Equilibrium

Equilibrium

Question

The equilibrium constant at 298 K for a reaction A+B ⇌ C+D is 100. If the initial concentration of all the four species were 1 M each, then equilibrium concentration of D (in mol L−1 ) will be:

  • 0.818

  • 1.818

  • 1.182

  • 0.182

Answer

B.

1.818

space space space space space space space space space space space space space space space space space space space space space straight A space space space space space space plus space space space straight B space rightwards harpoon over leftwards harpoon for space space space space space space space space space of space straight C space space plus space space space space space straight D
subscript Intially space at space straight t space equals 0 space space space space space space space space 1 space space space space space space space space space space space space space space space space 1 space space space space space space space space space space space space space space space space space space space 1 space space space space space space space space space space space space space space space 1 end subscript
to the power of at space equilibrium space space space space space space space 1 minus straight x space space space space space space space space space space 1 minus straight x space space space space space space space space space space space space space space space 1 plus straight x space space space space space space space space space space space 1 plus straight x end exponent
straight K subscript eq space equals space fraction numerator left square bracket CD right square bracket over denominator left square bracket straight A right square bracket left square bracket straight B right square bracket end fraction space equals fraction numerator left parenthesis 1 plus straight x right parenthesis left parenthesis 1 plus straight x right parenthesis over denominator left parenthesis 1 minus straight x right parenthesis left parenthesis 1 minus straight x right parenthesis end fraction space equals space fraction numerator left parenthesis 1 plus straight x right parenthesis squared over denominator left parenthesis 1 minus straight x right parenthesis squared end fraction
Or space 100 space equals space open parentheses fraction numerator 1 plus straight x over denominator 1 minus straight x end fraction close parentheses squared
10 space equals space fraction numerator 1 plus straight x over denominator 1 minus straight x end fraction
or space 10 minus 10 straight x space equals space 1 space plus space straight x
10 minus 1 space space equals space straight x space plus space 10 straight x
9 space equals space 11 space straight x
straight x space equals space 9 over 11 space equals space 0.818 space
left square bracket straight D right square bracket space equals space 1 space plus straight x space equals space 1 space plus space 0.818 space equals space 1.818 space space space

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