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 charge in couloms required to complete the electrolysis

Options

A. 24125
B. 48250
C. 96500
D. 19300

Explanation

To solve the problem, we need to determine the total charge in coulombs required to complete the electrolysis of a 4.0 M NaCl solution when 500 mL of it is electrolyzed. Here’s a step-by-step breakdown of the solution:

### Step 1: Calculate the number of moles of NaCl in the solution.
The molarity (M) of a solution is defined as the number of moles of solute per liter of solution.

Given:
- Molarity of NaCl = 4.0 M
- Volume of solution = 500 mL = 0.500 L

Using the formula:
\[ \text{Number of moles} = \text{Molarity} \times \text{Volume (in L)} \]
\[ \text{Number of moles of NaCl} = 4.0 \, \text{mol/L} \times 0.500 \, \text{L} = 2.0 \, \text{mol} \]

### Step 2: Write the electrolysis reaction.
During the electrolysis of NaCl, the following reaction occurs:
\[ 2 \, \text{NaCl} \, \text{(aq)} \rightarrow 2 \, \text{Na}^+ \, \text{(aq)} + \text{Cl}_2 \, \text{(g)} + 2 \, \text{e}^- \]

### Step 3: Determine the number of moles of electrons involved.
From the balanced equation, we see that 2 moles of electrons are produced for every 2 moles of NaCl that are electrolyzed. Therefore, for 2 moles of NaCl:
\[ \text{Moles of electrons} = 2 \, \text{moles of NaCl} \times \frac{2 \, \text{moles of e}^-}{2 \, \text{moles of NaCl}} = 2 \, \text{moles of e}^- \]

### Step 4: Calculate the total charge required.
The total charge (Q) required can be calculated using Faraday's law of electrolysis, which states that:
\[ Q = n \times F \]
Where:
- \( n \) = number of moles of electrons
- \( F \) = Faraday's constant (approximately 96500 coulombs)

Substituting the values:
\[ Q = 2 \, \text{mol} \times 96500 \, \text{C/mol} = 193000 \, \text{C} \]

### Final Answer:
The total charge required to complete the electrolysis is **193000 coulombs**.

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