Question
The number of moles of $$KMn{O_4}$$ that will be needed to react with one mole of sulphite ion in acidic solution is
A.
$$\frac{4}{5}$$
B.
$$\frac{2}{5}$$
C.
$$1$$
D.
$$\frac{3}{5}$$
Answer :
$$\frac{2}{5}$$
Solution :
$$\eqalign{
& 2KMn{O_4}\,\, + \,\,3{H_2}S{O_4}\,\,\, \to {K_2}S{O_4} + 2MnS{O_4} + 3{H_2}O + 5\left[ O \right] \cr
& \left[ {MnO_4^ - + \,8{H^ + } + \,5{e^ - }\,\,\, \to M{n^{2 + }} + 4{H_2}O} \right] \times 2\left[ {SO_3^{2 - } + {H_2}O \to SO_4^{2 - } + 2{H^ + } + 2{e^ - }} \right] \times 5 \cr
& \overline {2MnO_4^ - + 6{H^ + } + 5SO_3^{2 - } \to 2M{n^{2 + }} + 5SO_4^{2 - } + 3{H_2}O\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \cr} $$
$$5\,moles$$ of sulphite ions react with $$ = 2\,moles$$ of $$MnO_4^ - $$
So, $$1{\text{ }}mole$$ of sulphite ions react with $$ = \frac{2}{5}moles$$ of $$MnO_4^ - .$$