The composition of a sample of cuprous sulphide is found to be $C{u}_{1.92}{S}_{1.00}$ due to metal deficient defect. The molar ratio of $C{u}^{+2}$ and $C{u}^{+}$ ions in the crystal is x and y. Find the value of $\frac{\text{x }+\text{ y}}{6}$ is___

Molecular formula of cuprous oxide $C{u}_{2}S$

one mole of $C{u}^{+2}$ replaces two moles of $C{u}^{+}$

Now moles of $C{u}^{+2}$ present in the sample = 2 – 1.92 = 0.08

$\begin{array}{l}\therefore \%ofC{u}^{+2}=\frac{0.08}{1.92}\times 100=4.17\%\\ \%ofC{u}^{+}=100-4.17=95.83\%\\ RatioofC{u}^{+2}andC{u}^{+}=\frac{4.17}{95.83}=\frac{1}{23}\\ \therefore \frac{\text{x }+\text{ y}}{3}\\ =8\end{array}$