Question

Consider the standard galvanic cell based on the following halfreactions: $$\begin{array}{r}\mathrm{Cu}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Cu} \\ \mathrm{Ag}^{+}+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}\end{array}$$ The electrodes in this cell are \(\mathrm{Ag}(s)\) and \(\mathrm{Cu}(s)\). Does the cell potential increase, decrease, or remain the same when the following changes occur to the standard cell? a. \(\operatorname{CuSO}_{4}(s)\) is added to the copper half-cell compartment (assume no volume change). b. \(\mathrm{NH}_{3}(a q)\) is added to the copper half-cell compartment. [Hint: \(\mathrm{Cu}^{2+}\) reacts with \(\mathrm{NH}_{3}\) to form \(\left.\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}(a q) .\right]\) c. \(\mathrm{NaCl}(s)\) is added to the silver half-cell compartment. [Hint: \(\mathrm{Ag}^{+}\) reacts with \(\mathrm{Cl}^{-}\) to form \(\left.\mathrm{AgCl}(s) .\right]\) d. Water is added to both half-cell compartments until the volume of solution is doubled. e. The silver electrode is replaced with a platinum electrode. $$\mathrm{Pt}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Pt} \quad \mathscr{E}^{\circ}=1.19 \mathrm{~V}$$

Short answer

a. The cell potential will increase. b. The cell potential will decrease. c. The cell potential will decrease. d. The cell potential remains the same. e. The cell potential remains the same.

Step-by-step solution

a. Adding CuSO4 to the copper half-cell

When CuSO4 is added to the copper half-cell, the concentration of Cu^{2+} ions will increase in the compartment. According to the Nernst equation, an increase in Cu^{2+} ions concentration will produce an increase in cell potential. Therefore, the cell potential will increase.

b. Adding NH3(aq) to the copper half-cell

When NH3 is added to the copper half-cell compartment, the Cu^{2+} ions react with NH3 to form Cu(NH3)_{4}^{2+} ions, decreasing the initial concentration of the Cu^{2+} ions. According to the Nernst equation, a decrease in Cu^{2+} ions concentration will produce a decrease in cell potential. Therefore, the cell potential will decrease.

c. Adding NaCl to the silver half-cell

When NaCl is added to the silver half-cell, the Ag^{+} ions will react with Cl^{-} ions to form AgCl(s), which results in decreasing the concentration of Ag^{+} ions in the silver half-cell compartment. According to the Nernst equation, a decrease in Ag^{+} ions concentration will produce a decrease in cell potential. Therefore, the cell potential will decrease.

d. Doubling the volume of both half-cell compartments

When the volume of both half-cell compartments is doubled, the concentrations of the ions will be halved. According to the Nernst equation, halving the concentrations in both compartments will not change the cell potential, since the ratio of the ion concentrations remains the same. Therefore, the cell potential remains the same or unchanged.

e. Replacing the silver electrode with a platinum electrode

When the silver electrode is replaced with a platinum electrode, the half-reaction involving the silver ions is not directly affected. The cell potential depends on the half-reactions and not the electrode material, as long as the electrode is inert and allows electron transfer. Therefore, the cell potential remains the same.

Key concepts

Nernst Equation

The Nernst equation is a fundamental tool in electrochemistry that helps us calculate the cell potential of a galvanic cell under non-standard conditions. This equation takes into account the effect of ion concentrations on cell potential. It is given by:\[E = E^\circ - \frac{RT}{nF} \ln Q\]where:

• \(E\) is the cell potential at non-standard conditions.
• \(E^\circ\) is the standard cell potential.
• \(R\) is the universal gas constant.
• \(T\) is the temperature in Kelvin.
• \(n\) is the number of moles of electrons transferred in the half-reaction.
• \(F\) is Faraday's constant.
• \(Q\) is the reaction quotient, which is the ratio of product concentrations to reactant concentrations.

The Nernst equation allows us to predict changes in cell potential when the concentration of ions in the cell changes. For instance, adding CuSO₄ to the copper half-cell increases the concentration of Cu²⁺ ions, leading to an increase in cell potential according to this equation.

Cell Potential

Cell potential, denoted by \(E\), is a measure of the electromotive force generated by a galvanic cell. It essentially indicates the cell’s ability to drive an electric current. The larger the cell potential, the greater the voltage the cell can produce. Cell potential is influenced by various factors:

• Concentration of ions: A change in ion concentration can affect the cell potential significantly. For example, the decrease in Cu²⁺ concentration due to the reaction with NH₃ results in a decreased cell potential.
• Temperature: Although frequently considered constant for simplicity, variations in temperature can alter cell potential.
• Nature of electrodes: While the electrode material usually doesn't affect the potential directly unless it participates in the reaction, it provides the surface for electron exchange.

In standard conditions (1 M concentration, 1 atm pressure, and 25°C), the standard cell potential \(E^\circ\) can be calculated from the standard potentials of the two half-reactions involved.

Half-Reactions

Half-reactions are the foundation of understanding galvanic cells. They represent the oxidation and reduction processes separately. In the copper-silver galvanic cell discussed, the key half-reactions are:

• Copper half-reaction: \(\mathrm{Cu}^{2+} + 2\mathrm{e}^- \rightarrow \mathrm{Cu}\)
• Silver half-reaction: \(\mathrm{Ag}^+ + \mathrm{e}^- \rightarrow \mathrm{Ag}\)

Oxidation occurs at the anode, and reduction at the cathode, producing distinct half-reactions.
Understanding these reactions is crucial because they determine how electrons flow through the circuit. The concentration of the reactants and products in each half-reaction can shift according to Le Chatelier's Principle, affecting cell potential through the Nernst Equation.
For instance, the addition of NaCl to the silver half-cell reduces the concentration of Ag⁺ ions by forming AgCl, thus lowering cell potential.

Electrode Material

Electrode material in a galvanic cell plays a vital role, though it is important to distinguish between reactive and inert electrodes. Inert electrodes, like platinum, do not participate in chemical reactions. They merely facilitate electron flow.
In the given exercise, replacing a silver electrode with platinum does not change the cell potential as the reaction continues unaffected. The silver ions in solution still get reduced to silver atoms, which can get deposited on platinum because it's a good conductor.

• Metallic Electrodes: These often participate in half-reactions, like Cu in the copper half-reaction.
• Inert Electrodes: Such as platinum, they provide a surface for the reaction without altering it, beneficial in scenarios where strong oxidizing or reducing conditions exist.

Choice of electrode can depend on factors like cost, availability, and especially the need for resistance to corrosion and chemical reactivity. In many cases, platinum is used in academic settings for its inertness and reliability.