X gm of metal gave Y gm of its oxide, so equivalent mass of metal is :

Options

A. `((X)/(Y-X))xx8`
B. `((Y-X)/(X))xx8`
C. `((Y+X)/(X))xx8`
D. `(X)/(Y)xx8`

Answer

To find the equivalent mass of the metal given that X grams of metal produce Y grams of its oxide, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Reaction**:
The metal (M) reacts with oxygen (O) to form its oxide (MO). The reaction can be represented as:
\[ M + O \rightarrow MO \]

2. **Define the Masses**:
- Let the mass of the metal be \( X \) grams.
- Let the mass of the oxide formed be \( Y \) grams.

3. **Calculate the Mass of Oxygen**:
The mass of oxygen in the oxide can be calculated as:
\[ \text{Mass of Oxygen} = Y - X \]
This is because the total mass of the oxide (Y) is the sum of the mass of the metal (X) and the mass of oxygen.

4. **Determine the Equivalent Mass of Metal**:
The equivalent mass of the metal can be calculated using the formula:
\[ \text{Equivalent mass of metal} = \frac{X}{\text{moles of oxygen reacted}} \]
The number of moles of oxygen reacted can be calculated using the molar mass of oxygen, which is 16 g/mol. Thus, the moles of oxygen in \( Y - X \) grams is:
\[ \text{Moles of Oxygen} = \frac{Y - X}{16} \]

5. **Substituting into the Equivalent Mass Formula**:
Now substituting the moles of oxygen into the equivalent mass formula:
\[ \text{Equivalent mass of metal} = \frac{X}{\frac{Y - X}{16}} = \frac{X \times 16}{Y - X} \]

### Final Answer:
The equivalent mass of the metal is given by:
\[ \text{Equivalent mass of metal} = \frac{16X}{Y - X} \]