A voltaic cell is constructed with two \(\mathrm{Zn}^{2+}-\) Zn electrodes. The two half-cells have \(\left[\mathrm{Zn}^{2+}\right]=1.8 M\) and \(\left[\mathrm{Zn}^{2+}\right]=1.00 \times 10^{-2} M,\) respectively. (a) Which electrode is the anode of the cell? (b) What is the standard emf of the cell? (c) What is the cell emf for the concentrations given? (d) For each electrode, predict whether \(\left[\mathrm{Zn}^{2+}\right]\) will increase, decrease, or stay the same as the cell operates.

A voltaic cell, also known as a galvanic cell, is a type of electrochemical cell that generates electrical energy from spontaneous redox reactions occurring within the cell. It consists of two different metals connected by a salt bridge or a porous membrane and immersed in electrolyte solutions.

The essential function of a voltaic cell is to convert chemical energy into electrical energy. Each metal in the cell acts as an electrode: one is the anode, where oxidation occurs, and the other is the cathode, where reduction takes place. When connected in a circuit, electrons flow from the anode to the cathode through an external wire, producing an electric current.

Anode and Cathode in Voltaic Cells

The electrode where oxidation (loss of electrons) occurs is called the anode, while the electrode where reduction (gain of electrons) takes place is known as the cathode. The flow of electrons from anode to cathode is driven by the potential difference between the two electrodes.

The Nernst equation is a fundamental equation in electrochemistry that calculates the electromotive force (emf) of a cell under non-standard conditions. It shows the relationship between the cell potential and the reaction quotient, taking into account temperature and concentrations of reactants and products.

The equation is given as: \(E = E^\circ - \frac{RT}{nF} \ln{Q}\), where \(E\) is the cell potential under non-standard conditions, \(E^\circ\) is the standard emf of the cell, \(R\) is the universal gas constant, \(T\) is the temperature in Kelvin, \(n\) is the number of moles of electrons transferred in the reaction, \(F\) is the Faraday constant, and \(Q\) is the reaction quotient which reflects the ratio of product to reactant concentrations at any moment.

Redox reactions are chemical reactions involving the transfer of electrons between two species. An oxidation-reduction reaction comprises two half-reactions: oxidation, where a substance loses electrons, and reduction, where a substance gains electrons.

These reactions are fundamental to the operation of electrochemical cells. In the context of the cell, the anode sees oxidation as the loss of electrons occurs, while the cathode experiences reduction as it gains electrons. The flow of electrons through the external circuit is what powers the cell and makes it capable of doing electrical work.

The standard emf (electromotive force) of an electrochemical cell, denoted as \(E^\circ\), is the voltage or potential difference between two half-cells when they are in their standard states, which usually means solutes at 1 M concentration, gases at 1 bar pressure, and at a temperature of 25°C (298 K).

Standard emf is a measure of how far from equilibrium the cell reaction is when reactants and products are in their standard states. It is obtained by adding the standard reduction potentials of the two half-cells. However, if the two half-cells are identical, as in the given exercise, the standard emf is 0 V because there is no inherent tendency for electron transfer between identical materials.

The reaction quotient, \(Q\), mentioned in the Nernst equation, represents the ratio of the concentrations of the reaction products to the concentrations of the reactants at any given point in time. For a generic reaction, \(a\text{A} + b\text{B} \rightarrow c\text{C} + d\text{D}\), the reaction quotient is expressed as: \(Q = \frac{[C]^c [D]^d}{[A]^a [B]^b}\), where square brackets denote concentration.In an electrochemical cell, \(Q\) helps in calculating the voltage at any set of concentrations, not just when the system is at equilibrium. It reflects how the dynamic state of the cell changes as the reaction proceeds, which affects the cell's potential.

Identifying the anode and cathode in an electrochemical cell is crucial for understanding its operation. The anode is where the oxidation happens, and it is marked by a loss of electrons. Conversely, the cathode is the site of reduction, where a gain of electrons occurs.

In the solved exercise, the anode was determined by identifying which electrode had a lower concentration of \(Zn^{2+}\) ions, as the increased room for more ions will drive the spontaneous oxidation of zinc metal at that electrode. Conversely, the cathode was identified by the higher \(Zn^{2+}\) ion concentration, favoring the reduction of zinc ions to solid zinc. Through such analysis, we can anticipate the direction of electron flow which defines anode and cathode identities.