Problem 128 - A Complete Resource Book in Chemistry for JEE Main

Question

One litre of \(0.5 \mathrm{M} \mathrm{KCI}\) solution is electrolysed for one ninute in a current of \(16.08 \mathrm{~mA}\). Considering \(100 \%\) efficiency, the \(\mathrm{pH}\) of resulting solution will be a) 7 (b) 9 (c) 8 (d) 10

Step-by-Step Solution

Answer

The pH of the resulting solution is 9.

Step 1: Understand Electrolysis Concept

During the electrolysis of a solution, an electric current causes a non-spontaneous chemical reaction to occur. In this case, water in the potassium chloride solution can be electrolyzed into hydrogen gas and hydroxide ions, affecting the pH of the solution.

Step 2: Determine Hydroxide Ion Formation

Electrolysis involves the reduction of water at the cathode, producing hydroxide ions (OH-) and hydrogen gas (H2). The reaction at the cathode is: \( 2H_2O + 2e^- \rightarrow 2OH^- + H_2 \). This increases the pH of the solution.

Step 3: Calculate the Charge Passed Through the Solution

The charge (in coulombs) can be calculated using the formula \( Q = I \times t \). Here, \( I = 16.08\, \text{mA} = 0.01608\, \text{A} \) and \( t = 60\, \text{seconds} \). Thus, \( Q = 0.01608 \times 60 = 0.9648\, \text{Coulombs} \).

Step 4: Apply Faraday's Laws of Electolysis

One mole of electrons corresponds to \( 96500 \text{ C} \). The moles of electrons are given by \( \frac{0.9648}{96500} \approx 0.00001 \, \text{mol electrons} \). Since each hydroxide ion requires one electron: \( 0.00001 \, \text{mol electrons} = 0.00001 \, \text{mol OH}^- \).

Step 5: Calculate the Concentration of Hydroxide Ions

For a 1-liter solution, the concentration of hydroxide ions \([OH^-]\) is \( 0.00001 \, \text{mol/L} \).

Step 6: Find the pOH of the Solution

Use the formula \( \text{pOH} = -\log[OH^-] \) to find pOH: \( \text{pOH} = -\log(0.00001) = 5 \).

Step 7: Calculate the pH from pOH

Since \( \text{pH} + \text{pOH} = 14 \), we can calculate \( \text{pH} = 14 - 5 = 9 \).

Key Concepts

Electrolysis

Electrolysis is a fascinating chemical process where electrical energy is used to drive a non-spontaneous chemical reaction. In the case of a potassium chloride solution, applying an electric current can lead to the decomposition of water molecules, despite water not reacting easily under normal conditions.
By passing electricity through the solution, water undergoes electrolysis: chemicals that do not naturally break down on their own. This results in the formation of hydrogen gas and hydroxide ions.

• This process is crucial in the field of electrochemistry, providing a method to split compounds or purify metals.
• It also highlights the interplay between electricity and chemical reactions, where electrical energy is converted into chemical energy.

Understanding these basic principles of electrolysis paves the way for grasping more advanced topics like Faraday's laws, and how they influence the concentration of substances in a solution.

Faraday's Laws of Electrolysis

Faraday's Laws of Electrolysis are essential principles that link the movement of electric charge with chemical changes occurring during electrolysis. There are two laws:

• First Law: The amount of chemical reaction (or substance produced or consumed) at an electrode is directly proportional to the quantity of electricity that passes through the electrolyte.
• Second Law: For a given quantity of electricity, the mass of different substances produced or consumed at an electrode is proportional to their equivalent weights.

Applying these laws allows us to calculate the quantity of substances involved in the reaction. By determining the charge passed using the formula \( Q = I \times t \), and knowing the charge required to produce one mole of electrons \( (96500 \text{ C}) \), we can find out exactly how much of a substance, such as hydroxide ions, is produced during electrolysis.
This understanding is invaluable for conducting precise chemical processes and experiments.

pH Calculation

pH is a crucial measurement that indicates how acidic or basic a solution is. It is derived from the concentration of hydrogen ions in the solution but can also be calculated from the hydroxide concentration in basic solutions.
After producing hydroxide ions in the electrolysis process, we can calculate the concentration of these ions, as shown in the step-by-step solution.
The relationship between pH and pOH (the measure of hydroxide ion concentration) is given as:

• \( \text{pH} + \text{pOH} = 14 \)

By calculating the pOH from the hydroxide ion concentration, we can find the pH by subtracting the pOH from 14.
For a student solving chemical problems, mastering pH calculations is key, as it appears frequently in various electrochemical contexts.

Hydroxide Ion Formation

The formation of hydroxide ions during electrolysis is a clear illustration of how electrochemical reactions can alter the chemical makeup of a solution. At the cathode, water undergoes reduction, which is the gain of electrons, thereby forming hydroxide ions \( (OH^-) \) and hydrogen gas. The chemical reaction involved is:
\[ 2H_2O + 2e^- \rightarrow 2OH^- + H_2 \]
The production of \( OH^- \) ions increases the basicity of the solution, which corresponds to an increase in pH. This process is especially important when analyzing or adjusting the pH levels in electrochemical setups.

• Understanding how ions form and affect pH allows for control over solution properties during industrial applications.
• This forms the basis for further studies in complex electrochemical systems.

Recognizing these reactions is fundamental in electrochemistry, providing insights into both technical and practical applications.