An oxide of a metal (M) contains 40% by mass of oxygen. Metal (M) has atomic mass of 24. The empirical formula of the oxide is-

Options

A. `M_(2)O`
B. MO
C. `M_(2)O_(3)`
D. `M_(3)O_(4)`

Answer

To find the empirical formula of the oxide of metal (M) that contains 40% by mass of oxygen, we can follow these steps:

### Step 1: Assume the mass of the metal oxide
Assume the total mass of the metal oxide is 100 grams. This simplifies calculations, as percentages can be directly converted to grams.

### Step 2: Calculate the mass of oxygen
Since the oxide contains 40% by mass of oxygen:
\[ \text{Mass of oxygen} = 40\% \text{ of } 100 \text{ grams} = 40 \text{ grams} \]

### Step 3: Calculate the mass of the metal
The mass of the metal (M) can be calculated by subtracting the mass of oxygen from the total mass of the oxide:
\[ \text{Mass of metal} = 100 \text{ grams} - 40 \text{ grams} = 60 \text{ grams} \]

### Step 4: Calculate the number of moles of oxygen
The molar mass of oxygen (O) is 16 g/mol. To find the number of moles of oxygen:
\[ \text{Number of moles of oxygen} = \frac{\text{Mass of oxygen}}{\text{Molar mass of oxygen}} = \frac{40 \text{ grams}}{16 \text{ g/mol}} = 2.5 \text{ moles} \]

### Step 5: Calculate the number of moles of metal
The atomic mass of metal (M) is given as 24 g/mol. To find the number of moles of metal:
\[ \text{Number of moles of metal} = \frac{\text{Mass of metal}}{\text{Atomic mass of metal}} = \frac{60 \text{ grams}}{24 \text{ g/mol}} = 2.5 \text{ moles} \]

### Step 6: Determine the mole ratio
Now we have:
- Moles of metal (M) = 2.5
- Moles of oxygen (O) = 2.5

To find the simplest mole ratio, we divide both by the smallest number of moles:
\[ \text{Mole ratio of M to O} = \frac{2.5}{2.5} : \frac{2.5}{2.5} = 1 : 1 \]

### Step 7: Write the empirical formula
Since the mole ratio of metal (M) to oxygen (O) is 1:1, the empirical formula of the oxide is:
\[ \text{Empirical formula} = \text{MO} \]

### Final Answer
The empirical formula of the oxide is **MO**.

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