Question

Select the correct cell reaction of the cell \(\mathrm{Ag}(s)\left|\mathrm{Ag}^{+}(a q) \| \mathrm{Cu}^{2+}(a q)\right| \mathrm{Cu}(s)\) : (a) \(2 \mathrm{Ag}(s)+\mathrm{Cu}(s) \longrightarrow \mathrm{Cu}^{+2}(a q)+2 \mathrm{Ag}^{+}(a q)\) (b) \(\mathrm{Cu}(s)+2 \mathrm{Ag}^{+}(a q) \longrightarrow \mathrm{Cu}^{2+}(a q)+2 \mathrm{Ag}(s)\) (c) \(2 \mathrm{Ag}(s)+\mathrm{Cu}^{2+}(a q) \longrightarrow \mathrm{Cu}(s)+2 \mathrm{Ag}^{+}(a q)\) (d) \(\mathrm{Cu}^{2+}(a q)+2 \mathrm{Ag}^{+}(a q) \longrightarrow 2 \mathrm{Ag}(s)+\mathrm{Cu}(s)\)

Short answer

Option (c) is the correct cell reaction for the cell: \(2 \mathrm{Ag}(s) + \mathrm{Cu}^{2+}(a q) \rightarrow \mathrm{Cu}(s) + 2 \mathrm{Ag}^{+}(a q)\).

Step-by-step solution

Understand the galvanic cell setup

The given cell representation is of a galvanic cell where reduction takes place at the cathode (right side) and oxidation occurs at the anode (left side). For the cell notation \(\mathrm{Ag}(s) | \mathrm{Ag}^{+}(a q) \| \mathrm{Cu}^{2+}(a q)| \mathrm{Cu}(s)\)), silver \(\mathrm{Ag}\)) is the anode and copper \(\mathrm{Cu}\)) is the cathode. The silver electrode gets oxidized and the copper ions in solution get reduced.

Write down the half-reactions

The oxidation half-reaction at the anode is \(\mathrm{Ag}(s) \rightarrow \mathrm{Ag}^{+}(a q) + e^{-}\), and the reduction half-reaction at the cathode is \(\mathrm{Cu}^{2+}(a q) + 2e^{-} \rightarrow \mathrm{Cu}(s)\). These half-reactions happen simultaneously to maintain charge balance.

Combine the half-reactions to form the full cell reaction

Combine the oxidation and reduction half-reactions to form the full cell reaction, ensuring that electrons are balanced. \(2\mathrm{Ag}(s) \rightarrow 2\mathrm{Ag}^{+}(a q) + 2e^{-}\) (anode reaction) and \(\mathrm{Cu}^{2+}(a q) + 2e^{-} \rightarrow \mathrm{Cu}(s)\) (cathode reaction) combine to give \(2\mathrm{Ag}(s) + \mathrm{Cu}^{2+}(a q) \rightarrow 2\mathrm{Ag}^{+}(a q) + \mathrm{Cu}(s)\) which is overall cell reaction.

Key concepts

Electrochemical Cells

Understanding electrochemical cells is crucial when studying how galvanic cells operate. An electrochemical cell is a device that generates electrical energy from a chemical reaction. It consists of two different metals, or electrodes, immersed in electrolyte solutions. These electrodes are connected by a wire and a salt bridge that complete the circuit and allow for ion exchange, respectively.

Two main types of electrochemical cells are galvanic cells, also known as voltaic cells, and electrolytic cells. Galvanic cells convert chemical energy into electrical energy through spontaneous redox reactions, while electrolytic cells use electrical energy to drive non-spontaneous reactions. The galvanic cell described in the exercise involves silver and copper electrodes and operates due to the different tendencies of these metals to donate or accept electrons.

Redox Reactions

Redox reactions are chemical processes where one substance is reduced (gains electrons) and another is oxidized (loses electrons). In a galvanic cell, these reactions occur at two separate electrodes. The substance that loses electrons is being oxidized, which happens at the anode, and the substance gaining electrons is being reduced, occurring at the cathode.

The ability to recognize oxidation and reduction is key to understanding how galvanic cells function. Remember the OIL RIG mnemonic: Oxidation Is Loss, Reduction Is Gain of electrons. When breaking down the reaction occurring in the exercise, you'll notice one metal is oxidized by releasing electrons, and the other metal is reduced by gaining those electrons, thus allowing the electric current to flow through an external circuit.

Half-Reactions

Half-reactions are used to split the overall redox reaction into two separate processes: the oxidation half-reaction and the reduction half-reaction. This makes it easier to balance the reactions, especially when dealing with complex equations. In a galvanic cell, the oxidation half-reaction occurs at the anode, and the reduction half-reaction happens at the cathode.

For example, in the given exercise, the oxidation of silver occurs at the anode, forming silver ions and releasing electrons. Conversely, at the cathode, copper ions gain electrons and are reduced to solid copper. These half-reactions are essential to understand because they illustrate how the electrons flow from one electrode to the other, facilitating the current that powers devices.

Anode and Cathode Processes

In the context of galvanic cells, anodes and cathodes are the sites where oxidation and reduction occur, respectively. The anode is always the electrode where oxidation takes place. During this process, the metal loses electrons and enters the solution as positively charged ions. The electrons then travel through an external circuit to the cathode.

At the cathode, the reduction occurs. Here, ions in the solution gain electrons and are deposited onto the electrode as solid metal. It's important to note that in a galvanic cell, the anode has a negative charge because it's the source of electrons, while the cathode is positive as it receives electrons. The exercise demonstrates this concept through the behavior of silver and copper in the provided galvanic cell.