Problem 130 - A Complete Resource Book in Chemistry for JEE Main

Question

The hydrogen electrode is dipped in a solution of \(\mathrm{pH}=\) \(3.0\) at \(25^{\circ} \mathrm{C}\). The potential of hydrogen electrode would be(a) \(-0.177 \mathrm{~V}\) (b) \(0.177 \mathrm{~V}\) (c) \(1.77 \mathrm{~V}\) (d) \(0.277 \mathrm{~V}\)

Step-by-Step Solution

Answer

The potential of the hydrogen electrode is 0.177 V.

Step 1: Recall the Nernst Equation for Hydrogen Electrode

To find the potential of the hydrogen electrode, we need to use the Nernst equation: \[ E = E^0 - \left( \frac{RT}{nF} \right) \ln(Q) \]Where:- \( E^0 = 0 \) for the standard hydrogen electrode.- \( R \) is the universal gas constant.- \( T \) is the temperature in Kelvin.- \( n \) is the number of moles of electrons exchanged (which is 2 for hydrogen).- \( F \) is the Faraday constant.- \( Q \) is the reaction quotient, related to the \( pH \) of the solution.

Step 2: Calculate Reaction Quotient Using pH

For a hydrogen electrode reaction: \[ ext{H}_2(g) \rightarrow 2 ext{H}^+ + 2e^- \]The reaction quotient \( Q \) is the concentration of \( H^+ \), which we can calculate from the \( pH \) using the formula:\[ Q = [H^+] = 10^{- ext{pH}} = 10^{-3} \]

Step 3: Plug Values into Nernst Equation

Convert the temperature from Celsius to Kelvin: \[ T = 25^{\circ}C + 273 = 298K \]Substitute into the Nernst equation: \[ E = 0 - \left( \frac{8.314 \times 298}{2 \times 96485} \right) \ln(10^{-3}) \]This simplifies to:\[ E = - \left( \frac{0.0257}{2} \right) \ln(10^{-3}) \]

Step 4: Recalculate Using Logarithm Properties

To simplify further, recall that \( \ln(10^{-3}) = -3 \ln(10) \), and \( \ln(10) \approx 2.303 \):\[ E = - \left( 0.0257 \right) (-3 \times 2.303) \]This simplifies to:\[ E = 0.177 \, V \]

Key Concepts

Hydrogen Electrode

The hydrogen electrode is a fundamental concept in electrochemistry, commonly used as a reference point. Also known as the standard hydrogen electrode (SHE), it is essentially a half-cell where hydrogen gas at 1 atm pressure is in equilibrium with protons in an acidic solution.

• This half-cell has an assigned potential of 0 V by definition when at standard conditions, which makes it an ideal reference for measuring other electrodes' potentials.
• The hydrogen electrode reaction can be described by the reversible reaction: \[ \text{H}_2(g) \leftrightarrows 2\text{H}^+ + 2e^- \]
• In practice, it consists of a platinum electrode coated with a layer of platinum black, allowing hydrogen adsorption.

Remember, when discussing hydrogen electrodes, we analyze how conditions like concentration and temperature affect their potential.
Electronic equipment and designs often work with hydride electrochemical reactions, maintaining the electrochemical cell in a controlled environment.

pH and Electrochemistry

The concept of pH is integral to understanding electrochemistry. pH measures the acidity of a solution and directly relates to the concentration of hydrogen ions \([H^+]\).

• The pH value determines the concentration of hydrogen ions, which is defined as \( [H^+] = 10^{-\text{pH}} \).
• In electrochemical cells, pH plays a significant role because it influences the reaction quotient \(Q\) used in the Nernst equation.
• For hydrogen electrodes, a change in pH directly alters the electrode potential, indicating how acidic or basic the solution becomes.

In the context of our exercise, with a \( \text{pH} = 3.0 \), the hydrogen ion concentration becomes \( 10^{-3} \), which we use to calculate potential changes using the Nernst equation. This balance and conversion directly affect how much electrical work the electrochemical cell can perform and how its potential adjusts with varying pH levels.

Electrode Potential

Electrode potential refers to the voltage difference between an electrode and a reference electrode. It's a critical concept in predicting the direction and magnitude of electron flow in electrochemical cells.

• Calculated using the Nernst equation, the electrode potential shows how a cell's environment evolves and its internal electron flow dynamics.
• The Nernst equation adjusts the standard electrode potential \(E^0\) for any conditions that deviate from standard (1M, 25°C, and 1 atm). For the hydrogen electrode, \(E^0\) is 0 V.
• It includes terms for temperature (T), the universal gas constant (R), the number of electrons (n), and Faraday’s constant (F), helping translate chemical information into a linear scale of voltage.

When calculating electrode potential, understanding the logarithmic impact of concentration changes, such as from pH, becomes vital. Plugging the concentration values (derived from pH) into the Nernst equation gives us the real-time potential that a system helps us decide electronegative and electropositive paths in chemistry.