On electrolysis of water, a total of 1mole of gases is evolved. The...

$∵$ Only one mole of total gases are evolved and ${H}_{2}O$ decomposes as

${H}_{2}O\overset{decomposition}{→}{H}_{2} + \dfrac{1}{2}{O}_{2}$

i.e. total moles $= 1 + \dfrac{1}{2} = \dfrac{3}{2}$ moles by one mole of ${H}_{2}O$

Now,

$∵ \dfrac{3}{2}$ moles of gases are evolved by $= 1mole$ of ${H}_{2}O$

$∴ 1mole$ of gases are evolved by $= \dfrac{1}{3 / 2} = \dfrac{2}{3}$

Hence, $1mole$ of total gases are evolved by $\dfrac{2}{3}mole$ of ${H}_{2}O$.