Small K approximation

The basis of this lesson is the significance of the size of K as it relates to equilibrium position.

K = [product] / [reactant]

A large K value indicates that there is much more product than reactant.

A small K value indicates that there is much less product than reactant.

Since there is very little product actually produced, the change to the amount of reactant is minimal. So minimal that there is approximately no change to the amount of reactant at llbm compared to the amount of reactant initially. This approximation will simplify the calculation.

There is still product made. The amount of product is still represented by some multiple of 'X'.

Initially 0.200mol of A is placed into a 1.00L container, sealed and allowed to reach llbm.
Determine [B]llbm
Consider the generic equation:
    2A      -->        3B      +        2C      K = 3.50x10-5
I  0.200M             0                   0
C -2X                   +3X             +2X
E  0.200-2X*         3X                2X

but since K is small, 'X' is also very small
there 0.200-2X ~ 0.200M

K   =   [B]3[C]2 / [A]2

3.50x10-5 =  [3X]3[2X]2 / [0.200M]2
1.4x10-6 = 108X5
2.65x10-2 =X
0.079M = [B]llbm

Homework: - a few adjustments to the text info
p476 (7) - H2S <=> H2 + S  [ans=9.17X10-4 M]
p476 (8)  2HCl <=> H2 + Cl2 [H2/Cl2 llbm = 3.6x10-17M]
p481 (6)
p640 (15) [ans: O2 llbm = 1.9x10-3M]