On reduction with hydrogen , 3.6 g of an oxide of metal left 3.2 g of metal . If the simplest atomic weight of metal is 64, the simplest formula of the oxide is

Options

A. MO
B. `M_2O_3`
C. `M_2O`
D. `M_2O_5`

Answer

To find the simplest formula of the metal oxide based on the information provided, we can follow these steps:

### Step 1: Determine the mass of oxygen in the oxide
Given:
- Mass of metal oxide = 3.6 g
- Mass of metal = 3.2 g

To find the mass of oxygen in the oxide, we subtract the mass of the metal from the mass of the oxide:
\[ \text{Mass of oxygen} = \text{Mass of metal oxide} - \text{Mass of metal} = 3.6 \, \text{g} - 3.2 \, \text{g} = 0.4 \, \text{g} \]

### Step 2: Calculate the number of moles of metal and oxygen
Next, we calculate the number of moles of the metal and oxygen using their respective atomic masses.

- Atomic mass of metal = 64 g/mol
- Atomic mass of oxygen = 16 g/mol

**For metal:**
\[ \text{Moles of metal} = \frac{\text{Mass of metal}}{\text{Atomic mass of metal}} = \frac{3.2 \, \text{g}}{64 \, \text{g/mol}} = 0.05 \, \text{mol} \]

**For oxygen:**
\[ \text{Moles of oxygen} = \frac{\text{Mass of oxygen}}{\text{Atomic mass of oxygen}} = \frac{0.4 \, \text{g}}{16 \, \text{g/mol}} = 0.025 \, \text{mol} \]

### Step 3: Determine the mole ratio of metal to oxygen
Now, we can find the simplest mole ratio by dividing the number of moles of each by the smallest number of moles calculated.

**Mole ratio of metal to oxygen:**
\[ \text{Ratio of metal} = \frac{0.05}{0.025} = 2 \]
\[ \text{Ratio of oxygen} = \frac{0.025}{0.025} = 1 \]

Thus, the mole ratio of metal to oxygen is 2:1.

### Step 4: Write the simplest formula of the oxide
From the mole ratio, we can write the simplest formula of the metal oxide:
\[ \text{Simplest formula} = \text{M}_2\text{O} \]

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

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