Chemistry · General chemistry II · Worked example
Reverse, scale and combine equilibrium constants
At a certain temperature, Kc = 0.50 for N₂(g) + 3H₂(g) ⇌ 2NH₃(g). Find Kc for (a) 2NH₃(g) ⇌ N₂(g) + 3H₂(g) and (b) 2N₂(g) + 6H₂(g) ⇌ 4NH₃(g).
Reverse the equation
Reversing swaps products and reactants, so the new expression is the reciprocal of the old one, and so is its value.
Double the coefficients
Every exponent doubles, so the expression becomes [NH₃]⁴/([N₂]²[H₂]⁶), the square of the original. K is squared.
Adding equations
When two equations add to a third, the third’s expression is the product of the other two, so its K is K₁K₂. Reversing and scaling first, then multiplying, gives K for any combination.
Result
(a) Kc = 2.0; (b) Kc = 0.25.
Your turn
For A ⇌ B, K₁ = 4.0, and for B ⇌ C, K₂ = 0.50. Find K for A ⇌ C.
Show the answer and explanation
K = 2.0.
Adding A ⇌ B and B ⇌ C gives A ⇌ C, so K = K₁K₂ = (4.0)(0.50) = 2.0.
Keep exploring
In Equilibrium & ICE tables, test a mixture of 1.0 M each of NH₃, N₂ and H₂ against the reversed reaction with K = 2.0: Q = 1.0 < K, so ammonia decomposes. The original equation with K = 0.50 gives Q = 1.0 > K and the same change, described in reverse.
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