Problem 114 - Chemistry and Chemical Reactivity

Question

A (a) Is it easier to reduce water in acid or base? To evaluate this, consider the half-reaction \(2 \mathrm{H}_{2} \mathrm{O}(\ell)+2 \mathrm{e}^{-} \rightarrow 2 \mathrm{OH}^{-}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g})\) \(E^{*}=-0.83 \mathrm{V}\) (b) What is the reduction potential for water for solutions at \(\mathrm{pH}=7\) (neutral) and \(\mathrm{pH}=1\) (acid)? Comment on the value of \(E^{\circ}\) at \(\mathrm{pH}=1\)

Step-by-Step Solution

Answer

It is easier to reduce water in a neutral solution than in an acidic one, as \( E^{\circ} \) at \( \text{pH} = 1 \) is more negative.

Step 1: Review Basic Concepts

In electrochemistry, the ease of a redox reaction is described by its electrode potential. Higher electrode potential indicates greater ease for reduction.

Step 2: Understand Given Half-Reaction

The half-reaction provides the standard reduction potential, \( E^{*} = -0.83 \, \text{V} \), for the conversion of water to hydroxide ions and hydrogen gas.

Step 3: Apply the Nernst Equation

The actual reduction potential can be determined by using the Nernst Equation: \[E = E^* + \frac{0.0592}{n} \log Q\] where \( n \) is the number of moles of electrons transferred (which is 2 in this case) and \( Q \) is the reaction quotient.

Step 4: Calculate Reduction Potential at Different pH Levels

For \( \text{pH} = 7 \), we use the relationship \( Q = \left( \frac{[\text{OH}^-]^2}{[\text{H}_2]} \right) \) with \([\text{OH}^-] = 10^{-7}\) (neutral water), assuming \([H_2] = 1\):\[E = -0.83 + \frac{0.0592}{2} \log \left( 10^{-14} \right) = -0.83 - 0.41 = -1.24 \, \text{V}\]For \( \text{pH} = 1 \), with \([\text{OH}^-] = 10^{-13}\):\[E = -0.83 + \frac{0.0592}{2} \log \left( 10^{-26} \right) = -0.83 - 0.77 = -1.60 \, \text{V}\]

Step 5: Discuss Comparison

The reduction potential at \( \text{pH} = 1 \) is more negative compared to \( \text{pH} = 7 \), indicating that reduction is more difficult in acidic environments.

Key Concepts

Reduction Potential

In electrochemistry, reduction potential is a key concept that describes the tendency of a chemical species to acquire electrons and thereby be reduced. It is often expressed in volts (V), and a positive reduction potential signifies that a substance can readily accept electrons and undergo reduction.

• High reduction potential means the species is a good oxidizing agent.
• Low or negative reduction potential indicates it is less likely to gain electrons.

In the context of water reduction, the half-reaction is: \( 2 \text{H}_2\text{O}(\ell) + 2 \text{e}^- \rightarrow 2 \text{OH}^- (\text{aq}) + \text{H}_2(\text{g}) \), with a standard reduction potential \( E^* = -0.83 \text{V} \). This negative value means it is energy-intensive for water to gain electrons under standard conditions.

Nernst Equation

The Nernst Equation is a fundamental equation used to determine the reduction potential of a redox reaction under non-standard conditions. It accounts for changes in concentration, pressure, and temperature. The equation is given by: \[ E = E^* + \frac{0.0592}{n} \log Q \]
Here:

• \( E \) is the reduction potential under specific conditions.
• \( E^* \) is the standard reduction potential.
• \( n \) is the number of electrons transferred in the reaction (2 for the water reduction reaction).
• \( Q \) is the reaction quotient, reflecting the ratio of product and reactant concentrations.

By applying the Nernst Equation, we can evaluate how the potential changes with factors such as pH and concentrations, revealing more about the spontaneous nature of redox reactions in varied environments.

pH Effect on Redox Reactions

pH substantially impacts redox reactions, as it alters the concentration of hydrogen or hydroxide ions, thus affecting the reaction quotient \( Q \) in the Nernst Equation. This influence can shift the reduction potentials of reactions.

• In acidic environments (low pH), the concentration of hydrogen ions is high, which can make certain reductions harder.
• In basic environments (high pH), hydroxide ions dominate, potentially favoring reactions involving their consumption or formation.

For water's reduction: - At \( \text{pH} = 7 \), representative of neutral conditions, the reduction potential is \( -1.24 \text{V} \). - At \( \text{pH} = 1 \), a strongly acidic condition, the reduction potential further drops to \( -1.60 \text{V} \). This shows reduction is more difficult in acidic conditions because the potential becomes more negative, signifying lesser feasibility for electron uptake and reduction to occur. Understanding how pH affects redox reactions is crucial for applications like batteries, electroplating, and biological systems.