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

Options

A. a.45
B. b.9
C. c.18
D. d.27

Explanation

To find the atomic mass of element M in the oxide \( M_2O_3 \) where the percentage of element M is 53%, we can follow these steps:

### Step 1: Determine the total mass of the compound
Let the total mass of the compound \( M_2O_3 \) be \( x \).

### Step 2: Calculate the mass of element M
Since 53% of \( x \) is the mass of element M, we can express this mathematically:
\[ \text{Mass of M} = \frac{53}{100} \times x = 0.53x \]

### Step 3: Calculate the mass of oxygen
The remaining percentage (100% - 53%) gives us the percentage of oxygen in the compound:
\[ \text{Mass of O} = 100\% - 53\% = 47\% \]
Thus, the mass of oxygen can be expressed as:
\[ \text{Mass of O} = \frac{47}{100} \times x = 0.47x \]

### Step 4: Calculate the total mass of oxygen in \( M_2O_3 \)
The molecular formula \( M_2O_3 \) indicates that there are 3 atoms of oxygen. The molar mass of oxygen is approximately 16 g/mol. Therefore, the total mass of oxygen in \( M_2O_3 \) is:
\[ \text{Total mass of O} = 3 \times 16 = 48 \text{ g} \]

### Step 5: Set up the equation for total mass
Since the total mass of oxygen is also equal to \( 0.47x \), we can set up the equation:
\[ 0.47x = 48 \]

### Step 6: Solve for \( x \)
To find \( x \), we rearrange the equation:
\[ x = \frac{48}{0.47} \approx 102.13 \text{ g} \]

### Step 7: Calculate the mass of element M
Now that we have the total mass of \( M_2O_3 \), we can find the mass of element M:
\[ \text{Mass of M} = x - \text{Mass of O} = 102.13 - 48 = 54.13 \text{ g} \]

### Step 8: Find the atomic mass of element M
Since there are 2 atoms of M in the formula \( M_2O_3 \), the atomic mass of M can be calculated as follows:
\[ \text{Atomic mass of M} = \frac{\text{Mass of M}}{2} = \frac{54.13}{2} \approx 27.07 \text{ g/mol} \]

### Conclusion
The atomic mass of element M is approximately 27 g/mol.