Redox equations are balanced either by ion-electron method or by oxidation number method. Both methods lead to the correct from of the balanced equation. The ion electron methodd has two advantages. So some chemists prefer to use the ion-electron method for redox reactions carried out in dilute aqueous solutions, where free ions have more or less independent existance.
The oxidation state method for redox reactions is mostly used for solid chemicals or for reactions in concentrated acid media.
For the reaction
`As_(2)S_(3)rarrAs^(5+)+SO_(4)^(2-)`
the `n`-factor is

Options

A. `11`
B. `28`
C. `61`
D. `(5)/(3)`

Explanation

To find the n-factor for the reaction \( \text{As}_2\text{S}_3 \rightarrow \text{As}^{5+} + \text{SO}_4^{2-} \), we need to analyze the changes in oxidation states and the number of electrons transferred during the redox process. Here’s a step-by-step solution:

### Step 1: Identify Oxidation States
- In \( \text{As}_2\text{S}_3 \), arsenic (As) has an oxidation state of +3, and sulfur (S) has an oxidation state of -2.
- In the products, arsenic is oxidized to \( \text{As}^{5+} \) and sulfur is reduced to \( \text{SO}_4^{2-} \) where sulfur has an oxidation state of +6.

### Step 2: Determine Changes in Oxidation States
- For arsenic:
- Change from +3 to +5:
- Each As atom goes from +3 to +5, which is an increase of 2.
- Since there are 2 arsenic atoms, the total change for arsenic is \( 2 \times 2 = 4 \) electrons lost (oxidation).

- For sulfur:
- Change from -2 to +6:
- Each sulfur atom goes from -2 to +6, which is an increase of 8.
- Since there are 3 sulfur atoms, the total change for sulfur is \( 3 \times 8 = 24 \) electrons gained (reduction).

### Step 3: Calculate Total n-Factor
- The n-factor is defined as the total number of electrons transferred in the reaction.
- Total electrons transferred = electrons lost by arsenic + electrons gained by sulfur:
\[ n = 4 + 24 = 28 \]

### Final Answer
Thus, the n-factor for the reaction \( \text{As}_2\text{S}_3 \rightarrow \text{As}^{5+} + \text{SO}_4^{2-} \) is **28**.

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