At a particular temperature, for the reaction, `aA+bB hArr dC+cD`, equilibrium constant is `K`. Find out the equilibrium constants for the following reactions at the same temperature.
(1) `maA+mbBhArr mdC+mcD`
(2) `(1)/(m)aA+(1)/(m)bB hArr (1)/(m) dC+(1)/(m)cD`

Explanation

For the reaction, `aA+bBhArr dC+cD` the equilibrium constant, `K=([C]^(d)xx[D]^(c))/([D]^(a)xx[B]^(b))`
Now, (1) for the reaction, `maA+bbBhArr mdC+mcD`
equilibrium constant, `K_(1)=([C]^(md)xx[D]^(mc))/([A]^(ma)xx[B]^(mb))`
`={([C]^(d)xx[D]^(c))/([A]^(a)xx[B]^(b))}^(m)=K^(m)`
(2) For the reaction, `(1)/(m)aA+(1)/(m)bB hArr (1)/(m)dC+(1)/(m)cD`, the equilibrium constant, `K_(2)=([C]^(d//m)xx[D]^(c//m))/([A]^(a//m)xx[B]^(b//m))`
`={([C]^(d)xx[D]^(c))/([A]^(a)xx[B]^(b))}^(1//m)=(K)^(1//m)`