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. `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 total mass of the compound
The total mass of the compound \(X_4O_6\) is given as \(10 \, g\).

### Step 2: Determine the mass of element X in the compound
The mass of element X in the compound is given as \(5.72 \, g\).

### Step 3: Calculate the mass of oxygen in the compound
To find the mass of oxygen in the compound, we subtract the mass of X from the total mass of the compound:
\[ \text{Mass of O} = \text{Total mass} - \text{Mass of X} = 10 \, g - 5.72 \, g = 4.28 \, g \]

### Step 4: Calculate the number of moles of oxygen
The atomic mass of oxygen (O) is \(16 \, g/mol\). To find the number of moles of oxygen in the compound, we use the formula:
\[ \text{Moles of O} = \frac{\text{Mass of O}}{\text{Atomic mass of O}} = \frac{4.28 \, g}{16 \, g/mol} = 0.2675 \, mol \]

### Step 5: Determine the number of moles of the compound
In the molecular formula \(X_4O_6\), there are 6 moles of oxygen for every mole of the compound. Therefore, the number of moles of the compound \(X_4O_6\) can be calculated as:
\[ \text{Moles of } X_4O_6 = \frac{\text{Moles of O}}{6} = \frac{0.2675 \, mol}{6} = 0.04458 \, mol \]

### Step 6: Calculate the total mass of element X in the compound
From the molecular formula \(X_4O_6\), we know that there are 4 moles of X for every mole of the compound. Thus, the moles of X can be calculated as:
\[ \text{Moles of X} = 4 \times \text{Moles of } X_4O_6 = 4 \times 0.04458 \, mol = 0.17832 \, mol \]

### Step 7: Calculate the atomic mass of element X
We know the mass of X in the compound is \(5.72 \, g\). The atomic mass of X can be calculated using the formula:
\[ \text{Atomic mass of X} = \frac{\text{Mass of X}}{\text{Moles of X}} = \frac{5.72 \, g}{0.17832 \, mol} \approx 32.1 \, g/mol \]

### Final Answer
The atomic mass of element X is approximately \(32.1 \, g/mol\).

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