# Chemistry, Calculate K?

Calculate K for the following reaction:

A + 2 B ⇌ 2 C + D

given the following K values:

A ⇌ D + 2 E K1 = 22.44

C ⇌ B + E K2 = 57.52

### 1 Answer

- pisgahchemistLv 72 years agoFavorite Answer
Equilibrium constant .....

Target equation:

A + 2B <==> 2C + D ............... K = ???

(1) A <==> D + 2E ................... K1 = 22.44

(2) C <==> B + E ..................... K2 = 57.52

Reverse equation (2) and double it. The new value of K is (1/K2)²

(3) 2B + 2E <==> 2C ............... K3 = (1/K2)² = 3.02x10^-4

Add equations (1) and (3). 2E cancels out. K = K1 x K3

A + 2B <==> 2C + D ................ K = 22.44 x 3.02x10^-4 = 6.78x10^-3

I hope you see why doubling the coefficients in equation (3) squares the equilibrium constant. That is pretty obvious. But you might be wondering why K = K1 x K3.

K1 = [D][E]² / [A]

K3 = [C]² / [B]²[E]²

K1 x K3 = [D][E]² / [A] x [C]² / [B]²[E]²

K1 x K3 = [D][E]²[C]² / [A][B]²[E]² .............. cancel out [E]²

K1 x K3 = [D][C]² / [A][B]²

Write K expression for target equation

K = [C]²[D] / [A][B]² ................. ................. which is the same as K1 x K3