If the weight of metal oxide is x g containing y g of oxygen, the equivalent weight of metal will be

Options

A. `E= (8x)/(y)`
B. `E= (8(y-x))/(x)`
C. `E= (y)/(8)`
D. `E= (8(x-y))/(y)`

Answer

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

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Weight of metal oxide = \( x \) g
- Weight of oxygen in the metal oxide = \( y \) g

2. **Calculate the Weight of the Metal:**
- The weight of the metal can be calculated by subtracting the weight of oxygen from the weight of the metal oxide.
\[ \text{Weight of metal} = x - y \text{ g} \]

3. **Determine the Equivalent Weight of Oxygen:**
- The equivalent weight of oxygen can be calculated using its atomic weight and valency. The atomic weight of oxygen is 16 g/mol and its valency is 2.
\[ \text{Equivalent weight of oxygen} = \frac{\text{Atomic weight}}{\text{Valency}} = \frac{16}{2} = 8 \text{ g/equiv} \]

4. **Relate the Weight of Metal to the Weight of Oxygen:**
- We know that for \( y \) g of oxygen, the weight of the metal is \( x - y \) g. We can express the equivalent weight of the metal in terms of the weight of oxygen.
- For 1 g of oxygen, the weight of the metal can be calculated as:
\[ \text{Weight of metal for 1 g of oxygen} = \frac{x - y}{y} \text{ g} \]

5. **Calculate the Equivalent Weight of the Metal:**
- Now, to find the equivalent weight of the metal, we multiply the weight of the metal for 1 g of oxygen by the equivalent weight of oxygen (which is 8 g/equiv):
\[ \text{Equivalent weight of metal} = 8 \times \frac{x - y}{y} \text{ g} \]

6. **Final Expression:**
- Therefore, the equivalent weight of the metal is given by:
\[ \text{Equivalent weight of metal} = \frac{8(x - y)}{y} \text{ g} \]