SATHEE: Chemical and Ionic Equilibrium

Chemical and Ionic Equilibrium - Result Question 12

####12. The equilibrium constant at $298 K$ for a reaction, $A + B ⇌ C + D$ is 100 . If the initial concentrations of all the four species were $1 M$ each, then equilibrium concentration of $D$ (in $m o l L^{- 1}$ ) will be

(2016 Main)

(a) 0.818

(b) 1.818

(d) 0.182

Show Answer

Solution:

$\begin{aligned} A + B ⇌ C + D & \begin{array}{lllll} Initially at t = 0 & 1 & 1 & 1 & 1 \end{array} & At equilibrium \begin{array}{llll} 1 - x & 1 - x & 1 + x & 1 + x \end{array} & K_{e q} = \frac{[C] [D]}{[A] [B]} = \frac{(1 + x) (1 + x)}{(1 - x) (1 - x)} = \frac{(1 + x)^{2}}{(1 - x)^{2}} & 100 = {(\frac{1 + x}{1 - x})}^{2} or 10 = \frac{1 + x}{1 - x} & or 10 - 10 x = 1 + x & 10 - 1 = x + 10 x & 9 = 11 x & x = \frac{9}{11} = 0.818 & ∴ [D] = 1 + x = 1 + 0.818 = 1.818 \end{aligned}$

Chemical and Ionic Equilibrium 91

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Chemical and Ionic Equilibrium - Result Question 12

Solution:

Chemical and Ionic Equilibrium 91

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