A Question about Chemical Equilibrium

[vijayramakrishnan]

say we have a reaction:

N₂O₄ <====> 2NO₂


for this reaction,if initial number of moles of N₂O₄ is 'a' can we write

t = 0 a -
at equilbrium a-x 2x

similarly can we do the same for pressure i.e.
if initial pressure is p,then can we say

t=0 p -
at equilbrium p-y 2y

if yes why? and is x=y,i.e is the number of moles x dissociated equal to decrease in pressure of reactant?
and is this method valid for all reversible reaction irrespective of the stoichiometric coefficient of reactants and products

please help.

 

[James Pelezo]

Physics Forums - Equilibrium N₂O₄(g) <=> 2NO₂(g)

------------------- N2O4(g) ---- <=> --- 2NO2(g)
Ci: ------------------ a ------------------------ 0 ---
∆C:---------------- -x ---------------------- +2x ---
Ceq: ------------- a - x -------------------- 2x ---

Kc = [NO₂]²/[N₂O₄] = (2x)²/(a – x) = 4x²/(a – x) => K_c(a – x) = 4x² => K_c·a - K_c·x = 4x²

4x² + K_c·x + (-K_c·a) = 0

x = [-b ± (b² – 4ac)^1/2]/2a

a = 4, b = K_c , c = -K_c·a

substitute into quadratic; solve for x …

[N₂O₄] = a – x

[NO2₂] = 2x