Chemical reaction involve interaction of atoms and molecules. A large number of atoms/molecules (approximately `6.022xx10^(23)`)are present in a few grams of any chemical compound varying with their atomic/molrcular mass. To handle such a large numbers conveniently, the mole concept was introduced. This concept has implications in diverse areas such as analytical in diverse areas such as analytical chemistry, biochemistry, electrochemistry and radiochemistry. The following example illustrates a typical case, involving chemical/ electrochemical reaction, which requires a clear understanding of the mole concept.
A 4.0 molar aqueous solution of NaCl is prepared and 500 mL of this solution is electrolysed. This leads to the evolution of chlorine gas at one of teh electrodes (atomic mass: Na=23, Hg=200, 1F=96500 coulombs)
The total number of moles of chlorine gas evolved is

Options

A. 0.5
B. 1
C. 2
D. 3

Explanation

To solve the problem of determining the total number of moles of chlorine gas (\(Cl_2\)) evolved during the electrolysis of a 4.0 M NaCl solution, we can follow these steps:

### Step 1: Understand the relationship between NaCl and Cl2
During the electrolysis of sodium chloride (NaCl), chlorine gas is evolved at the anode. The balanced chemical equation for the electrolysis of NaCl can be represented as:
\[ 2 \text{NaCl} \rightarrow \text{Cl}_2 + 2 \text{Na} \]
From this equation, we can see that 2 moles of NaCl produce 1 mole of chlorine gas (\(Cl_2\)).

### Step 2: Calculate the number of moles of NaCl in the solution
We know the molarity (M) of the NaCl solution and the volume (V) of the solution. The formula to calculate the number of moles (\(n\)) is:
\[ n = M \times V \]
Given:
- Molarity (M) = 4.0 M
- Volume (V) = 500 mL = 0.5 L (since 1 L = 1000 mL)

Now, substituting the values:
\[ n = 4.0 \, \text{mol/L} \times 0.5 \, \text{L} = 2.0 \, \text{mol} \]

### Step 3: Relate moles of NaCl to moles of Cl2
From the balanced equation, we know that 2 moles of NaCl produce 1 mole of \(Cl_2\). Therefore, we can calculate the moles of chlorine gas evolved:
\[ \text{Moles of } Cl_2 = \frac{\text{Moles of NaCl}}{2} = \frac{2.0 \, \text{mol}}{2} = 1.0 \, \text{mol} \]

### Conclusion
The total number of moles of chlorine gas evolved during the electrolysis of the 500 mL of 4.0 M NaCl solution is **1.0 mol**.

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