Question

The equilibrium,

$p-$xyloquinone $+$ methylene white $\to p-$xylohydroquinone $+$ methylene blue, may be studied conveniently by observing the difference in color of methylene white and methylene blue.

One millimole of methylene blue was added to $1$ litre of solution that was $0.24M$ in $p-$xylohydroquinone and $0.012M$ in $p-$xyloquinone.

It was then found that $4\%$ of the added methylene blue was reduced to methylene white. What is the equilibrium constant for the above reaction? The equation is balanced with one mole each of $4$ substances.

Answer 1

The initial number of moles, change and the equilibrium number of moles are as given below.

	p-xyloquinone	methylene white	p-xylohydroquinone	methylene blue
Initial moles	0.012	0	0.24	0.001
Equilibrium moles	$0.012+4\times {10}^{-5}=0.01204$	$4\times {10}^{-5}$	$0.24-4\times {10}^{-5}=0.01204$	$0.001-4\times {10}^{-5}=9.6\times {10}^{-4}$

The expression for the equilibrium constant is $K=\frac{[p-xylohydroquinone]\left[methyleneblue\right]}{[p-xyloquinone]\left[methylenewhite\right]}$
Substitute values in the above expression.
$K=\frac{0.23996\times 9.6\times {10}^{-4}}{0.01204\times 4\times {10}^{-5}}=478$
Hence, the value of the equilibrium constant is 478.