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 in the metal oxide, we can follow these steps:

### Step 1: Understand the Given Information
We are given:
- Weight of metal oxide = \( x \) g
- Weight of oxygen in the metal oxide = \( y \) g

### Step 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:
\[ \text{Weight of metal} = \text{Weight of metal oxide} - \text{Weight of oxygen} \]
\[ \text{Weight of metal} = x - y \text{ g} \]

### Step 3: Determine the Equivalent Weight of Oxygen
The equivalent weight of oxygen is known to be 8 g. This is because:
\[ \text{Equivalent weight of oxygen} = \frac{\text{Molecular weight of oxygen}}{\text{Valency of oxygen}} = \frac{16}{2} = 8 \text{ g} \]

### Step 4: Set Up the Relation for Equivalent Weights
Using the relation for equivalent weights:
\[ \frac{\text{Equivalent weight of metal}}{\text{Equivalent weight of oxygen}} = \frac{\text{Weight of metal}}{\text{Weight of oxygen}} \]
Substituting the known values:
\[ \frac{E}{8} = \frac{x - y}{y} \]

### Step 5: Solve for the Equivalent Weight of the Metal
Rearranging the equation to solve for \( E \):
\[ E = 8 \times \frac{x - y}{y} \]
Thus, we can express the equivalent weight of the metal as:
\[ E = \frac{8(x - y)}{y} \]

### Conclusion
The equivalent weight of the metal is given by the formula:
\[ E = 8 \times \frac{x - y}{y} \]