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Equilibrium

Question
CBSEENCH11006421

One mole of straight H subscript 2 straight O and one mole of CO are taken in a 10-litre vessel and heated to 725K. At equilibrium, 40% of water (by mass) reacts with carbon monoxide according to the equation

straight H subscript 2 straight O left parenthesis straight g right parenthesis space plus space CO left parenthesis straight g right parenthesis space space rightwards harpoon over leftwards harpoon space space space space straight H subscript 2 left parenthesis straight g right parenthesis space plus space CO subscript 2 left parenthesis straight g right parenthesis.

Calculate the equilibrium constant for the reaction. 

Solution

40% by mass of water = 40% by mole of water
40% of one mole of water = fraction numerator 1 cross times 40 over denominator 100 end fraction equals 0.4 space mole
              straight H subscript 2 straight O left parenthesis straight g right parenthesis space plus space CO left parenthesis straight g right parenthesis space space rightwards harpoon over leftwards harpoon space space space straight H subscript 2 left parenthesis straight g right parenthesis space plus space CO subscript 2 left parenthesis straight g right parenthesis
Initial mole    1          1                 0           0
Final mole   1-0.4       1-0.4           0.4         0.4
               = 0.6         = 0.6
According to the law of chemical equilibrium,
           
  straight K subscript straight c space equals space fraction numerator open square brackets straight H subscript 2 left parenthesis straight g right parenthesis close square brackets space open square brackets CO subscript 2 left parenthesis straight g right parenthesis close square brackets over denominator open square brackets straight H subscript 2 straight O left parenthesis straight g right parenthesis close square brackets space open square brackets CO left parenthesis straight g right parenthesis close square brackets end fraction
Substituting the values, we have,
 
  straight K subscript straight c space equals space fraction numerator begin display style fraction numerator 0.4 over denominator 10 end fraction end style cross times begin display style fraction numerator 0.4 over denominator 10 end fraction end style over denominator begin display style fraction numerator 0.6 over denominator 10 end fraction end style cross times begin display style fraction numerator 0.6 over denominator 10 end fraction end style end fraction space equals space 0.44