Silver oxide $$\left( {A{g_2}O} \right)$$  decomposes at temperature $${300^ \circ }C$$  yielding metallic silver and oxygen gas. A $$1.60\,g$$  sample of impure silver oxide yields $$0.104\,g$$  of oxygen gas. What is the per cent by mass of the silver oxide in the sample?

Solution :
$$\eqalign{ & {\text{Let }}mass{\text{ of}}\,A{g_2}O = x\,g \cr & A{g_2}O \to 2Ag + \frac{1}{2}{O_2} \cr & xg \cr & 232\,g\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{1}{2} \times 32 = 16\,g\,{O_2} \cr & \frac{{16}}{{232}} \times x = 0.104 \Rightarrow x = 1.508\,g \cr & \% \,\,{\text{of}}\,A{g_2}O = \frac{{1.508}}{{1.6}} \times 100 = 94.25\% \cr} $$