Final answer:
The equilibrium constant for the reverse reaction BrCl(g) → ½ Br2(g) + ½ Cl2(g) is found by taking the reciprocal of the original K value and raising it to the power of 2, resulting in approximately 2.97 x 10-4.
Step-by-step explanation:
The given equilibrium reaction is Br2(g) + Cl2(g) ⇌ 2 BrCl(g) with an equilibrium constant (K) value of 58.0. To find the equilibrium constant for the reverse reaction, which is BrCl(g) → ½ Br2(g) + ½ Cl2(g), the reciprocal of the original K value must be taken and then each concentration term should be raised to the power of its stoichiometric coefficient in the balanced equation. Since the stoichiometric coefficients for Br2 and Cl2 are 1/2 in the reverse reaction, the expression for the reverse reaction K is 1/K1/(1/2)
For the reaction Br2(g) + Cl2(g) ⇌ 2 BrCl(g) with K=58.0, the equilibrium constant for the reverse reaction would therefore be (1/58.0)1/(1/2) or (1/58.0)2 which equals 1/(58.0)2 or approximately 2.97 x 10-4.