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Derive the values of equilibrium constants KP and KC for a general reaction 

x A + y B ⇌ lC + mD

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Let us consider a reversible reaction x A + y B ⇌ lC + mD 

where A, B are the reactants C and D are the product and x, y. l and m are the stoichiometric coefficients of A. B, C and D respectively. Applying the law of mass action the rate of forward reaction.

rf ∝ [A]x [B]y or rf Kf [A]x [B]y

Similarly the rate of backward reaction

rb ∝ [C]l [D]m or rb = Kb [C]l [D]m

where Kf and Kb are proportionality constants. 

At equilibrium, Rate of forward reaction (rf) = Rate of backward reaction (rb)

where KC is the equilibrium constant in terms of concentration. At a given temperature, the ratio of the product of active masses of reaction products raised to the respective stoichiometric coefficients in the balanced chemical equation to that of the reactants is a constant known as equilibrium constant.

If the reactants and products of the above reaction are in gas phase, then the equilibrium constant can be written in terms of partial pressures

where PA, PB, PC and PD are the partial pressure of gases A, B, C and D respectively.

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