In the reaction, `2S_(2)O_(3)^(2-)+I_(2)rarrS_(4)O_(6)^(2-)+2I^(-)`. The eq. wt. of `Na_(2)S_(2)O_(3)` is equal to its:

Options

A. Mol. wt.
B. Mol. wt./2
C. `2xx"mol. w.t."`
D. Mol. w.t./6

Explanation

To find the equivalent weight of \( \text{Na}_2\text{S}_2\text{O}_3 \) in the given reaction, we can follow these steps:

### Step 1: Identify the reaction
The reaction given is:
\[ 2 \text{S}_2\text{O}_3^{2-} + \text{I}_2 \rightarrow \text{S}_4\text{O}_6^{2-} + 2 \text{I}^- \]

### Step 2: Determine oxidation states
1. For \( \text{S}_2\text{O}_3^{2-} \):
- Let the oxidation state of sulfur (S) be \( x \).
- The equation for oxidation state is:
\[ 2x + 3(-2) = -2 \implies 2x - 6 = -2 \implies 2x = 4 \implies x = +2 \]
- So, the oxidation state of sulfur in \( \text{S}_2\text{O}_3^{2-} \) is +2.

2. For \( \text{S}_4\text{O}_6^{2-} \):
- Let the oxidation state of sulfur be \( y \).
- The equation for oxidation state is:
\[ 4y + 6(-2) = -2 \implies 4y - 12 = -2 \implies 4y = 10 \implies y = +2.5 \]
- So, the oxidation state of sulfur in \( \text{S}_4\text{O}_6^{2-} \) is +2.5.

### Step 3: Calculate the change in oxidation state
- The change in oxidation state for sulfur from \( +2 \) to \( +2.5 \) is:
\[ \Delta = 2.5 - 2 = 0.5 \]
- Since there are 2 sulfur atoms in \( \text{S}_2\text{O}_3^{2-} \), the total change in oxidation state for 2 moles is:
\[ \text{Total change} = 2 \times 0.5 = 1 \]

### Step 4: Determine the n-factor
- The n-factor is defined as the total change in oxidation state per mole of the substance.
- Here, the n-factor for \( \text{Na}_2\text{S}_2\text{O}_3 \) is 1.

### Step 5: Calculate the equivalent weight
- The equivalent weight (EW) is calculated using the formula:
\[ \text{Equivalent Weight} = \frac{\text{Molecular Weight}}{\text{n-factor}} \]
- Since the n-factor is 1, we have:
\[ \text{Equivalent Weight} = \frac{\text{Molecular Weight}}{1} = \text{Molecular Weight} \]

### Conclusion
Thus, the equivalent weight of \( \text{Na}_2\text{S}_2\text{O}_3 \) is equal to its molecular weight.

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