Chemical Equilibrium, Small K equilibrium Values.?

Question

When reasonable algebraic methods fail, it is sometimes possible to make simplifying assumptions in order to solve equilibrium problems. This is possible only when K equilibrium is very small or very large, For Example:
2 CF4(g) + 4 H2O(g) = O2(g) + 8 HF(g) + 2 CO(g)
Kp = 2.1 x 10^-23 at 373K
CF4(g) and H2O(g) at partial pressures 2.0atm each are injected into an empty sealed vessel. Calculate the equilibrium partial pressure of HF(g).

Answer 1

.. .. .. .. .. 2CF4 + 4H2O <=> O2 + 8HF + 2CO
Initial .. .. .. 2 .. .. .. .. 2
React .. .. 2x .. .. .. .. 4x
Produce .. .. .. .. .. .. .. .. .. .. .. .x .. .. 8x .. .. .. 2x
At Equil. .2-2x .. .. .. 2-4x .. .. ..x .. .. 8x .. .. .. 2x

Kp= P(O2) *P(HF)^8 *PCO)^2 / (P(CF4)^2 * P(H2O)^4) =>
Kp= x*(8x)^8*(2x)^2 / ((2-2x)^2 *(2-4x)^4)

We assume that x << 2 so that 2-2x=2-4x=2 then

Kp= 2^2*8^8*x^11 /2^2*2^4 = 2^24*x^11/2^4 = 2^20*x^11
(because 8^8= (2^3)^8= 2^(3*8)=2^24)

so x= (Kp/2^20)^(1/11) = ((2.1*10^-23)/(2^20))^(1/11) =0.0025 so our assumption is valid

P(HF)= 8x= 8*0.0025= 0.02

Answer 2

It only potential that the made of the concentrations of the reactants equals the made of the concentrations of the products, no longer something particular. In different words, if A and B are the reactants and C and D are the products, [A][B]=[C][D].