An oxide of metal M has 40% by mass of oxygen. Metal M has relative atomic mass of 24. The empirical formula of the oxide is:

Options

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

Answer

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

### Step 1: Determine the mass percentages
Given that the oxide contains 40% by mass of oxygen, we can deduce that the remaining mass must be metal M. Therefore:
- Mass percentage of metal M = 100% - 40% = 60%

### Step 2: Calculate the mass of each component in a hypothetical 100 g sample
Assuming we have 100 g of the oxide:
- Mass of metal M = 60 g
- Mass of oxygen = 40 g

### Step 3: Calculate the number of moles of metal M
The relative atomic mass of metal M is given as 24. To find the number of moles of metal M, we use the formula:
\[ \text{Number of moles of M} = \frac{\text{Mass of M}}{\text{Molar mass of M}} = \frac{60 \text{ g}}{24 \text{ g/mol}} = 2.5 \text{ moles} \]

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

### Step 5: Determine the mole ratio
Now, we can find the simplest mole ratio between metal M and oxygen:
- Moles of M : Moles of O = 2.5 : 2.5 = 1 : 1

### Step 6: Write the empirical formula
Since the ratio of moles of metal M to moles of oxygen 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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