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Question

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


A
58
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B
29
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C
5.8
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D
2.9
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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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