A metal Y forms a sulphate which is isomorphous with ${\mathrm{MgSO}}_4. 7{\mathrm{H}}_2\mathrm{O}$. Find the at. wt. of the metal if $0.8912 \mathrm{g}$of the metal displaces $2.97 \mathrm{g}$ of silver (at. wt.,$\mathrm{Ag}= 107.9$). 

One metal displaces another metal (silver), this implies that number of equivalents of both metals are equal.

$\begin{array}{ccc}\mathrm{No}. \mathrm{of} \mathrm{equivalents} \mathrm{of} \mathrm{metal} \left(\mathrm{M}\right)& =& \mathrm{No}. \mathrm{of} \mathrm{equivalents} \mathrm{of} \mathrm{silver}\\ \frac{\mathrm{Weight}}{\mathrm{Equivalent} \mathrm{weight} \mathrm{of} \mathrm{M}}& =& \frac{\mathrm{Weight}}{\mathrm{Equivalent} \mathrm{weight} \mathrm{of} \mathrm{Ag}}\\ \frac{0.8912}{\mathrm{Equivalent} \mathrm{weight} \mathrm{of} \mathrm{M}}& =& \frac{2.97}{108}\\ \mathrm{Equivalent} \mathrm{weight} \mathrm{of} \mathrm{M}& =& 32.4\end{array}$

Sulphate of metal $\mathrm{Y}$ is isomorphous with  ${\mathrm{MgSO}}_4\cdot 7{\mathrm{H}}_2\mathrm{O}$, this indicates that both has the same unit parameters. Valency factor of ${\mathrm{MgSO}}_4·7{\mathrm{H}}_2\mathrm{O}$ is 2 and because of being isomorphous, metal Y also has the same valency factor, 2.

$\begin{array}{ccc}\mathrm{Atomic} \mathrm{weight} \mathrm{of} \mathrm{M}& =& \mathrm{Equivalent} \mathrm{weight} \mathrm{of} \mathrm{M}\times \mathrm{Valency} \mathrm{factor}\\ & =& 32.4\times 2\\ & =& 64.8\end{array}$