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

Options

A. 58
B. 29
C. 5.8
D. 2.9

Explanation

To find the equivalent mass of the metal from the decomposition of a metallic carbonate, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of metallic carbonate (MCO₃) = 2.0 g
- Mass of metallic oxide (MO) = 1.5 g

2. **Set Up the Relationship:**
- The decomposition of the metallic carbonate can be represented as:
\[ \text{MCO}_3 \rightarrow \text{MO} + \text{CO}_2 \]
- From the equation, we know that the ratio of the weights of the metallic carbonate to the metallic oxide is related to their equivalent weights.

3. **Use the Formula:**
- The ratio of the weights can be expressed as:
\[ \frac{\text{Weight of MCO}_3}{\text{Weight of MO}} = \frac{\text{Equivalent mass of metal}}{\text{Equivalent mass of metal} + \text{Equivalent mass of CO}_3^{2-}} \]
- Let the equivalent mass of the metal be \( x \).

4. **Calculate the Equivalent Mass of CO₃²⁻:**
- The atomic weight of carbon (C) = 12 g/mol
- The atomic weight of oxygen (O) = 16 g/mol
- Therefore, the molecular weight of CO₃ = 12 + (16 × 3) = 60 g/mol
- The valence factor for CO₃²⁻ = 2 (since it has a charge of -2).
- Thus, the equivalent mass of CO₃²⁻:
\[ \text{Equivalent mass of CO}_3^{2-} = \frac{60}{2} = 30 \text{ g/equiv} \]

5. **Calculate the Equivalent Mass of O²⁻:**
- The atomic weight of oxygen (O) = 16 g/mol
- The valence factor for O²⁻ = 2 (since it has a charge of -2).
- Thus, the equivalent mass of O²⁻:
\[ \text{Equivalent mass of O}^{2-} = \frac{16}{2} = 8 \text{ g/equiv} \]

6. **Substitute Values into the Ratio:**
- Now substituting the known values into the ratio:
\[ \frac{2.0}{1.5} = \frac{x + 30}{x + 8} \]

7. **Cross Multiply and Simplify:**
- Cross-multiplying gives:
\[ 2.0(x + 8) = 1.5(x + 30) \]
- Expanding both sides:
\[ 2.0x + 16 = 1.5x + 45 \]

8. **Rearranging the Equation:**
- Rearranging gives:
\[ 2.0x - 1.5x = 45 - 16 \]
\[ 0.5x = 29 \]

9. **Solving for x:**
- Therefore:
\[ x = \frac{29}{0.5} = 58 \text{ g/equiv} \]

10. **Conclusion:**
- The equivalent mass of the metal is **58 g/equiv**.