The equilibrium constant for the reaction
SO₃( g)⇌ SO₂( g)+1/2O₂( g)
is K_c=4.9× 10⁻². The value of K_c for the reaction given below is 2SO₂( g)+O₂( g)⇌ 2SO₃( g) is :

Solution

Chemistry ma’am · 3 steps

The new reaction is the old one reversed and doubled, so flip K and then square it.

1. Compare the reactions. Turn SO₃ ⇌ SO₂ + 1/2 O₂ around and you get SO₂ + 1/2 O₂ ⇌ SO₃. Multiply that by 2 and you get the required 2SO₂ + O₂ ⇌ 2SO₃.
2. Two rules. Reversing a reaction turns K into 1/K. Multiplying the whole equation by n raises K to the power n.

   K_c' = (1/K_c)² = 1/(4.9 × 10⁻²)² = 1/(2.401 × 10⁻³)

3. So. K_c' ≈ 416.5, which matches option (b), 416.

The idea to keep. Write the new reaction in terms of the given one. Reversing gives 1/K, multiplying by n gives Kⁿ, and adding reactions multiplies their K values.

Answer from the NTA final answer key. Solution by PrepWiser.