The total number of Faradays required to oxidize the following separately`:`
`a. 1 mol of S_(2)O_(3)^(2-)` in acid medium
`b. 1 ` Equivalent of `S_(2)O_(3)^(2-)` in acid medium

Explanation

To solve the problem of determining the total number of Faradays required to oxidize the given species, we will break it down into two parts as specified in the question.

### Part (a): Oxidizing 1 mol of \( S_2O_3^{2-} \) in acid medium

1. **Identify the oxidation reaction**:
The oxidation of thiosulfate ion (\( S_2O_3^{2-} \)) in acidic medium can be represented as:
\[ S_2O_3^{2-} \rightarrow \frac{1}{2} S_4O_6^{2-} + e^- \]

2. **Determine the number of electrons involved**:
From the reaction, we see that 1 mole of \( S_2O_3^{2-} \) produces \( \frac{1}{2} \) mole of \( S_4O_6^{2-} \) and releases 1 electron.

3. **Calculate the Faradays required**:
Since 1 Faraday is required to transfer 1 mole of electrons, the total number of Faradays required to oxidize 1 mole of \( S_2O_3^{2-} \) is:
\[ \text{Faradays required} = 1 \text{ Faraday} \]

### Part (b): Oxidizing 1 Equivalent of \( S_2O_3^{2-} \) in acid medium

1. **Define 1 equivalent**:
1 equivalent of a substance is defined as the amount that can donate or accept 1 mole of electrons in a redox reaction.

2. **Determine the oxidation reaction for 1 equivalent**:
The complete oxidation of \( S_2O_3^{2-} \) can be represented as:
\[ S_2O_3^{2-} + 8H^+ + 8e^- \rightarrow 2 HSO_4^{-} \]

3. **Calculate the number of Faradays required**:
From the reaction, we see that 1 mole of \( S_2O_3^{2-} \) requires 8 moles of electrons to fully oxidize. Therefore, the total number of Faradays required for 1 equivalent (which corresponds to the transfer of 1 mole of electrons) is:
\[ \text{Faradays required} = 8 \text{ Faradays} \]

### Summary of Results:
- For part (a): 1 Faraday is required to oxidize 1 mole of \( S_2O_3^{2-} \).
- For part (b): 8 Faradays are required to oxidize 1 equivalent of \( S_2O_3^{2-} \).

### Final Answer:
- (a) 1 Faraday
- (b) 8 Faradays

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