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

Options

A. `32am u`
B. `27am u`
C. `42am u`
D. `98a m u`

Explanation

To solve the problem, we need to find the atomic mass of the element \( X \) in the compound \( X_4O_6 \). Here are the steps to arrive at the solution:

### Step 1: Write the molecular formula and identify the components
The molecular formula of the compound is \( X_4O_6 \). This means there are 4 atoms of element \( X \) and 6 atoms of oxygen in the compound.

### Step 2: Calculate the molar mass of the compound
The molar mass of the compound \( X_4O_6 \) can be expressed in terms of the atomic mass of \( X \) (let's denote it as \( x \)):
- The molar mass of oxygen (O) is 16 g/mol.
- Therefore, the molar mass of \( X_4O_6 \) is:
\[ \text{Molar mass of } X_4O_6 = 4x + 6 \times 16 = 4x + 96 \text{ g/mol} \]

### Step 3: Set up the equation based on the given mass
We know that 10 g of \( X_4O_6 \) contains 5.72 g of \( X \). We can set up a proportion:
\[ \frac{4x}{4x + 96} = \frac{5.72}{10} \]

### Step 4: Cross-multiply to solve for \( x \)
Cross-multiplying gives us:
\[ 10 \cdot 4x = 5.72 \cdot (4x + 96) \]
Expanding both sides:
\[ 40x = 22.88x + 549.12 \]

### Step 5: Rearrange the equation
Now, we will rearrange the equation to isolate \( x \):
\[ 40x - 22.88x = 549.12 \]
\[ 17.12x = 549.12 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 17.12 to find \( x \):
\[ x = \frac{549.12}{17.12} \approx 32.07 \text{ g/mol} \]

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

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