0.2 mol `A_(x)B_(y)to0.5` mol `A_(2)+0.4molB_(3)`. From this data the molecular formula of AB

Options

A. `AB_(2)`
B. `A_(2)B_(2)`
C. `A_(4)B_(5)`
D. `A_(5)B_(6)`

Explanation

To determine the molecular formula of \( AB \) from the given reaction:

**Given Reaction:**
\[ 0.2 \, \text{mol} \, A_xB_y \rightarrow 0.5 \, \text{mol} \, A_2 + 0.4 \, \text{mol} \, B_3 \]

### Step 1: Simplify the Moles
First, we can simplify the moles of the reactants and products by multiplying all values by 5 to make calculations easier.

- Moles of \( A_xB_y \):
\[ 0.2 \times 5 = 1 \, \text{mol} \]

- Moles of \( A_2 \):
\[ 0.5 \times 5 = 2.5 \, \text{mol} \]

- Moles of \( B_3 \):
\[ 0.4 \times 5 = 2 \, \text{mol} \]

### Step 2: Determine Moles of A
From the reaction, we know that 1 mole of \( A_xB_y \) produces \( X \) moles of \( A \). Since 2.5 moles of \( A_2 \) are produced, we can find the total moles of \( A \).

- Each mole of \( A_2 \) contains 2 moles of \( A \):
\[ \text{Moles of } A = 2 \times 2.5 = 5 \, \text{mol} \]

### Step 3: Determine Moles of B
Similarly, we can find the moles of \( B \) produced from \( B_3 \).

- Each mole of \( B_3 \) contains 3 moles of \( B \):
\[ \text{Moles of } B = 2 \times 3 = 6 \, \text{mol} \]

### Step 4: Establish the Ratio
From the above calculations, we have:
- Moles of \( A = 5 \)
- Moles of \( B = 6 \)

Thus, the molecular formula of \( AB \) can be expressed as:
\[ A_5B_6 \]

### Conclusion
The molecular formula of \( AB \) is \( A_5B_6 \).

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