The oxide of a metal has `32%` oxygen. Its equivalent weight would be

Options

A. (a)`34`
B. (b)`32`
C. (c )`17`
D. (d)`8`

Explanation

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

### Step 1: Determine the mass of the metal oxide
Assume the mass of the metal oxide is 100 grams. This assumption simplifies the calculations.

### Step 2: Calculate the mass of oxygen in the metal oxide
Given that the metal oxide contains 32% oxygen, we can calculate the mass of oxygen:
\[ \text{Mass of Oxygen} = 32\% \text{ of } 100 \text{ g} = 32 \text{ g} \]

### Step 3: Calculate the mass of the metal in the metal oxide
The mass of the metal in the oxide can be found by subtracting the mass of oxygen from the total mass of the metal oxide:
\[ \text{Mass of Metal} = \text{Total Mass of Metal Oxide} - \text{Mass of Oxygen} = 100 \text{ g} - 32 \text{ g} = 68 \text{ g} \]

### Step 4: Calculate the equivalent weight of oxygen
The equivalent weight of an element is calculated using the formula:
\[ \text{Equivalent Weight} = \frac{\text{Molar Mass}}{\text{Valency}} \]
For oxygen, the molar mass is 16 g/mol and the valency is typically 2 (as it forms O²⁻ ions). Thus, the equivalent weight of oxygen is:
\[ \text{Equivalent Weight of Oxygen} = \frac{16}{2} = 8 \text{ g/equiv} \]

### Step 5: Calculate the equivalent weight of the metal
Using the formula for equivalent weight of the metal in the oxide:
\[ \text{Equivalent Weight of Metal} = \frac{\text{Mass of Metal}}{\text{Mass of Oxygen}} \times \text{Equivalent Weight of Oxygen} \]
Substituting the values we have:
\[ \text{Equivalent Weight of Metal} = \frac{68 \text{ g}}{32 \text{ g}} \times 8 \text{ g/equiv} \]

### Step 6: Perform the calculation
Calculating the above expression:
\[ \text{Equivalent Weight of Metal} = \frac{68}{32} \times 8 = 2.125 \times 8 = 17 \text{ g/equiv} \]

### Conclusion
Thus, the equivalent weight of the metal is **17 g/equiv**.

---