Problem 142 - A Complete Resource Book in Chemistry for JEE Main

Question

The reversible reduction potential of pure water is \(-0.413 \mathrm{~V}\) under \(1.00 \mathrm{~atm} \mathrm{H}_{2}\) pressure. If the reduction is considered to be \(2 \mathrm{H}^{+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_{2}\), calculate \(\mathrm{pH}\) of pure water. (a) 6 (b) 7 (c) 3 (d) 5

Step-by-Step Solution

Answer

The pH of pure water is 7.

Step 1: Understanding the Nernst Equation

The Nernst equation is used to relate the reduction potential at any condition to the standard reduction potential, temperature, and concentrations of reactants and products. The equation is given by: \[ E = E^0 - \frac{RT}{nF} \ln \left( \frac{[products]}{[reactants]} \right) \]For the given reaction \(2 \text{H}^+ + 2\text{e}^- \rightarrow \text{H}_2\), this reduces to:\[ E = E^0 - \frac{0.0592}{2} \log \left( \frac{1}{(\text{H}^+)^2} \right) \]where \(E^0\) is the standard reduction potential and \(E\) is the given potential (-0.413 V). In pure water, \(E^0 = 0\) V for the standard hydrogen electrode.

Step 2: Setting Up the Nernst Equation for Pure Water

In pure water, the concentration of hydrogen ions [H extsuperscript{+}] can be expressed in terms of pH: \([H extsuperscript{+}] = 10^{-\text{pH}}\). Substituting into the Nernst equation gives:\[ -0.413 = 0 - \frac{0.0592}{2} \log \left( 10^{2\cdot \text{pH}} \right) \]

Step 3: Simplifying the Equation

The equation can be simplified further:\[ -0.413 = -0.0592 \cdot \text{pH} \]By solving for pH, we can rearrange the equation as:\[ \text{pH} = \frac{-0.413}{-0.0592} \]

Step 4: Calculating the pH

Carrying out the division gives:\[ \text{pH} = \frac{0.413}{0.0592} \approx 6.975 \]This value rounds to the nearest whole number which is 7.

Key Concepts

Reversible Reduction Potential

In electrochemistry, the concept of reversible reduction potential is crucial. It refers to the ability of a chemical species to gain electrons and be reduced. This potential is directly linked to the notion of equilibrium in redox reactions. Understanding it helps us predict the direction of redox reactions and analyze their energetics.

The reversible reduction potential is often measured relative to the Standard Hydrogen Electrode (SHE). This measurement involves electrode systems under standard conditions, typically 1 M concentration and 1 atm pressure. What's more interesting is the role of reversible reduction potential in altering with any deviation from these conditions, like changes in temperature or concentration.

This potential is crucial when performing calculations with the Nernst equation, a powerful tool to determine how changes in conditions affect the potential. When you understand reversible reduction potential properly, you can predict how different chemical species will behave under non-standard conditions.

pH Calculation

pH measures the acidity or basicity of a solution. A deep understanding of pH calculation is important when using the Nernst equation for reactions involving hydrogen ions \(\text{H}^{+}\).

• The \(\text{pH}\) value is defined as \(\text{pH} = -\log[\text{H}^{+}]\).
• At 25°C, pure water has a neutral pH of 7 because the concentration of hydrogen ions \( [\text{H}^{+}] = 10^{-7} \, \text{M}\).
• This neutral point shifts with temperature, but it’s usually around 7.

The pH level of a solution can dramatically influence the chemical processes and it represents the solution's equilibrium with hydrogen ions.

When the potential is determined by the Nernst equation, substituting the equation with hydrogen ion concentration leads us directly to the calculation of pH. This relationship allows chemists to predict the acidity or basicity of unknown solutions through electrochemical measurements.

Standard Hydrogen Electrode

The Standard Hydrogen Electrode (SHE) is a pivotal reference electrode in electrochemical reactions. It establishes a base point for measuring electrode potentials and is conventionally assigned a potential of 0 volts under standard conditions.

SHE relies on the basic reaction: \(2\text{H}^{+} + 2\text{e}^{-} \rightarrow \text{H}_{2}\). This reaction is used to determine the electrode potentials of other substances in a cell. Here are the conditions used:

• 1 M hydrogen ion concentration.
• 1 atm pressure for hydrogen gas.
• 25°C temperature.

SHE provides a reliable and repeatable standard. This base ensures that measurements of cell potential are consistent and comparable across different experiments and research studies. Understanding SHE is crucial for comprehending many electrochemical processes, including those described by the Nernst equation in calculating potentials outside standard conditions.