3 g of an oxide of a metal is converted to chloride completely and ir yielded 5 g of chloride. The equivalent weight of the metal is

Options

A. 33.25
B. 3.325
C. 12
D. 20

Answer

To find the equivalent weight of the metal from the given data, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data**:
- Weight of the metal oxide (WO) = 3 g
- Weight of the metal chloride (WC) = 5 g

2. **Write the Formula for Equivalent Weight**:
The equivalent weight of a metal can be calculated using the formula:
\[ \text{Equivalent weight of metal} (E) = \frac{\text{Weight of metal oxide}}{\text{Weight of metal chloride}} \]

3. **Express the Weights in Terms of the Metal and Its Oxide**:
Let the equivalent weight of the metal be \( E \).
The molecular weight of the oxide can be expressed as:
\[ \text{Weight of metal oxide} = E + 8 \quad \text{(where 8 is the equivalent weight of oxygen)} \]
The molecular weight of the chloride can be expressed as:
\[ \text{Weight of metal chloride} = E + 35.5 \quad \text{(where 35.5 is the equivalent weight of chlorine)} \]

4. **Set Up the Equation**:
From the information given:
\[ 3 = E + 8 \quad \text{(for the oxide)} \]
\[ 5 = E + 35.5 \quad \text{(for the chloride)} \]

5. **Rearranging the Equations**:
From the first equation:
\[ E = 3 - 8 = -5 \quad \text{(not valid, check the setup)} \]
From the second equation:
\[ E = 5 - 35.5 = -30.5 \quad \text{(also not valid)} \]

6. **Correct the Approach**:
We need to relate the weights correctly:
\[ 3E + 106.5 = 5E + 40 \]

7. **Solve for E**:
Rearranging gives:
\[ 3E + 106.5 = 5E + 40 \]
\[ 2E = 106.5 - 40 \]
\[ 2E = 66.5 \]
\[ E = \frac{66.5}{2} = 33.25 \]

8. **Final Result**:
The equivalent weight of the metal is \( 33.25 \, \text{g/equiv} \).