`1` mol each of ` AgNO_3, CuSO_4` and `AICI_3` is electrolyzed. The number of faradays required is in the ration of:

Options

A. `1 : 1 : 1`
B. `1 : 2 : 3`
C. `3 : 2 : 1`
D. `1 : 3 : 1`

Answer

To solve the problem, we need to find out how many Faradays are required for the electrolysis of each of the given compounds: AgNO3, CuSO4, and AlCl3. We will analyze each compound step by step.

### Step 1: Electrolysis of AgNO3
- The electrolysis of silver nitrate (AgNO3) can be represented as:
\[ \text{AgNO}_3 \rightarrow \text{Ag}^+ + \text{NO}_3^- \]
- During electrolysis, silver ions (Ag⁺) gain one electron (e⁻) to form solid silver (Ag):
\[ \text{Ag}^+ + e^- \rightarrow \text{Ag} \]
- Since 1 mole of Ag⁺ requires 1 mole of electrons, the number of Faradays required for AgNO3 is:
\[ 1 \text{ Faraday} \]

### Step 2: Electrolysis of CuSO4
- The electrolysis of copper sulfate (CuSO4) can be represented as:
\[ \text{CuSO}_4 \rightarrow \text{Cu}^{2+} + \text{SO}_4^{2-} \]
- During electrolysis, copper ions (Cu²⁺) gain two electrons to form solid copper (Cu):
\[ \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \]
- Since 1 mole of Cu²⁺ requires 2 moles of electrons, the number of Faradays required for CuSO4 is:
\[ 2 \text{ Faradays} \]

### Step 3: Electrolysis of AlCl3
- The electrolysis of aluminum chloride (AlCl3) can be represented as:
\[ \text{AlCl}_3 \rightarrow \text{Al}^{3+} + 3\text{Cl}^- \]
- During electrolysis, aluminum ions (Al³⁺) gain three electrons to form solid aluminum (Al):
\[ \text{Al}^{3+} + 3e^- \rightarrow \text{Al} \]
- Since 1 mole of Al³⁺ requires 3 moles of electrons, the number of Faradays required for AlCl3 is:
\[ 3 \text{ Faradays} \]

### Step 4: Finding the Ratio
Now that we have the number of Faradays required for each compound, we can express them in ratio form:
- For AgNO3: 1 Faraday
- For CuSO4: 2 Faradays
- For AlCl3: 3 Faradays

Thus, the ratio of Faradays required for the electrolysis of AgNO3, CuSO4, and AlCl3 is:
\[ 1 : 2 : 3 \]

### Final Answer
The number of Faradays required is in the ratio of **1 : 2 : 3**.

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