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 processes occurring when equal amounts of electricity are passed through the solutions of AX and BX2.

### Step-by-Step Solution:

1. **Identify the ions in the solutions**:
- For AX, we have A^+ and X^- ions.
- For BX2, we have B^2+ and 2X^- ions.

2. **Determine the number of electrons required for deposition**:
- The cation A^+ requires 1 electron to be reduced to A.
- The cation B^2+ requires 2 electrons to be reduced to B.

3. **Define the relationship between moles and electricity**:
- According to Faraday's laws of electrolysis, the amount of substance deposited is directly proportional to the quantity of electricity passed.
- Let’s denote the total charge passed as Q (in Coulombs). The relationship can be expressed as:
- For A:
\[ \text{moles of A deposited (Y)} = \frac{Q}{F} \quad \text{(where F is Faraday's constant)} \]
- For B:
\[ \text{moles of B deposited (Z)} = \frac{Q}{2F} \quad \text{(since B requires 2 electrons)} \]

4. **Relate the moles of A and B**:
- Since the same amount of electricity (Q) is passed through both solutions, we can express Y and Z in terms of Q:
- \( Y = \frac{Q}{F} \)
- \( Z = \frac{Q}{2F} \)

5. **Establish the relationship between Y and Z**:
- From the equations for Y and Z, we can relate them:
\[ Z = \frac{Y}{2} \]
- Rearranging gives:
\[ Y = 2Z \]

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

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