4 g of a metal oxide contains 1.6 g-oxygen, then equivalent mass of the metal is

Options

A. 3.2
B. 24
C. 12
D. 20

Answer

To find the equivalent mass of the metal in the metal oxide, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of metal oxide = 4 g
- Mass of oxygen in the oxide = 1.6 g

2. **Calculate the Mass of the Metal:**
- Mass of metal = Mass of metal oxide - Mass of oxygen
- Mass of metal = 4 g - 1.6 g = 2.4 g

3. **Determine the Equivalent Weight of Oxygen:**
- The equivalent weight of a substance can be calculated using the formula:
\[ \text{Equivalent weight} = \frac{\text{Atomic mass}}{\text{Valency}} \]
- For oxygen:
- Atomic mass of oxygen = 16 g/mol
- Valency of oxygen = 2
- Therefore, the equivalent weight of oxygen =
\[ \frac{16}{2} = 8 \text{ g/equiv} \]

4. **Set Up the Equation Using the Equivalent Weight Concept:**
- According to the equivalent weight relationship:
\[ \frac{\text{Mass of metal}}{\text{Mass of oxygen}} = \frac{\text{Equivalent weight of metal}}{\text{Equivalent weight of oxygen}} \]
- Let the equivalent weight of the metal be \( X \).
- Substituting the known values:
\[ \frac{2.4 \text{ g}}{1.6 \text{ g}} = \frac{X}{8} \]

5. **Cross-Multiply and Solve for \( X \):**
- Cross-multiplying gives:
\[ 2.4 \times 8 = 1.6 \times X \]
\[ 19.2 = 1.6X \]
- Now, divide both sides by 1.6:
\[ X = \frac{19.2}{1.6} = 12 \text{ g/equiv} \]

6. **Conclusion:**
- The equivalent mass of the metal is 12 g/equiv.