A certain compound has the molecular formula `X_(4)O_(6)`. If `10 g` of `X_(4) O_(6)` has `5.72 g X`, the atomic mass of `X` is

Options

A. 32 amu
B. 37 amu
C. 42 amu
D. 98 amu

Explanation

To find the atomic mass of element X in the compound \( X_4O_6 \), we can follow these steps:

### Step 1: Determine the molecular mass of \( X_4O_6 \)
The molecular formula \( X_4O_6 \) indicates that there are 4 atoms of element X and 6 atoms of oxygen. We denote the atomic mass of X as \( a \).

The molecular mass of \( X_4O_6 \) can be expressed as:
\[ \text{Molecular mass of } X_4O_6 = 4a + 6 \times 16 \]
Here, the atomic mass of oxygen is approximately 16 g/mol. Therefore:
\[ \text{Molecular mass of } X_4O_6 = 4a + 96 \text{ g/mol} \]

### Step 2: Set up the equation based on the given mass of the compound
We know that 10 g of \( X_4O_6 \) contains 5.72 g of element X. The mass of X in the compound can be expressed in terms of the total mass and the molecular mass:
\[ \text{Mass of } X = \frac{4a}{4a + 96} \times 10 \]
Setting this equal to the given mass of X:
\[ \frac{4a}{4a + 96} \times 10 = 5.72 \]

### Step 3: Solve the equation for \( a \)
To solve for \( a \), we can rearrange the equation:
\[ 4a \times 10 = 5.72 \times (4a + 96) \]
Expanding both sides:
\[ 40a = 5.72 \times 4a + 5.72 \times 96 \]
\[ 40a = 22.88a + 549.12 \]
Now, isolate \( a \):
\[ 40a - 22.88a = 549.12 \]
\[ 17.12a = 549.12 \]
Now, divide both sides by 17.12:
\[ a = \frac{549.12}{17.12} \approx 32.07 \]

### Conclusion
The atomic mass of element X is approximately \( 32.07 \) g/mol.

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