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Equilibrium

Question
CBSEENCH11006387

The reaction,
CO left parenthesis straight g right parenthesis space plus space 3 straight H subscript 2 space rightwards harpoon over leftwards harpoon space space space CH subscript 4 left parenthesis straight g right parenthesis space plus space straight H subscript 2 straight O left parenthesis straight g right parenthesis is at equilibrium at 1300K in a 1 L flask. It also contains 0.30 mol of CO, 0.10 mol of H2 and 0.02 mol of H2O and an unknown amount of CH4 in the flask. Determine the concentration of CH4 in the mixture. The equilibrium constant, Kc, for the reaction at the given temperature is 3.90.

Solution
The given reversible reaction is
CO left parenthesis straight g right parenthesis space plus space 3 straight H subscript 2 left parenthesis straight g right parenthesis space space space rightwards harpoon over leftwards harpoon space space CH subscript 4 left parenthesis straight g right parenthesis plus space straight H subscript 2 straight O left parenthesis straight g right parenthesis
Applying the law of chemical equilibrium
 space straight K subscript straight c space equals space fraction numerator open square brackets CH subscript 4 left parenthesis straight g right parenthesis close square brackets space open square brackets straight H subscript 2 straight O left parenthesis straight g right parenthesis close square brackets over denominator open square brackets CO left parenthesis straight g right parenthesis space open square brackets straight H subscript 2 left parenthesis straight g right parenthesis close square brackets close square brackets end fraction space... left parenthesis 1 right parenthesis
Putting the values in expression (1), we have,
                 3.90 space equals space fraction numerator open square brackets CH subscript 4 left parenthesis straight g right parenthesis close square brackets space open square brackets 0.02 close square brackets over denominator left parenthesis 0.30 right parenthesis thin space left parenthesis 0.10 right parenthesis cubed end fraction
 [Molar conc  = No. of moles because volume of flask = 1L]
or space space open square brackets CH subscript 4 left parenthesis straight g right parenthesis close square brackets space equals space fraction numerator 3.90 space cross times space 0.30 space cross times space left parenthesis 0.10 right parenthesis cubed over denominator 0.02 end fraction
space space space space space space space space space space space space space space space space space space space equals space 0.0585 space straight M
space space space space space space space space space space space space space space space space space space space space equals space 5.85 space cross times space 10 to the power of negative 2 end exponent straight M