For the reaction, $A + B ⇌ 2 C$ . The value of equilibrium constant is 100 at 298K. If intial concentration of all three species are 1M each, then the equilibrium concentration of C is $x \times 10^{- 2} M$ . The value of $x$ is ____ nearest integer.

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Detailed Solution

$A + B ⇌ 2 C$
1 1 1
1-X 1-X 1-X
$K_{C} = \frac{{(1 + 2 X)}^{2}}{(1 - X) (1 - X)}$
$100 = \frac{{(1 + 2 X)}^{2}}{{(1 - X)}^{2}}$
$10 = \frac{1 + 2 X}{1 - X}$
$X = \frac{3}{4}$
Equilibrium conc. of C = 1+2X
= 1+2(3/4)
= 2.5 m
$= 25 \times 10^{- 1}$

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