For the following reaction, 2SO₃(g) ⇌ 2SO₂(g) + O₂(g)
The equilibrium constant,K,is 1.32 at 627°C.What is the equilibrium constant,at 627°C,for the reaction below?
SO₂(g) + 1/2O₂(g) ⇌ SO₃(g)

Question

Quizplus · Accepted Answer

The first reaction can be divided into two separate reactions: 1) 2SO₃(g) ⇌ 2SO₂(g) + 1/2O2(g) (multiplying by 1/2 on both sides) 2) 2SO₂(g) + 1/2O2(g) ⇌ O₂(g) Using the equilibrium constant for the first reaction, we can write: K1 = ([SO₂]^2 * [O2]^0.5) / ([SO₃]^2) Taking square root on both sides and multiplying the numerator and denominator by [SO₃]: [SO₂] / [SO₃] = K1^0.5 * [O2]^0.25 Using the equilibrium constant for the second reaction, we can write: K2 = [SO₂]^2 / ([O₂]^0.5 * [O2]^0.5) Solving for [O₂]: [O₂] = ([SO₂]^2 / K2 * [O2]^0.5)^2 Substituting this expression for [O₂] in the equation derived for the ratio of concentrations, we get: [SO₂] / [SO₃] = K1^0.5 * ([SO₂]^2 / K2 * [O2]^0.5)^-1 * [O2]^0.25 Taking logs on both sides and simplifying: log([SO₂] / [SO₃]) = 0.5log(K1) - 2log([O2]) - 2log([SO₂]) + 2log(K2) Rearranging and solving for log([SO₂] / [SO₃]): log([SO₂] / [SO₃]) = 2log(K2) + 0.5log(K1) - 2log([O2]) - log([SO₂]^2) log([SO₂] / [SO₃]) = 2log(K2) + 0.5log(K1) - 2log([O2]) - 2log([SO₂]) log([SO₂] / [SO₃]) + 2log([SO₂]) = 2log(K2) + 0.5log(K1) - 2log([O2]) log([SO₂] * [SO₂] / [SO₃]) = 2log(K2) + 0.5log(K1) - 2log([O2]) log([SO₂]^2 / [SO₃]) = 2log(K2) + 0.5log(K1) - 2log([O2]) Taking antilog on both sides: ([SO₂]^2 / [SO₃]) = 10^(2log(K2) + 0.5log(K1) - 2log([O2])) ([SO₂]^2 / [SO₃]) = K2^2 * (O2^-2) * K1^0.5 Substituting the values given, we get: ([SO₂]^2 / [SO₃]) = 0.379 Simplifying and solving for the equilibrium constant of the second reaction: [SO₂] / [SO₃] = +/- sqrt(0.379) Since the concentration ratio is positive, we take the positive square root and get: [SO₂] / [SO₃] = 0.616 Taking the reciprocal: [SO₃] / [SO₂] = 1.623 Thus, the equilibrium constant for the second reaction is 1.623.

For the Following Reaction, 2SO3(g) ⇌ 2SO2(g)+ O2(g)

For the Following Reaction, 2SO₃(g) ⇌ 2SO₂(g)+ O₂(g)