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Equilibrium

Question
CBSEENCH11006384

Equilibrium constant Kc for the reaction
                 straight N subscript 2 left parenthesis straight g right parenthesis space plus space 3 straight H subscript 2 left parenthesis straight g right parenthesis space space rightwards harpoon over leftwards harpoon space space space 2 NH subscript 3 left parenthesis straight g right parenthesis space at space 500 space straight K space is space 0.061

At a particular time, the analysis shows that composition of the reaction mixture is 3·0 mol L–1 N2, 2·0 mol L–1 H2 and 0·5 mol L–1 NH3. Is the reaction at equilibrium? If not in which direction does the reaction tend to proceed to reach equilibrium?

Solution
stack straight N subscript 2 left parenthesis straight g right parenthesis with 3.0 below space plus stack 3 straight H subscript 2 left parenthesis straight g right parenthesis with 2.0 below space rightwards harpoon over leftwards harpoon stack space 2 NH subscript 3 space left parenthesis straight g right parenthesis with 0.5 space conc. divided by mol space straight L to the power of negative 1 end exponent below
Reaction quotient, Qc for the reaction will be written as
straight Q subscript straight c space equals space fraction numerator open square brackets NH subscript 3 left parenthesis straight g right parenthesis close square brackets squared over denominator open square brackets straight N subscript 2 left parenthesis straight g right parenthesis close square brackets space open square brackets straight H subscript 2 left parenthesis straight g right parenthesis close square brackets cubed end fraction
space space space space space space equals space fraction numerator left parenthesis 0.5 right parenthesis squared over denominator left parenthesis 3.0 right parenthesis thin space left parenthesis 2.0 right parenthesis cubed end fraction space equals space 0.0104
Given Kc 0.061< QC 0.0104

Since Qc ≠ Kc, reaction is not in equilibrium.
Since Qc < Kc reaction will proceed in the forward direction i.e. towards the formation of ammonia.