Suppose two elements $A$ and $B$ chemically combine to form two distinct compounds $\mathrm{AB}_2$ a

Question

Suppose two elements $A$ and $B$ chemically combine to form two distinct compounds $\mathrm{AB}_2$ and $\mathrm{A}_2\mathrm{B}_3$. If 0.2 mole of $\mathrm{AB}_2$ weighs 16 g and 0.1 mole of $\mathrm{A}_2\mathrm{B}_3$ weighs 15.4 g, the atomic weights of $A$ and $B$ are respectively

Professor PC Thomas Classes · Answer

(a) : Let atomic weights of $A$ and $B$ be $a$ and $b$. For $\mathrm{AB}_2$: Molar mass = $16 / 0.2 = 80 \mathrm{~g/mol}$, so $a + 2b = 80$. For $\mathrm{A}_2\mathrm{B}_3$: Molar mass = $15.4 / 0.1 = 154 \mathrm{~g/mol}$, so $2a + 3b = 154$. Multiplying the first equation by 2 yields $2a + 4b = 160$. Subtracting the second equation ($2a + 3b = 154$) from this gives $b = 6$. Substituting $b=6$ into the first equation yields $a + 12 = 80$, solving to $a = 68$.