In the estimation `Na_(2)S_(2)O_(3)`of using`Br_(2)` the equivalent weight of `Na_(2)S_(2)O_(3)` is :

Options

A. `M//2`
B. `M//8`
C. `M//3`
D. M

Explanation

To find the equivalent weight of sodium thiosulfate (\(Na_2S_2O_3\)) when estimating it using bromine (\(Br_2\)), we can follow these steps:

### Step 1: Write the balanced chemical equation
The reaction between sodium thiosulfate and bromine can be represented as follows:

\[ Na_2S_2O_3 + Br_2 \rightarrow Na_2SO_4 + H_2SO_4 + HBr \]

### Step 2: Determine the oxidation states
In sodium thiosulfate (\(Na_2S_2O_3\)), we need to determine the oxidation states of sulfur. The oxidation states can be calculated as follows:

1. Let the oxidation state of sulfur in \(S_2O_3^{2-}\) be \(x\).
2. The equation for the oxidation states is:
\[ 2x + 3(-2) = -2 \quad \text{(charge of thiosulfate)} \]
Simplifying this gives:
\[ 2x - 6 = -2 \implies 2x = 4 \implies x = +2 \]

### Step 3: Identify the oxidation states in the products
In the product \(Na_2SO_4\), the oxidation state of sulfur is \(+6\).

### Step 4: Calculate the change in oxidation state
The change in oxidation state for sulfur during the reaction is:
- From \(+2\) in \(Na_2S_2O_3\) to \(+6\) in \(Na_2SO_4\).

The change in oxidation state (\(n\)) can be calculated as:
\[ n = \text{(final oxidation state)} - \text{(initial oxidation state)} = 6 - 2 = 4 \]

### Step 5: Calculate the equivalent weight
The equivalent weight of a substance is given by the formula:
\[ \text{Equivalent weight} = \frac{\text{Molar mass}}{n} \]

The molar mass of \(Na_2S_2O_3\) can be calculated as follows:
- Sodium (Na): \(23 \times 2 = 46\)
- Sulfur (S): \(32 \times 2 = 64\)
- Oxygen (O): \(16 \times 3 = 48\)

Thus, the molar mass of \(Na_2S_2O_3\) is:
\[ 46 + 64 + 48 = 158 \text{ g/mol} \]

Now substituting the values into the equivalent weight formula:
\[ \text{Equivalent weight} = \frac{158}{4} = 39.5 \text{ g/equiv} \]

### Final Answer
The equivalent weight of \(Na_2S_2O_3\) when estimating it using \(Br_2\) is \(39.5 \text{ g/equiv}\).

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