Question

$A\left(g\right)+2\left(B\right)g\iff 2C\left(g\right)+D\left(g\right)$ was studied using an initial concentration of B which was 1.5 times that of A. But the equilibrium concentration of A and B were found to be equal. Then $K_c$ for the equilibrium is:

• A. 4
• B. 8
• C. 6
• D. 12

Answer 1

The correct option is A 4

Th equilibrium reaction is $A\left(g\right)+2\left(B\right)g\iff 2C\left(g\right)+D\left(g\right)$.

The expression for the equilibrium constant is $K_c=\frac{\left[C{]}^2\right[D]}{\left[A\right][B{]}^2}$.

Let the initial concentration of A be 1 M.

The following table lists the concentrations of different species.

	A	B	C	D
Initial	1	1.5	0	0
Change	-x	-2x	2x	x
Equilibrium	1-x	1.5-2x	2x	x

But the equilibrium concentrations of A and B are the same.

Hence, $1-x=1.5-2x$.

or $x=0.5$.

Thus the equilibrium concentrations of A,B,C and D are 0.5M, 0.5M, 1M and 0.5M respectively.

Substitute the values in the expression for the equilibrium constant.

$K_c=\frac{1^2\times 0.5}{0.5\times {0.5}^2}=4$.