In an experiment, 4g of `M_(2)O_(x)` oxide was reduced to 2.8g of the metal. If the atomic mass of the metal is `56g"mol"^(-1)`, the number of oxygen atoms in the oxide is:

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the given data
- Mass of the oxide (M₂Oₓ) = 4 g
- Mass of the metal (M) = 2.8 g
- Atomic mass of the metal = 56 g/mol

### Step 2: Calculate the mass of oxygen in the oxide
To find the mass of oxygen in the oxide, we subtract the mass of the metal from the mass of the oxide:
\[ \text{Mass of oxygen} = \text{Mass of oxide} - \text{Mass of metal} = 4 \, \text{g} - 2.8 \, \text{g} = 1.2 \, \text{g} \]

### Step 3: Calculate the moles of the metal
Using the formula for moles:
\[ \text{Moles of metal} = \frac{\text{mass of metal}}{\text{molar mass of metal}} = \frac{2.8 \, \text{g}}{56 \, \text{g/mol}} = 0.05 \, \text{mol} \]

### Step 4: Calculate the moles of oxygen
Using the molar mass of oxygen (16 g/mol):
\[ \text{Moles of oxygen} = \frac{\text{mass of oxygen}}{\text{molar mass of oxygen}} = \frac{1.2 \, \text{g}}{16 \, \text{g/mol}} = 0.075 \, \text{mol} \]

### Step 5: Set up the relationship between moles of metal and moles of oxygen
From the formula of the oxide M₂Oₓ, we know:
\[ \frac{\text{Moles of metal}}{2} = \frac{\text{Moles of oxygen}}{x} \]
Where \( x \) is the number of oxygen atoms in the oxide.

### Step 6: Substitute the values and solve for x
Substituting the values we calculated:
\[ \frac{0.05}{2} = \frac{0.075}{x} \]
Cross-multiplying gives:
\[ 0.05x = 2 \times 0.075 \]
\[ 0.05x = 0.15 \]
Now, solving for \( x \):
\[ x = \frac{0.15}{0.05} = 3 \]

### Conclusion
The number of oxygen atoms in the oxide \( M₂Oₓ \) is **3**.

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