Given that the equilibrium constant for the reaction 2SO2(g) + O2(g)⇌2SO3(g) has a value of 278 at a particular temperature. What is the value of the equilibrium constant for the following reaction at the same temperature?

Let the given equilibrium reaction be:
2SO2(g) + O2(g) ⇌ 2SO3(g) Kc1 = 278
Let the second reaction be:
SO3(g) ⇌ SO2(g) + 1/2O2(g)
We need to find the equilibrium constant for this reaction (Kc2).
We can obtain the second reaction by reversing the first reaction and dividing it by 2.
Reversing the first reaction gives:
2SO3(g) ⇌ 2SO2(g) + O2(g) Kc1' = 1/Kc1 = 1/278
Dividing by 2 gives:
SO3(g) ⇌ SO2(g) + 1/2O2(g) Kc2 = (Kc1')^(1/2) = (1/278)^(1/2)
Kc2 = √(1/278) ≈ 0.06
The closest option is 6.0 × 10⁻². However, the options given seem to contain errors in formatting (incorrect use of combining characters). Assuming the exponents are correctly meant to be negative, the correct answer is approximately 0.06 which is closest to 6.0 x 10⁻² (option 1).