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Characteristics of Equilibrium Constant

1 mole of H...

Question

$1$ mole of $H_{2} O$ and $1$ mole of $C O$ are heated in a $10$ litre vessel at $1259 K$ . $40 % H_{2} O$ reacts with $C O$ according to the following equations,
$H_{2} O (g) + C O (g) ⇌ H_{2} (g) + C O_{2} (g)$ ;
Calculate equilibrium constant for the reaction.

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Solution

$H_{2} O + C O = H_{2} + C O_{2}$
at t=0 1 1 0 0
at eqm (1-x) (1-x) x x
$H_{2} O$ reacted = 40% of 1 mol of $H_{2} O$ = 0.4 mol
x = 0.4 mol
(1 - x ) = 1 - 0.4 = 0.6 mol

$K_{c} = \frac{[H 2] [C O 2]}{[H 2 O] [C O]}$
$= x . x / (1 - x) . (1 - x)$
$= x^{2} / (1 - x)^{2}$
$= (0.4)^{2} / (0.6)^{2}$
= 0.444

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