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Equilibrium

Question
CBSEENCH11006422

Reaction between N2 and O2 takes place as follows:
               2 straight N subscript 2 left parenthesis straight g right parenthesis space plus space straight O subscript 2 left parenthesis straight g right parenthesis space space space rightwards harpoon over leftwards harpoon space space space 2 straight N subscript 2 straight O left parenthesis straight g right parenthesis
If a mixture of 0.482 mol of N2 and 0.933 mol of O2 is placed in a 10 L reaction vessel and allowed to form N2O at a temperature for which Kc = 2·0 × 10–37, determine the composition of equilibrium mixture.

Solution
The given reversible chemical reaction is
           2N2(g)     +    O2(g)       rightwards harpoon over leftwards harpoon     2N2O(g)
Initial     0.482 mol      0.933 mol
At equi.  4.482 - x        0.933 minus straight x over 2        x
Molar conc. fraction numerator 0.482 minus straight x over denominator 10 end fraction space space fraction numerator 0.933 minus begin display style x over 2 end style over denominator 10 end fraction     straight x over 10
As K = 2·0 × 10–37 is very small, this means that the amount of N2 and O2 reacted (x) is very very small. Hence, at equilibrium, we have
open square brackets straight N subscript 2 close square brackets space equals space 0.482 space mol space straight L to the power of negative 1 end exponent
open square brackets straight O subscript 2 close square brackets space equals space 0.0933 space mol space straight L to the power of negative 1 end exponent
open square brackets straight N subscript 2 straight O close square brackets space equals space 0.1 space straight x
According to the law of chemical equilibrium,
    straight K subscript straight c space equals space fraction numerator open square brackets straight N subscript 2 straight O 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 squared space open square brackets straight O subscript 2 left parenthesis straight g right parenthesis close square brackets end fraction space... left parenthesis 1 right parenthesis
Putting the values in expression (1), we have,
             straight K subscript straight c space equals space fraction numerator left parenthesis 0.1 straight x right parenthesis squared over denominator left parenthesis 0.0482 right parenthesis squared left parenthesis 0.0933 right parenthesis end fraction
space space space space space space equals space 2.0 space cross times space 10 to the power of negative 37 end exponent space space space space space left square bracket Given right square bracket
On solving straight x space equals space 6.6 space cross times 10 to the power of negative 20 end exponent
open square brackets straight N subscript 2 straight O close square brackets space equals space 0.1 space straight x space equals space 0.1 space cross times space 6.6 space cross times space 10 to the power of negative 20 end exponent
space space space space space space space space space space equals space 6.6 space cross times space 10 to the power of negative 21 end exponent space mol space straight L to the power of negative 1 end exponent