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For a reaction,
$A (g) + 2 B (g) ⇌ C (g) + D (g) + E (g); K_{e q} = 2$
Calculate equilibrium concentration of B if initial 10 moles of A are mixed with 20 moles of B in a 2 liter rigid container

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$\frac{10}{3} M$

$\frac{40}{3} M$

$\frac{20}{3} M$

$\frac{4}{3} M$

answer is B.

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Detailed Solution

$A (g) + 2 B (g) ⇌ C (g) + D (g) + E (g); K_{e q} = 2$

t=0 $10 20$

t=t $\frac{10 - x}{2} \frac{20 - 2 x}{2} \frac{x}{2} \frac{x}{2} \frac{x}{2}$

$2 = \frac{x^{3}}{(10 - x) (20 - 2 x)^{2}}$

$8 = \frac{x^{3}}{(10 - x)^{3}}$

$\Rightarrow 2 = \frac{x}{10 - x}$

$\Rightarrow 20 - 2 x = X$

$\Rightarrow 20 = 3 x$

$\Rightarrow x = \frac{20}{3}$

$[B] = \frac{20 - \frac{40}{3}}{2}$ $= \frac{20}{6} = \frac{10}{3} M$

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