7.15 At 700 K, equilibrium constant for the reaction:

H2 (g) + I2 (g) 2HI (g)

is 54.8. If 0.5 mol L–1 of HI(g) is present at equilibrium at 700 K, what are the concentration of H2(g) and I2(g) assuming that we initially started with HI(g) and allowed it to reach equilibrium at 700?

It is given that equilibrium constant Kc for the reaction
H2g+I2g2HIg is 54.8.
Therefore, at equilibrium, the equilibrium constant for the reaction 
K'c for the reaction
2HIgH2g+I2gHI=0.5 molL-1 will be 1/54.8. 
Let the concentrations of hydrogen and iodine at equilibrium be x molL-1
H2=I2 =x mol L-1Therefore, H2I2HI2=K'cx×x0.52=154.8x2=0.2554.8x=0.068 molL-1approx.
Hence, at equilibrium,  H2=I2=0.068 mol L-1.