Element 'A' reacts with oxygen to form a compound `A_(2)O_(3)`. If 0.359 gram of 'A' react to give 0.559 gram of the compound, atomic weight of 'A' will be

Options

A. 51
B. 43.08
C. 49.7
D. 47.9

Explanation

To find the atomic weight of element 'A' that reacts with oxygen to form the compound \( A_2O_3 \), we can follow these steps:

### Step 1: Understand the Given Information
- We have the mass of element 'A' which is \( 0.359 \, \text{g} \).
- The mass of the compound \( A_2O_3 \) formed is \( 0.559 \, \text{g} \).

### Step 2: Calculate the Mass of Oxygen in the Compound
To find the mass of oxygen in the compound, we can subtract the mass of 'A' from the mass of \( A_2O_3 \):
\[ \text{Mass of O} = \text{Mass of } A_2O_3 - \text{Mass of A} \]
\[ \text{Mass of O} = 0.559 \, \text{g} - 0.359 \, \text{g} = 0.200 \, \text{g} \]

### Step 3: Determine the Equivalent Weights
The equivalent weight of oxygen can be calculated using its molar mass and its n-factor. The molar mass of oxygen (O) is \( 16 \, \text{g/mol} \) and since it has a charge of -2 in the compound, the n-factor is 2. Thus, the equivalent weight of oxygen is:
\[ \text{Equivalent weight of O} = \frac{\text{Molar mass of O}}{\text{n-factor}} = \frac{16}{2} = 8 \, \text{g/equiv} \]

### Step 4: Calculate the Number of Equivalents of Oxygen
Now, we can find the number of equivalents of oxygen in the compound:
\[ \text{Number of equivalents of O} = \frac{\text{Mass of O}}{\text{Equivalent weight of O}} = \frac{0.200 \, \text{g}}{8 \, \text{g/equiv}} = 0.025 \, \text{equiv} \]

### Step 5: Determine the Number of Equivalents of 'A'
Since the compound \( A_2O_3 \) has 2 moles of 'A' for every 3 moles of oxygen, the number of equivalents of 'A' will be equal to the number of equivalents of oxygen:
\[ \text{Number of equivalents of A} = \text{Number of equivalents of O} = 0.025 \, \text{equiv} \]

### Step 6: Calculate the Equivalent Weight of 'A'
The equivalent weight of 'A' can be calculated using the mass of 'A' and its number of equivalents:
\[ \text{Equivalent weight of A} = \frac{\text{Mass of A}}{\text{Number of equivalents of A}} = \frac{0.359 \, \text{g}}{0.025 \, \text{equiv}} = 14.36 \, \text{g/equiv} \]

### Step 7: Calculate the Atomic Weight of 'A'
The atomic weight of 'A' can be calculated by multiplying the equivalent weight by the n-factor. For \( A_2O_3 \), the n-factor for 'A' is 3 (since there are 2 atoms of 'A' in the formula):
\[ \text{Atomic weight of A} = \text{Equivalent weight of A} \times \text{n-factor} = 14.36 \, \text{g/equiv} \times 3 = 43.08 \, \text{g/mol} \]

### Final Answer
The atomic weight of element 'A' is \( 43.08 \, \text{g/mol} \).

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