Question

Number of moles of $S{O}_4^{2-}$ ion in one mole of the salt is

• A. 2
• B. 4
• C. 3
• D. 1

Answer 1

The correct option is C 3

Let the formula of the hydrated salt be $M_2(S{O}_4{)}_n.m{H}_{2}O$.

Thus the hydrated metal salt contains n sulphate ions and m water molecules.

The equivalent of metal is equal to the equivalent of sulphate ion.

The equivalent of sulphate ions is $\frac{\text{mass of sulphate ions}}{\frac{\text{molar mass of sulphate ions}}{\text{charge on sulphate ions}}}=\frac{43.2}{\frac{96}{2}}$
The equivalent of metal is $\frac{\text{mass of metal}}{\frac{\text{molar mass of metal}}{\text{charge on metal}}}=\frac{8.1}{\frac{a}{n}}$

Here a is the molar mass of metal and is calculated from specific heat of 0.24 cal/g.

Atomic mass $\times$ specific heat $=6.4$

Atomic mass $=\frac{6.4}{specificheat}=\frac{6.4}{0.24}=26.67$

Equivalent of metal $=$ equivalent of $S{O}_4^{2-}$

Thus, $\frac{8.1}{\frac{a}{n}}=\frac{43.2}{\frac{96}{2}}$

The value of n is $n=\frac{43.2\times 2\times a}{96\times 8.1}=\frac{43.2\times 2\times 26.67}{96\times 8.1}=2.96\approx 3.0$.

The molecular formula of the salt is $M_2(S{O}_4{)}_3.m{H}_{2}O$.

Thus, 1 mole of salt contains 3 moles of sulphate ions.