A metal `M` of equivalent mass `E` forms an oxide of molecular formula `M_(x)O_(y)` The atomic mass of the metal is given by the correct equation .

Options

A. `2E(y//x)`
B. `yxE`
C. `E//y`
D. `y//E`

Explanation

To find the atomic mass of the metal \( M \) given its equivalent mass \( E \) and the molecular formula of its oxide \( M_xO_y \), we can follow these steps:

### Step 1: Understand the molecular formula
The molecular formula \( M_xO_y \) indicates that \( x \) atoms of metal \( M \) combine with \( y \) atoms of oxygen.

### Step 2: Define the atomic mass
Let the atomic mass of metal \( M \) be \( A \) grams.

### Step 3: Calculate the mass of metal and oxygen
The total mass of the metal in the compound is:
\[ \text{Mass of metal} = x \times A \text{ grams} \]
The mass of oxygen in the compound can be calculated as follows:
\[ \text{Mass of oxygen} = y \times 16 \text{ grams} \quad (\text{since the atomic mass of oxygen is 16 g/mol}) \]

### Step 4: Relate the equivalent mass to the atomic mass
The equivalent mass of a substance is defined as the mass of the substance that combines with or displaces 1 mole of hydrogen or 8 grams of oxygen. For the metal oxide \( M_xO_y \), we can equate the equivalent mass of the metal to the mass of metal that combines with a certain mass of oxygen.

The equivalent mass of oxygen in terms of the number of moles is:
\[ \text{Equivalent mass of oxygen} = \frac{16}{y} \text{ grams} \]
Thus, the equivalent mass of the metal can be expressed as:
\[ E = \frac{x \times A}{y} \]

### Step 5: Solve for the atomic mass \( A \)
Rearranging the equation for equivalent mass, we can express the atomic mass \( A \) in terms of the equivalent mass \( E \):
\[ A = \frac{E \times y}{x} \]

### Step 6: Finalize the equation
To express \( A \) in a more useful form, we can multiply both sides by 2:
\[ A = \frac{2E \times y}{x} \]

### Conclusion
Thus, the atomic mass of the metal \( M \) is given by:
\[ A = \frac{2Ey}{x} \]

The correct option from the provided choices is **Option A: \( \frac{2Ey}{x} \)**.

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