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

Options

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

Answer

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

### Step 1: Understand the relationship between metal, its oxide, and oxygen.
The metal reacts with oxygen to form its oxide. Therefore, if we have X grams of metal oxide, we can express the mass of the metal and the mass of oxygen in the oxide.

### Step 2: Calculate the mass of the metal.
The mass of the metal can be calculated as:
\[ \text{Mass of metal} = \text{Mass of metal oxide} - \text{Mass of oxygen} \]
Thus, we have:
\[ \text{Mass of metal} = X - Y \text{ grams} \]

### Step 3: Use the equivalent weight relationship.
According to the oxide method, the relationship between the weights can be expressed as:
\[ \frac{\text{Weight of metal}}{\text{Equivalent weight of metal}} = \frac{\text{Weight of oxygen}}{\text{Equivalent weight of oxygen}} \]

### Step 4: Rearrange the equation to find the equivalent weight of the metal.
From the above equation, we can rearrange it to find the equivalent weight of the metal:
\[ \text{Equivalent weight of metal} = \frac{\text{Weight of metal} \times \text{Equivalent weight of oxygen}}{\text{Weight of oxygen}} \]

### Step 5: Substitute the known values.
We know:
- Weight of metal = \( X - Y \) grams
- Equivalent weight of oxygen = 8 grams (since the equivalent weight of oxygen is 8 g/mol)
- Weight of oxygen = Y grams

Substituting these values into the equation gives:
\[ \text{Equivalent weight of metal} = \frac{(X - Y) \times 8}{Y} \]

### Step 6: Final expression for equivalent mass of the metal.
Thus, the equivalent mass of the metal can be expressed as:
\[ \text{Equivalent mass of metal} = \frac{8(X - Y)}{Y} \]

### Conclusion
The equivalent mass of the metal is given by the formula:
\[ \text{Equivalent mass of metal} = \frac{8(X - Y)}{Y} \]

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