Problem 73 - Chemistry and Chemical Reactivity

Question

In the electrolysis of \(\mathrm{HNO}_{3}(\mathrm{aq}),\) hydrogen is produced at the cathode. According to a table of reduction potentials, \(\mathrm{NO}_{3}^{-}(\mathrm{aq})\) is easier to reduce than \(\mathrm{H}^{+}(\mathrm{aq}) .\) Suggest a possible reason why \(\mathrm{H}_{2}\) formed rather than NO. What is the product formed at the anode? Write an equation for the anode reaction.

Step-by-Step Solution

Answer

Hydrogen forms due to kinetic factors; oxygen forms at the anode with water oxidation.

Step 1: Analyze the Reduction Potentials

Look up the reduction potentials of the species involved. The reduction potential for \( \mathrm{NO}_{3}^{-} \) is more positive than that of \( \mathrm{H}^{+} \), making \( \mathrm{NO}_{3}^{-} \) thermodynamically favored to be reduced over \( \mathrm{H}^{+} \). However, kinetic factors or reaction overpotential influences actual reactions during electrolysis.

Step 2: Consider Kinetic Factors

Even if \( \mathrm{NO}_{3}^{-} \) has a more favorable reduction potential, kinetic barriers might prevent its reduction. High activation energy or slow reaction kinetics can make \( \mathrm{H}^{+} \) reduction more feasible, leading to hydrogen formation despite unfavorable thermodynamics.

Step 3: Identify Anode Reaction

At the anode, oxidation occurs. Given that the solution is \( \mathrm{HNO}_{3} \), water or nitrate ions might participate in oxidation. Typically, water is oxidized to produce oxygen gas \( \mathrm{O}_{2} \), as the oxidation of water is common under standard conditions.

Step 4: Write Anode Reaction Equation

The half-reaction for water oxidation is: \[ 2\mathrm{H}_{2}\mathrm{O}(\mathrm{l}) \rightarrow \mathrm{O}_{2}(\mathrm{g}) + 4\mathrm{H}^{+}(\mathrm{aq}) + 4\mathrm{e}^{-} \]. This is the likely reaction at the anode.

Key Concepts

Reduction Potentials

Reduction potentials are essential in understanding why certain reactions occur during electrolysis. These potentials indicate the tendency of a chemical species to gain electrons and be reduced. Substances with more positive reduction potentials are more likely to be reduced. So, according to their reduction potential values,

• \( \mathrm{NO}_{3}^{-} \)
• \( \mathrm{H}^{+} \)

it could seem that nitrate ions should be reduced before hydrogen ions. However, even with these calculable tendencies, thermodynamics don't always predict the actual outcome due to other influencing factors.

Kinetic Factors

Kinetic factors greatly influence which reactions occur during electrolysis, even when reduction potentials suggest otherwise. A reaction might be thermodynamically favored, but if it has slow reaction kinetics or high activation energy, it may not proceed easily.
For example, in our scenario involving the electrolysis of \( \mathrm{HNO}_{3} \), the conversion of \( \mathrm{NO}_{3}^{-} \) to \( \mathrm{NO} \) may face kinetic hindrances. This includes needing high energy or time to overcome reaction barriers. Consequently, the reduction of \( \mathrm{H}^{+} \) ions, even though less favorable thermodynamically compared to \( \mathrm{NO}_{3}^{-} \), occurs more readily.

Anode Reaction

During electrolysis, oxidation occurs at the anode, where electrons are released. In the case of an aqueous \( \mathrm{HNO}_{3} \) solution, the substances available for oxidation include water and nitrate ions.
Typically, water is the more likely candidate for oxidation under these conditions. This is because

• water is more abundant,
• its oxidation is energetically feasible.

While theoretically, nitrate ions could also oxidize, the more straightforward \(\text{oxidation of water prevails due to common practices and energetics.}\)

Hydrogen Production

Despite the thermodynamic preference for the reduction of \( \mathrm{NO}_{3}^{-} \) ions, hydrogen production is observed at the cathode during the electrolysis of \( \mathrm{HNO}_{3} \). This occurs due to the kinetic factors discussed earlier.
Less energy and a faster reaction route for the

• reduction of hydrogen ions to form hydrogen gas,

ultimately determine which reaction predominates. The presence of electrolytic conditions further helps bypass the thermodynamic hurdles, enabling hydrogen gas evolution even when it seems less favored at first glance.

Water Oxidation

Water oxidation is a critical reaction occurring at the anode during the electrolysis of \( \mathrm{HNO}_{3} \). This process involves the conversion of water molecules into oxygen gas, protons, and electrons, following the chemical equation:\[2\mathrm{H}_{2}\mathrm{O}(\mathrm{l}) \rightarrow \mathrm{O}_{2}(\mathrm{g}) + 4\mathrm{H}^{+}(\mathrm{aq}) + 4\mathrm{e}^{-}\]This reaction is both common and favored in aqueous solutions because

• it generates crucial products like oxygen and protons,
• maintains overall charge balance in the system.

By allowing water to oxidize, the system ensures the continued facilitation of electron flow, necessary for the electrolytic process to proceed efficiently.