decomposition - equilibrium - chemistry (8.11)

Question

The value of the equilibrium constant Ke for the decomposition of the gas diiodo I2 in iodine atoms is 3.6 x 10 -10 at a specific temperature. Calculate the equilibrium concentration of the iodine atoms when 0.50 mol of diiodine is heated to the same temperature in a 5.0 liter reaction vessel.

A. 3.0 10^-6

B. 3.6 10^-11

C. 1.3. 10^-5

D. 6.0. 10^-6 (correct answer)

please help me solve this step by step

Answer 1

Concentration of I₂ = 0.5 mol I₂ / 5.0 L = 0.1 M

I₂ ==> 2I^- ... balanced equation

0.1......0.....Initial

-x.....+2x....Change

0.1-x..2x....Equilibrium

K = [I^-]² / [I₂]

3.6x10^-10 = (2x)² / 0.1-x) and if x is small relative to 0.1, we can ignore and not use the quadratic

3.6x10^-10 = 4x² / 0.1

4x² = 3.6x10^-11

x2 = 9x10^-12

x = 3.0x10^-6 (Answer A)

Not sure how the correct answer is 6.0x10^-3, unless I made a math error some place.