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5 moles of $$\text{AB}_2$$ weigh $$125 \times 10^{-3}\text{ kg}$$ and 10 moles of $$\text{A}_2\text{B}_2$$ weigh $$300 \times 10^{-3}\text{ kg}$$. The molar mass of A ($$M_A$$) and molar mass of B ($$M_B$$) in $$\text{kg mol}^{-1}$$ are
Molar mass of $$\text{AB}_2 = \frac{125}{5} = 25\text{ g mol}^{-1}$$, so $$M_A + 2M_B = 25$$. Molar mass of $$\text{A}_2\text{B}_2 = \frac{300}{10} = 30\text{ g mol}^{-1}$$, so $$M_A + M_B = 15$$. Subtracting gives $$M_B = 10$$ and $$M_A = 5\text{ g mol}^{-1}$$, i.e. $$M_A = 5 \times 10^{-3}$$ and $$M_B = 10 \times 10^{-3}\text{ kg mol}^{-1}$$.
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