Consider the following reaction and associated equilibrium constant: a A( g )? b

Question

Consider the following reaction and associated equilibrium constant:
aA(g)?bB(g), Kc = 3.5

Part A:

Find the equilibrium concentrations of A and B for a=1 and b=1. Assume that the initial concentration of A is 1.0 M and that no B is present at the beginning of the reaction.

Part B:

Find the equilibrium concentrations of A and B for a=2 and b=2. Assume that the initial concentration of A is 1.0 M and that no B is present at the beginning of the reaction.

Part C:

Find the equilibrium concentrations of A and B for a = 2 and b = 1. Assume that the initial concentration of A is 1.0 M and that no B is present at the beginning of the reaction.

Explanation / Answer

a A ---------- > bB
1 ............................0 ( at t=0)
(1-ax).........................(bx) ( at t= teq)

so,
K = (bx)^b/( 1-ax)^a.................(1)

so, for,
part(1) a=1 , b=1
so,
3.5 = x/(1-x)
x= 3.5/4.5 = 7/9 = 0.778

so,
equilibrium concentration of A = 1-0.778 = 0.222
equilibrium concentration of B = 0.778

similarly for
part (2), a= 2 , b= 2 ,
so,
from equation(1) ,

3.5 = ( 2x)^2/(1-2x)^2
solving it ,
x= 0.326
equilibrium concentration of A = 1-2x=1-2*0.326 = 0.348
equilibrium concentration of B =2x= 0.652

similarly for
part (3), a= 2 , b= 1 ,
so,
from equation(1) ,

3.5 = ( x)/(1-2x)^2

solving it ,
x= 0.343
equilibrium concentration of A = 1-2*(0.343) = 0.314
equilibrium concentration of B =0.343

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