When equal number of coulomb of electricity is passed through aqueous solution of AX and `BX_2` and if number of moles of A and B deposited respectively are Y and Z then -

Options

A. Y = Z
B. `Y gt Z`
C. Z = 2Y
D. Y = 2Z

Answer

To solve the problem, we need to analyze the electrochemical reactions occurring when equal amounts of electricity are passed through the solutions of AX and BX₂. We will derive the relationship between the moles of A and B deposited.

### Step-by-Step Solution:

1. **Identify the Dissociation of Compounds:**
- The compound AX dissociates in solution as:
\[ AX \rightarrow A^+ + X^- \]
- The compound BX₂ dissociates in solution as:
\[ BX_2 \rightarrow B^{2+} + 2X^- \]

2. **Determine the Charge Required for Deposition:**
- For the deposition of A from A⁺:
- 1 mole of A requires 1 mole of electrons (1 Faraday).
- For the deposition of B from B²⁺:
- 1 mole of B requires 2 moles of electrons (2 Faradays).

3. **Relate the Number of Moles Deposited:**
- Let \( Y \) be the number of moles of A deposited.
- Since 1 mole of A requires 1 Faraday, the total charge passed for A is \( Y \) Faradays.
- Let \( Z \) be the number of moles of B deposited.
- Since 1 mole of B requires 2 Faradays, the total charge passed for B is \( 2Z \) Faradays.

4. **Equal Charge Condition:**
- Since equal amounts of electricity (in Coulombs) are passed through both solutions, we can equate the total charge:
\[ Y = 2Z \]

5. **Rearranging the Equation:**
- From the equation \( Y = 2Z \), we can express this in terms of \( Z \):
\[ Z = \frac{Y}{2} \]

6. **Conclusion:**
- The relationship between the moles of A and B deposited is:
\[ Y = 2Z \]

### Final Answer:
The correct relationship is \( Y = 2Z \).