K = [B]/[A]. Assume that the change in concentration of A is x, so at equilibrium, [A] = 0.100 - x and [B] = x.
Substitute the expression for K and the equilibrium concentrations into the equation K = [B]/[A] and solve for x, which represents the equilibrium concentration of B.