I am currently attempting the following problem:

Nitric oxide and bromine react accordingly to the following reaction:

2NO(g) + Br

_{2}(g) <----------> 2NOBr(g)

The equilibrium constant at 300K is 134 atm

^{-1}What would be the partial pressures of all species if NO and Br

_{2}, both at an initial partial pressure of 0.3 atm, were allowed to come to equilibrium at this temperature?

My attempt:

Because the equilibrium constant is relatively large, I'm going to assume that the forward reaction goes towards completion

Creating an ICE table:

2NO(g) + Br

_{2}(g) <----------> 2NOBr(g)

Initial: 0.3 0.3 0

Change: -0.3 -0.15 +0.3

Equilibrium: 0 0.15 0.3

Considering the reverse reaction:

If I reverse the reaction, the equilibrium constant of the reverse reaction would be equal to 134

^{-1}Creating an ICE table:

2NOBr(g) <----------> 2NO(g) + Br

_{2}(g)

Initial: 0.3 0 0.15

Change: -2x +2x +x

Equilibrium 0.3 - 2x 2x 0.15 + x

The equation would be:

(2x)

^{2}(0.15+x)/(0.3-2x)

^{2} = 134

^{-1}Because the equilibrium constant is very small, I'm going to assume that x is negligible, and thus the equation becomes:

(2x)

^{2}(0.15)/(0.3)

^{2}Solving for x gives me 0.033, while the textbook, using successive approximations (it didn't consider the reverse reaction, and just solved the equation from the original reaction) got 0.026.

I'm wondering, did I do something wrong? Or is my answer more accurate than the textbooks?

Thank you in advance!