Cu2S and Ag2S are isomorphous compounds. The percentage of sulphur in Cu2S is 20.14 and that in Ag2S is 12.94. The atomic weight of copper is 63.57. Calculate the atomic weight of silver.

Question

$Cu _{2} S$ and $Ag _{2} S$ are isomorphous compounds. The percentage of sulphur in $Cu _{2} S$ is $20 \cdot 14$ and that in $Ag _{2} S$ is 12.94. The atomic weight of copper is 63.57. Calculate the atomic weight of silver.

Answer 1

SOLUTION : First, calculate the weight of each of $Cu$ and $Ag$ combining with fixed weight of sulphur and then apply the formula :

$\frac{\text { at.wt. of } C u}{\text { at. wt. of } A g}=\frac{\text { Wt. of } C u \text { combining with a fixed wt. of } S}{\text { wt. of } A g \text { combining with the same wt. of } S}$

Atomic weight of $Cu$ is given, at. wt. of $Ag$ can be worked out.

Given,

Now, $20 \cdot 14 g$ of sulphur combines with $79 \cdot 86 g$ of $Cu$

$\therefore 12.94 g$ of sulphur combines with $\frac{79 \cdot 86 \times 12 \cdot 94}{20 \cdot 14} g =51.31 g$ of $Cu$.

Give that $12.94 g$ of $S$ combines with $87 \cdot 06 g$ of $Ag$.

Here, the fixed weight of sulpliur $=12.94 g$

By formula

$\frac{51 \cdot 31}{87 \cdot 06}=\frac{63.57}{\text { at. wt. of } Ag }$

$\therefore$ Atomic weight of $A g=\frac{87 \cdot 06 \times 63 \cdot 57}{51 \cdot 31}=107 \cdot 86$.