`a_(1) `gm of the metal gave `a_(2) gm` of its oxide. Hence equivalent weight of the metal -

Options

A. `( a_(1))/( a_(2) - a_(1)) xx 8`
B. `( a_(2) -a_(1))/( a_(1)) xx 8 `
C. `((a_(2) + a_(1))/( a_(1)) xx8)`
D. `(a_(1))/( a_(2)) xx 8`

Answer

To find the equivalent weight of the metal based on the given weights of the metal and its oxide, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Let the weight of the metal be \( a_1 \) grams.
- Let the weight of the oxide be \( a_2 \) grams.

2. **Calculate the Weight of Oxygen**:
- The weight of oxygen in the oxide can be calculated as:
\[ \text{Weight of Oxygen} = a_2 - a_1 \]

3. **Determine the Equivalent Weight of Oxygen**:
- The atomic mass of oxygen is 16 g/mol, and its valency in oxides (as O^2-) is 2.
- Therefore, the equivalent weight of oxygen can be calculated as:
\[ \text{Equivalent Weight of Oxygen} = \frac{\text{Atomic Mass of Oxygen}}{\text{Valency}} = \frac{16}{2} = 8 \text{ grams} \]

4. **Calculate the Equivalent Weight of the Metal**:
- From the previous calculations, we know that \( a_1 \) grams of metal reacts with \( a_2 - a_1 \) grams of oxygen.
- The number of equivalents of oxygen reacting can be calculated as:
\[ \text{Equivalents of Oxygen} = \frac{a_2 - a_1}{8} \]
- Since the equivalents of metal will be equal to the equivalents of oxygen, we can set up the equation for the metal:
\[ \text{Equivalents of Metal} = \frac{a_1}{\text{Equivalent Weight of Metal}} = \frac{a_2 - a_1}{8} \]
- Rearranging gives:
\[ \text{Equivalent Weight of Metal} = \frac{a_1 \times 8}{a_2 - a_1} \]

5. **Final Expression**:
- Thus, the equivalent weight of the metal is given by:
\[ \text{Equivalent Weight of Metal} = \frac{8 a_1}{a_2 - a_1} \]