Problem 114 - Chemistry: The Central Science

Question

Gold metal dissolves in aqua regia, a mixture of concentrated hydrochloric acid and concentrated nitric acid. The standard reduction potentials \(\begin{aligned} \mathrm{Au}^{3+}(a q)+3 \mathrm{e}^{-}-\mathrm{Au}(s) & E_{\mathrm{red}}^{\circ} &=+1.498 \mathrm{~V} \\ \mathrm{AuCl}_{4}^{-}(a q)+3 \mathrm{e}^{-}--\rightarrow \mathrm{Au}(\mathrm{s})+4 \mathrm{Cl}^{-}(a q) & \\\ E_{\mathrm{red}}^{\circ} &=+1.002 \mathrm{~V} \end{aligned}\) are important in gold chemistry. (a) Use half-reactions to write a balanced equation for the reaction of Au and nitric acid to produce \(\mathrm{Au}^{3+}\) and \(\mathrm{NO}(\mathrm{g})\), and calculate the standard emf of this reaction. Is this reaction spontaneous? (b) Use half-reactions to write a balanced equation for the reaction of \(\mathrm{Au}\) and hydrochloric acid to produce \(\mathrm{AuCl}_{4}^{-}(a q)\) and \(\mathrm{H}_{2}(g)\), and calculate the standard emf of this reaction. Is this reaction spontaneous? (c) Use half-reactions to write a balanced equation for the reaction of Au and aqua regia to produce \(\mathrm{AuCl}_{4}^{-}(a q)\) and \(\mathrm{NO}(\mathrm{g})\), and calculate the standard emf of this reaction. Is this reaction spontaneous under standard conditions? (d) Use the Nernst equation to explain why aqua regia made from concentrated hydrochloric and nitric acids is able to dissolve gold.

Step-by-Step Solution

Answer

Reaction of Au with Nitric Acid (a): The standard emf is $+0.543~V$, making the reaction spontaneous. For the reaction of Au with Hydrochloric Acid (b): The standard emf is $+1.002~V$, also making the reaction spontaneous. For the reaction of Au with Aqua Regia (c): The standard emf is $+0.047~V$, making the reaction spontaneous under standard conditions. Use of Nernst Equation (d): For concentrated hydrochloric and nitric acids, the reaction quotient (Q) is less than 1. According to the Nernst equation, this causes the cell potential (E) to increase, making the dissolution of gold in aqua regia even more spontaneous.

Step 1: Identify the half-reactions involved in the process

For the reaction of gold with nitric acid, we are given that Au(s) and nitric acid react to produce Au⁠³⁺(aq) and NO(g). We have the reduction potential for the Au⁠³⁺/Au half-reaction. The nitric acid half-reaction needs to be determined.

Step 2: Find the half-reaction for nitric acid

The half-reaction for nitric acid converting to nitric oxide is: $$\mathrm{NO}_{3}^{-}(a q)+2 \mathrm{H}^{+}(a q)+1 \mathrm{e}^{-}\rightarrow \mathrm{NO}(\mathrm{g})+\mathrm{H}_2\mathrm{O}~~E_{\mathrm{red}}^{\circ} = +0.955~V$$

Step 3: Balance the half-reactions and calculate the standard emf

The balanced equation for the two half-reactions: Au⁠³⁺(aq) + 3e⁻ → Au(s) E⁰ = +1.498 V 3(NO₃⁻(aq) + 2H⁺(aq) + e⁻ → NO(g) + H₂O) × 3 E⁰ = +0.955 V Now, add the two half-reactions: Au(s) + 3NO₃⁻(aq) + 6H⁺(aq) → Au⁠³⁺(aq) + 3NO(g) + 3H₂O The standard emf for this reaction is: $$E^\circ = E_{\mathrm{red}}^{\circ} - E_{\mathrm{ox}}^{\circ} = (+1.498~\mathrm{V})-(+0.955~\mathrm{V}) = +0.543~\mathrm{V}$$

Step 4: Determine if the reaction is spontaneous

Since the standard emf is positive, this reaction is spontaneous under standard conditions. (b) Reaction of Au with Hydrochloric Acid

Step 1: Identify the half-reactions involved in the process

For the reaction of gold with hydrochloric acid, we are given that Au(s) and hydrochloric acid react to produce AuCl₄⁻(aq) and H₂(g). We have the reduction potential for the AuCl₄⁻/Au half-reaction. The hydrochloric acid half-reaction needs to be determined.

Step 2: Find the half-reaction for hydrochloric acid

The half-reaction for hydrochloric acid converting to hydrogen gas is: $$\mathrm{2 H}^{+}(a q)+2 \mathrm{e}^{-} \rightarrow \mathrm{H}_{2}(\mathrm{g})~~E_{\mathrm{red}}^{\circ} = +0.000~V$$

Step 3: Balance the half-reactions and calculate the standard emf

The balanced equation for the two half-reactions: AuCl₄⁻(aq) + 3e⁻ → Au(s) + 4Cl⁻ E⁰ = +1.002 V (2H⁺(aq) + 2e⁻ → H₂(g)) × 3 E⁰ = +0.000 V Now, add the two half-reactions: AuCl₄⁻(aq) + 6H⁺(aq) → Au(s) + 4Cl⁻ + 3H₂(g) The standard emf for this reaction is: $$E^\circ = E_{\mathrm{red}}^{\circ} - E_{\mathrm{ox}}^{\circ} = (+1.002~\mathrm{V})-(+0.000~\mathrm{V}) = +1.002~\mathrm{V}$$

Step 4: Determine if the reaction is spontaneous

Since the standard emf is positive, this reaction is spontaneous under standard conditions. (c) Reaction of Au with Aqua Regia

Step 1: Combine the previously found half-reactions for nitric and hydrochloric acids

We will use the AuCl₄⁻ half-reaction from part (b) and the nitric acid half-reaction from part (a). We can then balance the equation by multiplying the nitric acid half-reaction by 3, similar to part (a).

Step 2: Balance the half-reactions and calculate the standard emf

Adding the two balanced half-reactions: Au(s) + 4HNO₃(aq) + 6HCl(aq) → AuCl₄⁻(aq) + 3NO(g) + 2H₂O + 6H₂O The standard emf for this reaction is: $$E^\circ = E_{\mathrm{red}}^{\circ} - E_{\mathrm{ox}}^{\circ} = (+1.002~\mathrm{V})-(+0.955~\mathrm{V}) = +0.047~\mathrm{V}$$

Step 3: Determine if the reaction is spontaneous

Since the standard emf is positive, this reaction is spontaneous under standard conditions. (d) Explanation using the Nernst Equation

Step 1: Write down the Nernst Equation

The Nernst Equation is given by: $$E = E^\circ - \frac{RT}{nF} \ln Q$$ where E is the cell potential, R is the gas constant, T is the temperature, n is the number of moles of electrons involved in the reaction, F is the Faraday's constant, and Q is the reaction quotient.

Step 2: Apply the Nernst Equation to the reaction

For the reaction of gold with aqua regia, the concentration of reactants (hydrochloric and nitric acids) is significantly higher than the standard conditions. The reaction quotient, Q, will be much smaller than 1 due to the high concentration of reactants and low concentration of products. According to the Nernst Equation, if Q is smaller than 1, the cell potential (E) will be higher than the standard cell potential (E⁰). In this case, the potential E increases, making the reaction even more spontaneous. Therefore, gold dissolves in aqua regia made from concentrated hydrochloric and nitric acids because the reaction is spontaneous under these conditions, as illustrated by the Nernst Equation.

Key Concepts

Standard Electrode Potential

The standard electrode potential, commonly represented as \( E^\circ \), describes the inherent tendency of a chemical species to acquire electrons. This is an integral concept of electrochemistry, helping us understand how easily ions are reduced to their elemental state. A more positive standard electrode potential means the element has a strong tendency to gain electrons. For instance, in the case of our exercise, the reduction potential for the reaction of \( \text{Au}^{3+} \) to gold metal is +1.498 V. This indicates gold's strong ability to attract electrons and reduce to its metallic form. Understanding these potentials is crucial for determining whether a reaction is spontaneous. The more pronounced the positive value, the more favorable the reduction process. This is especially relevant in the reactions involved in dissolving gold in aqua regia, where the ability for gold ions to reduce is compared against the oxidizing power of aqua regia constituents.

Nernst Equation

The Nernst Equation provides a way to calculate the cell potential of an electrochemical reaction under non-standard conditions. Unlike standard electrode potentials, which assume 1 M concentrations, real-world reactions often occur under different conditions, necessitating this formula. Given by \[ E = E^\circ - \frac{RT}{nF} \ln Q \], where:

• \(E\) is the cell potential under non-standard conditions
• \(R\) is the universal gas constant (8.314 J/mol·K)
• \(T\) is the temperature in Kelvin
• \(n\) is the number of moles of electrons transferred
• \(F\) is Faraday's constant (96,485 C/mol e⁻)
• \(Q\) is the reaction quotient

This equation shows us that increased concentrations of reactants boost the cell potential. In the context of aqua regia dissolving gold, the elevated concentrations of concentrated hydrochloric and nitric acids significantly increase the reactivity, impacting spontaneity as per the Nernst Equation.

Redox Reactions

Redox reactions, or reduction-oxidation reactions, are chemical processes where the oxidation state of atoms are changed through the transfer of electrons. In the realm of electrochemistry, they are the backbone of generating electrical energy from chemical reactions.Every redox reaction consists of two half-reactions: oxidation and reduction. In oxidation, a species loses electrons, whereas in reduction, a species gains electrons. Balancing these two half-reactions is key to understanding electrochemical reactions. In our exercise, we explore how gold can be transformed through reactions with nitric and hydrochloric acids. These reactions change the oxidation states of gold from metallic gold (\( ext{Au} \)) to various ionic forms, facilitating electron exchange crucial for the process.Being familiar with redox reactions enables us to decipher complex electrochemical processes like those found in aqua regia's reaction with gold.

Spontaneity of Reactions

Spontaneity of electrochemical reactions addresses whether or not a reaction can occur on its own. This concept is largely determined by the standard electromotive force (emf) of a reaction. A positive emf indicates a spontaneous reaction under standard conditions. For example, in the exercise, we calculated a positive emf for each of the reactions involving gold, implying that the reactions will efficiently proceed on their own.Spontaneity can also be analyzed using the Nernst Equation under non-standard conditions. The cell potential \( E \) in such a scenario can tilt the spontaneity by factoring in concentrations and temperature.Ultimately, understanding spontaneity helps students determine the feasibility of electrochemical processes. This is especially pertinent to the reactions between gold and aqua regia, where high reactivity of the acids ensures the spontaneous dissolution of gold.