# $A + B \rightleftharpoons C + D$ One mole each of A and B and 3 moles each of C and D are placed in 1L flask, if equilibrium constant is 2.25. Equilibrium concentrations of A and C will be in the ratio:

(a) 2 : 3

(b) 3 : 2

(c) 1 : 2

(d) 2 : 1

Answer: 2 : 3

$A + B \rightleftharpoons C + D$
1___1____3___3   at t=0 = Initial concentration
1-x_1-x__3+x__3+x   at t=t' At equilibrium

At equilibrium,
equilibrium constant $K = \frac{[C][D]}{[A][B]} = \frac{(3+x)^2}{(1-x)^2}$
$2.25 = \frac{(3+x)^2}{(1-x)^2}$
$\therefore \frac{3+x}{1-x} = 1.5$
$\Rightarrow 3+x = 1.5 - 1.5x$
$\Rightarrow 2.5 x = -1.5$
$\Rightarrow x = \frac{-15}{25} = \frac{-3}{5}$

Concentrations of A and C,
$[A] = 1 - x = 1 + \frac{3}{5} = \frac{8}{5}$
$[C] = 3 + x = 3 - \frac{3}{5} = \frac{12}{5}$

Ratio of concentration od A and C at equilibrium,
[A] : [C] = 8 : 12
or [A] : [C] = 2 : 3

answered Nov 16, 2013
edited Nov 23, 2013