What is the equilibrium concentration of H2 in the gaseous mixture?

Question

H2(g) + I2(g) ↔ 2HI Temperature = 731K

2.40 mol of H2 and 2.40 mol of I2 are placed in a 1.00 L vessel. What is the equilibrium concentration of H2 in the gaseous mixture?
The equilibrium constant is K = 49.0

Answer 1

K = [HI]^2/[H2][I2]

say at equilibrium concentration of [HI] = x

for every mole HI produced 1/2 mole H2 is used, same with I2.

at eq. [H2] = 2.4 - 1/2 x = [I2]

so 49 = x^2/(2.4-.5x)^2 ==> 7 = x/2.4 - 0.5x

or

16.8 = 4.5 x ==> x = 3.67

So at eq [H2] = 2.4 - 1/2(3.67) = 0.565 M

Answer 2

x squared/(2.4 - x) squared = 49. Now take roots.

x/(2.4 - x) = 7. Solve for x, and your answer is 2.4 - x.