On reduction with hydrogen, `3.6 g` of an oxide of matel left `3.2 g` of metal. If the vapour density of metal is `32`, the simplest formula of the oxide would be

Options

A. (a)`MO`
B. (b)`M_(2)O_(3)`
C. (c )`M_(2)O`
D. (d)`M_(2)O_(5)`

Explanation

To find the simplest formula of the oxide of the metal, we can follow these steps:

### Step 1: Determine the mass of the metal and the mass of the oxide.
- Given:
- Mass of the oxide (MO) = 3.6 g
- Mass of the metal (M) = 3.2 g

### Step 2: Calculate the mass of oxygen in the oxide.
- The mass of oxygen in the oxide can be calculated by subtracting the mass of the metal from the mass of the oxide:
\[ \text{Mass of oxygen} = \text{Mass of oxide} - \text{Mass of metal} = 3.6 \, \text{g} - 3.2 \, \text{g} = 0.4 \, \text{g} \]

### Step 3: Calculate the molar mass of the metal using its vapor density.
- The vapor density (VD) of the metal is given as 32. The molar mass (M) can be calculated using the formula:
\[ \text{Molar mass} = 2 \times \text{Vapor density} = 2 \times 32 = 64 \, \text{g/mol} \]

### Step 4: Calculate the number of moles of metal and oxygen.
- Moles of metal (M):
\[ \text{Moles of metal} = \frac{\text{Mass of metal}}{\text{Molar mass of metal}} = \frac{3.2 \, \text{g}}{64 \, \text{g/mol}} = 0.05 \, \text{mol} \]

- Moles of oxygen (O):
\[ \text{Moles of oxygen} = \frac{\text{Mass of oxygen}}{\text{Molar mass of oxygen}} = \frac{0.4 \, \text{g}}{16 \, \text{g/mol}} = 0.025 \, \text{mol} \]

### Step 5: Determine the simplest ratio of moles of metal to moles of oxygen.
- The ratio of moles of metal to moles of oxygen:
\[ \text{Ratio} = \frac{\text{Moles of metal}}{\text{Moles of oxygen}} = \frac{0.05}{0.025} = 2 \]
- This means for every 2 moles of metal, there is 1 mole of oxygen.

### Step 6: Write the simplest formula of the oxide.
- Based on the ratio, the simplest formula of the oxide can be written as:
\[ \text{Metal}_2\text{O} \]
- Since the valency of the metal is 1 and the valency of oxygen is 2, the simplest formula of the oxide is:
\[ \text{M}_2\text{O} \]

### Final Answer:
The simplest formula of the oxide is \( \text{M}_2\text{O} \).

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