Equivalent mass of a metal M is 2.5 times that of oxygen. The minimum molecular mass of its oxide is

Options

A. 28
B. 42
C. 56
D. 112

Explanation

To solve the question regarding the minimum molecular mass of the oxide of a metal \( M \) whose equivalent mass is 2.5 times that of oxygen, we can follow these steps:

### Step 1: Determine the Equivalent Mass of Oxygen
The equivalent mass of an element can be calculated using the formula:
\[ \text{Equivalent mass} = \frac{\text{Molecular mass}}{\text{Valency}} \]
For oxygen:
- Molecular mass of oxygen (O) = 16 g/mol
- Valency of oxygen = 2 (since it can accept 2 electrons)

Using the formula:
\[ \text{Equivalent mass of O} = \frac{16}{2} = 8 \text{ g/equiv} \]

### Step 2: Calculate the Equivalent Mass of Metal \( M \)
According to the problem, the equivalent mass of metal \( M \) is 2.5 times that of oxygen:
\[ \text{Equivalent mass of M} = 2.5 \times \text{Equivalent mass of O} = 2.5 \times 8 = 20 \text{ g/equiv} \]

### Step 3: Determine the Valency of Metal \( M \)
To find the minimum molecular mass of the oxide, we need to determine the valency of metal \( M \). The equivalent mass of a metal is also defined as:
\[ \text{Equivalent mass} = \frac{\text{Molecular mass}}{\text{Valency}} \]
Let the molecular mass of metal \( M \) be \( M_m \). Then:
\[ 20 = \frac{M_m}{\text{Valency of M}} \]

### Step 4: Assume the Valency of Metal \( M \)
For the simplest oxide formation, we can assume that metal \( M \) has a valency of 2 (similar to oxygen). This is a common scenario for many metals. Therefore:
\[ 20 = \frac{M_m}{2} \]
From this, we can calculate the molecular mass of metal \( M \):
\[ M_m = 20 \times 2 = 40 \text{ g/mol} \]

### Step 5: Calculate the Minimum Molecular Mass of the Oxide \( M_2O \)
The molecular mass of the oxide \( M_2O \) can be calculated as follows:
\[ \text{Molecular mass of } M_2O = 2 \times M_m + \text{Molecular mass of O} \]
Substituting the values:
\[ \text{Molecular mass of } M_2O = 2 \times 40 + 16 = 80 + 16 = 96 \text{ g/mol} \]

### Final Answer
The minimum molecular mass of the oxide \( M_2O \) is **96 g/mol**.

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