Question

Consider the following reduction potentials: $$\begin{array}{ll}{\mathrm{Co}^{3+}+3 \mathrm{e}^{-} \longrightarrow \mathrm{Co}} & {\mathscr{E}^{\circ}=1.26 \mathrm{V}} \\ {\mathrm{Co}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Co}} & {\mathscr{E}^{\circ}=-0.28 \mathrm{V}}\end{array}$$ a. When cobalt metal dissolves in 1.0\(M\) nitric acid, will \(\mathrm{Co}^{3+}\) or \(\mathrm{Co}^{2+}\) be the primary product (assuming standard conditions)? b. Is it possible to change the concentration of \(\mathrm{HNO}_{3}\) to get a different result in part a? Concentrated \(\mathrm{HNO}_{3}\) is about 16 \(M\) .

Short answer

When cobalt metal dissolves in 1.0 M nitric acid under standard conditions, Co³⁺ will be the primary product. It is not possible to change this result by increasing the concentration of HNO₃, as even with concentrated HNO₃ (16 M), Co³⁺ will still be the primary product.

Step-by-step solution

Write the redox reaction with nitric acid

First, let's write the redox reaction that occurs when cobalt metal dissolves in nitric acid: \[2\mathrm{Co} + 6\mathrm{H}^+ + 6\mathrm{NO}_3^- \longrightarrow 2\mathrm{Co}^n+ + 6\mathrm{NO}_2 + 3\mathrm{H}_2\mathrm{O}\] Here, n is either 2 or 3, so we'll have to find out which cobalt ion, Co²⁺ or Co³⁺, will be the primary product.

Calculate E₀cell for both Co²⁺ and Co³⁺

Now we'll calculate the E₀cell for both possible reactions: For the Co³⁺/Co reaction: \[E^\circ_{cell} = E^\circ_{Co^{3+}/Co} = 1.26\ \mathrm{V}\] For the Co²⁺/Co reaction: \[E^\circ_{cell} = E^\circ_{Co^{2+}/Co} = -0.28\ \mathrm{V}\]

Use the Nernst equation to calculate the reduction potential for both reactions at 1.0 M HNO₃

The Nernst equation is given by: \[E = E^\circ - \frac{RT}{nF} \ln Q\] Let's plug in the reduction potentials, concentrations, and constants for both reactions: For Co³⁺/Co: \[E_{Co^{3+}/Co} = 1.26\ \mathrm{V} - \frac{8.314 \times 298\ \mathrm{K}}{3 \times 96485\ \mathrm{C/mol}} \ln\frac{[Co^{3+}]}{[Co]} = 1.26\ \mathrm{V}\] For Co²⁺/Co: \[E_{Co^{2+}/Co} = -0.28\ \mathrm{V} - \frac{8.314 \times 298\ \mathrm{K}}{2 \times 96485\ \mathrm{C/mol}} \ln\frac{[Co^{2+}]}{[Co]} = -0.28\ \mathrm{V}\] Since the concentration of Co remains constant in both reactions, we can compare them directly. The larger potential is for the Co³⁺/Co reaction, so Co³⁺ is the primary product under standard conditions.

Answer to part (a)

When cobalt metal dissolves in 1.0 M nitric acid under standard conditions, Co³⁺ will be the primary product.

Repeat the Nernst equation calculations for 16 M HNO₃

Now let's see if the result would change using concentrated HNO₃ (16 M). For Co³⁺/Co, keep its E unchanged: \[E_{Co^{3+}/Co} = 1.26\ \mathrm{V}\] For Co²⁺/Co, use the Nernst equation with 16 M HNO₃: \[E_{Co^{2+}/Co} = -0.28\ \mathrm{V} - \frac{8.314 \times 298\ \mathrm{K}}{2 \times 96485\ \mathrm{C/mol}} \ln\frac{[Co^{2+}]}{[Co]}\] The change in concentration of nitric acid does not affect the Nernst equation for Co²⁺/Co because it doesn't appear in the equation. Therefore, the calculated potential remains -0.28 V.

Answer to part (b)

It is not possible to change the result in part (a) by changing the concentration of HNO₃. Even with concentrated HNO₃ (16 M), Co³⁺ will still be the primary product when cobalt metal dissolves in nitric acid.

Key concepts

Reduction Potentials

Reduction potentials are essential in electrochemistry, helping to predict the direction of redox reactions. In simple terms, a reduction potential, denoted as \(E^\circ\), measures the tendency of a chemical species to be reduced. It is often given in volts (V).

A positive standard reduction potential indicates a greater tendency to gain electrons, thus being reduced. Conversely, a negative value suggests a preference to lose electrons, or oxidize. Hence, in our cobalt example,

• The reaction \(\text{Co}^{3+} + 3\text{e}^- \rightarrow \text{Co}\) has a reduction potential of \(1.26\,\text{V}\).
• The reaction \(\text{Co}^{2+} + 2\text{e}^- \rightarrow \text{Co}\) has a reduction potential of \(-0.28\,\text{V}\).

This means that \(\text{Co}^{3+}\) has a stronger tendency to be reduced to cobalt metal than \(\text{Co}^{2+}\) does. As a result, when cobalt metal interacts with nitric acid, \(\text{Co}^{3+}\) forms more readily.

Knowing reduction potentials allows us to predict which species will behave as oxidizing agents (accepting electrons) and which will behave as reducing agents (donating electrons).

Nernst Equation

The Nernst equation is a powerful tool in electrochemistry used to calculate the cell potential under non-standard conditions. It accounts for the effect of concentration on cell potentials. The equation is expressed as:\[ E = E^\circ - \frac{RT}{nF} \ln Q \] where:

• \(E\) is the cell potential under non-standard conditions.
• \(E^\circ\) is the standard cell potential.
• \(R\) is the universal gas constant (8.314 J/mol K).
• \(T\) is the temperature in Kelvin.
• \(n\) is the number of moles of electrons exchanged.
• \(F\) is the Faraday constant (96485 C/mol).
• \(Q\) is the reaction quotient, representing the ratio of product concentrations to reactant concentrations.

In the given problem, the Nernst equation demonstrates that changing the concentration of \(\text{HNO}_3\) doesn’t affect the potential for the \(\text{Co}^{2+}/\text{Co}\) couple because it doesn’t appear in the reaction quotient for this reaction. Consequently, even with the increased concentration of \(\text{HNO}_3\), the potential for \(\text{Co}^{2+}/\text{Co}\) remains constant, confirming \(\text{Co}^{3+}\) as the dominant product.

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, are chemical processes where electrons are transferred between substances. They play a crucial role in energy production and resource cycling in nature and technology.Key aspects of redox reactions include:

• Reduction: The gain of electrons by a molecule, atom, or ion.
• Oxidation: The loss of electrons.
• Oxidizing agent: A substance that gains electrons (is reduced itself).
• Reducing agent: A substance that loses electrons (is oxidized itself).

In the context of the cobalt and nitric acid reaction, cobalt metal acts as a reducing agent. When it dissolves in nitric acid, cobalt ions (\(\text{Co}^{3+}\) and \(\text{Co}^{2+}\)) are generated. The net transfer of electrons determines which cobalt species predominates.Identifying and balancing redox reactions require understanding the electron flow, which is depicted through oxidation states and half-equations. This aids in predicting reaction spontaneity and product formation.