`Cl_(2)` changes to` Cl^(-)` in cold NaOH. The equivalent weight of `Cl_(2)` will be :

Explanation

To find the equivalent weight of \( Cl_2 \) when it changes to \( Cl^- \) in cold NaOH, we can follow these steps:

### Step 1: Write the Reaction
The reaction of chlorine with sodium hydroxide can be represented as:
\[ Cl_2 + 2NaOH \rightarrow NaCl + NaClO + H_2 \]
In this reaction, chlorine (\( Cl_2 \)) is converted to chloride ions (\( Cl^- \)) and hypochlorite ions (\( ClO^- \)).

### Step 2: Determine the Oxidation States
- In \( Cl_2 \), the oxidation state of chlorine is 0.
- In \( Cl^- \), the oxidation state of chlorine is -1.
- In \( ClO^- \), the oxidation state of chlorine can be calculated as follows:
\[ x + (-2) = -1 \implies x = +1 \]
Thus, in \( ClO^- \), the oxidation state of chlorine is +1.

### Step 3: Calculate the Change in Oxidation States
- For \( Cl \) changing from 0 to -1 (in \( Cl^- \)):
- Change = \( 0 - (-1) = 1 \)
- For \( Cl \) changing from 0 to +1 (in \( ClO^- \)):
- Change = \( 0 - (+1) = 1 \)

### Step 4: Determine the Number of Moles of Chlorine
Since there are 2 moles of chlorine in \( Cl_2 \):
- For \( Cl^- \): The total change for 2 moles is \( 1 \times 2 = 2 \).
- For \( ClO^- \): The total change for 2 moles is also \( 1 \times 2 = 2 \).

### Step 5: Calculate the Total Change (n Factor)
The total change (n) can be calculated using the formula:
\[ \frac{1}{n} = \frac{1}{n_1} + \frac{1}{n_2} \]
Where \( n_1 = 2 \) (for \( Cl^- \)) and \( n_2 = 2 \) (for \( ClO^- \)):
\[ \frac{1}{n} = \frac{1}{2} + \frac{1}{2} = 1 \implies n = 1 \]

### Step 6: Calculate the Molecular Weight of \( Cl_2 \)
The molecular weight of \( Cl_2 \) is:
\[ \text{Molecular weight of } Cl_2 = 35.5 \times 2 = 71 \, \text{g/mol} \]

### Step 7: Calculate the Equivalent Weight
The equivalent weight is given by the formula:
\[ \text{Equivalent weight} = \frac{\text{Molecular weight}}{n} \]
Substituting the values:
\[ \text{Equivalent weight} = \frac{71}{1} = 71 \, \text{g/equiv} \]

### Final Answer
The equivalent weight of \( Cl_2 \) is **71 g/equiv**.

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