  Question

$$2.0g$$ of a metallic carbonate on decomposition gave $$1.5g.$$ of metallic oxide. The equivalent mass of metal is:

A
58  B
29  C
5.8  D
2.9  Solution

The correct option is A $$58$$Weight of metallic carbonate $$= 2.0 g$$Weight of metallic oxide $$= 1.5 g$$Equivalent weight $$= \cfrac{\text{Weight}}{\text{Valence factor}}$$As the valence factor of both, carbonate and oxide, is 2.$$\therefore$$ Equivalent weight of carbonate $$= \cfrac{60}{2} = 30$$Equivalent weight of oxide $$= \cfrac{16}{2} = 8$$Gram equivalent of metallic carbonate $$= \cfrac{\text{Given weight of carbonate}}{{E}_{metal} + {E}_{{C{O}_{3}}^{-2}}}$$Gram equivalent of metallic oxide $$= \cfrac{\text{Given weight of oxide}}{{E}_{metal} + {E}_{{O}^{-2}}}$$Let the equivalent weight of metal be x.Gram equivalent of metallic carbonate = Gram equivalent of metallic oxide $$\cfrac{\text{Given weight of carbonate}}{{E}_{metal} + {E}_{{C{O}_{3}}^{-2}}} = \cfrac{\text{Given weight of oxide}}{{E}_{metal} + {E}_{{O}^{-2}}}$$$$\Rightarrow \; \cfrac{2}{x + 30} = \cfrac{1.5}{x + 8}$$$$\Rightarrow \; 2 \left( x + 8 \right) = 1.5 \left( x + 30 \right)$$$$\Rightarrow \; 2x + 16 = 1.5x + 45$$$$\Rightarrow \; 0.5x = 45 - 16$$$$\Rightarrow \; x = 58$$Hence, the equivalent mass of metal is 58.Chemistry

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