The percentage of element M is 53 in its oxide of molecular formula `M_(2)O_(3)`. Its atomic mass is about

Options

A. `45`
B. `9`
C. `18`
D. `36`

Explanation

To find the atomic mass of element M in the oxide M₂O₃, we can follow these steps:

### Step 1: Define the variables
Let the atomic mass of element M be represented as \( X \).

### Step 2: Calculate the molecular weight of M₂O₃
The molecular weight of the compound M₂O₃ can be calculated as follows:
- The contribution from M: Since there are 2 atoms of M, the contribution is \( 2X \).
- The contribution from O: There are 3 atoms of oxygen, and the atomic mass of oxygen is approximately 16. Therefore, the contribution from oxygen is \( 3 \times 16 = 48 \).

Thus, the total molecular weight of M₂O₃ is:
\[ \text{Molecular weight of M₂O₃} = 2X + 48 \]

### Step 3: Set up the equation for percentage composition
According to the problem, the percentage of element M in M₂O₃ is given as 53%. The formula for percentage composition is:
\[ \text{Percentage of M} = \left( \frac{\text{Weight of M}}{\text{Total weight of M₂O₃}} \right) \times 100 \]
Substituting the values we have:
\[ 53 = \left( \frac{2X}{2X + 48} \right) \times 100 \]

### Step 4: Solve the equation
To solve for \( X \), we can rearrange the equation:
\[ 53 = \frac{2X}{2X + 48} \times 100 \]
Dividing both sides by 100:
\[ 0.53 = \frac{2X}{2X + 48} \]
Cross-multiplying gives:
\[ 0.53(2X + 48) = 2X \]
Expanding this:
\[ 1.06X + 25.44 = 2X \]
Rearranging gives:
\[ 2X - 1.06X = 25.44 \]
\[ 0.94X = 25.44 \]
Now, solving for \( X \):
\[ X = \frac{25.44}{0.94} \approx 27.1 \]

### Step 5: Conclusion
The atomic mass of element M is approximately 27.