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Equilibrium

Question
CBSEENCH11006379

What are the units of equilibrium constant (Kc)?

Solution
The units of Kc vary from reaction to reaction.
(i) Kc has no units when there is no change in a number of moles in a reaction.
For space example comma space straight N subscript 2 plus straight O subscript 2 space rightwards harpoon over leftwards harpoon space space 2 NO
straight K subscript straight c space equals space fraction numerator open square brackets NO close square brackets over denominator open square brackets straight N subscript 2 close square brackets space open square brackets straight O subscript 2 close square brackets end fraction space equals space fraction numerator left parenthesis mol space straight L to the power of negative 1 end exponent right parenthesis squared over denominator left parenthesis mol space straight L to the power of negative 1 end exponent right parenthesis space left parenthesis mol space straight L to the power of negative 1 end exponent right parenthesis end fraction
i.e. it is unitless.
(ii) Kc has units when the number of moles in the reaction differs, e.g.
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 2 NH subscript 3 left parenthesis straight g right parenthesis
space straight K subscript straight c space equals space fraction numerator open square brackets NH subscript 3 close square brackets squared over denominator open square brackets straight N subscript 2 close square brackets space open square brackets straight H subscript 2 close square brackets cubed end fraction
space space space space space space space equals fraction numerator left parenthesis mol space straight L to the power of negative 1 end exponent right parenthesis squared over denominator left parenthesis mol space straight L to the power of negative 1 end exponent right parenthesis thin space left parenthesis mol space straight L to the power of negative 1 end exponent right parenthesis cubed end fraction
space space space space space space space space equals fraction numerator 1 over denominator left parenthesis mol space straight L to the power of negative 1 end exponent right parenthesis squared end fraction space equals space mol to the power of negative 2 end exponent space straight L squared
Thus, straight K subscript straight c will have the units straight L squared space mol to the power of negative 2 end exponent.