For the reaction A + B ⇌ 2C the value of equilibrium constant is...

For the reaction

$A + B ⇌ 2C$

the value of equilibrium constant is $100$ at $298K$ . If the initial concentration of all the three species is $1M$ each, then the equilibrium concentration of $C$ is $x \times {10}^{- 1}M$ . The value of $x$ is _______. (Nearest integer)

Correct answer

Step-by-step solution

For the reaction A + B ⇌ 2C the value of equilibrium constant is 100 at 298K . If the initial concentration of all the

$K = {\left[C\right]}_{eq}^{2}{\left[A\right]}_{eq}{\left[B\right]}_{eq} = \dfrac{{\left(1 + 2x\right)}^{2}}{\left(1 - x\right)\left(1 - x\right)}$

$100 = {\left(\dfrac{1 + 2x}{1 - x}\right)}^{2}$

\left(\dfrac{1 + 2x}{1 - x}\right) = 10 $</p><p>$ x = \dfrac{3}{4} $</p><p>\left[C\right]{e}_{q .} = 1 + 2x$

$= 1 + 2\left(\dfrac{3}{4}\right)$

$= 2 . 5M$

$= 25 \times {10}^{- 1}M$

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