# Galvanic Cells

### What Is a Galvanic Cell?

Galvanic cells, also called voltaic cells, are physical setups in which oxidation-reduction reactions can produce an electric current.

Redox reactions, in which one species loses electrons while another species gains them, can be divided into half-reactions. In practical application, the species involved can be physically divided into half-cells. These reactions can be demonstrated using a system called an electrochemical cell that either produces or uses electrical energy.

A galvanic cell, also called a voltaic cell, is an electrochemical cell formed when metal strips connected by a wire are immersed in different solutions and the solutions are connected by a salt bridge. Each metal strip in the galvanic cell is an electrode, an electrical conductor through which current enters or leaves an electrochemical cell. The anode is the electrode where the oxidation half-reaction takes place. The cathode is the electrode where the reduction half-reaction takes place. The solutions contain aqueous ions of the two electrodes. The salt bridge is an inert connection between the two half-cells, composed of either a glass tube filled with an inert salt solution or a strip of filter paper soaked in an inert salt solution, that transfers ions between the half-cells. This bridge does not take part in the reaction.

As the redox reaction continues, electrons are transferred from one half-cell to the other. This creates a positive charge on one half-cell and a negative charge on the other half cell. The ions in the salt bridge move within the salt bridge to balance out this difference. The salt bridge allows the two half-cells to remain electrically neutral.

#### Galvanic Cell

The galvanic cell forms a circuit, a path through which electrons flow. This creates electric current, the flow of electric charge. This current can be used to measure the difference in electric potential, or the amount of work required to move one charged particle from one point to another, of the half-cells. This difference in electric potential between the half-cells is expressed as voltage.

Galvanic cell notation is a shorthand method of describing the setup of a galvanic cell. For example, a galvanic cell containing a zinc (Zn) electrode immersed in zinc sulfate (ZnSO4) on the anode side and a copper (Cu) electrode immersed in copper sulfate (CuSO4) on the cathode side is written as ${\rm{Zn}}\vert{\rm{Zn}}^{2+}(1\;{\rm{M}})\parallel{\rm{Cu}}^{2+}(1\;{\rm{M}})\vert{\rm{Cu}}$ in galvanic cell notation. The concentrations of the aqueous solutions affect the rate of the redox reaction and therefore are given in the notation. The vertical bar | in galvanic cell notation represents a phase boundary. It is used instead of the arrow that is commonly used in chemical reactions. The double vertical bars represent the salt bridge of the galvanic cell.

In this notation, the components that make up the cell are written in order, starting with the anode and then moving through each solution to the cathode, resulting in an oxidation half-reaction on the left and a reduction half-reaction on the right. Spectator ions that do not take part in the electrical reaction, such as the sulfate ions in each solution, are not included in this notation.

If the species in a galvanic cell is a poor conductor of electricity, an inert electrode—that is, an electrode that does not take part in the chemical reaction but serves only to transfer electrons—may be used. Platinum, for example, is an element that does not take part in the chemical reaction and is commonly used as an inert electrode. Consider a galvanic cell in which a magnesium (Mg) electrode is immersed in a solution of magnesium chloride (MgCl2) and a platinum (Pt) electrode is immersed in hydrochloric acid (HCl). In this galvanic cell, platinum is an inert electrode. Hydrogen ions (H+) still get reduced in the hydrochloric acid (HCl) solution, releasing hydrogen gas (H2). The galvanic cell notation is ${\rm{Mg}}(s)\vert{\rm{Mg}}^{2+}(aq)\parallel{\rm{H}}^+(aq)\vert{\rm{H}}_2(g)\vert{\rm{Pt}}(s)$. Platinum is included in the notation even though it is inert because it acts as a catalyst for the hydrogen reaction.

### Standard Reduction Potentials

The standard reduction potential, the tendency of the species to be reduced under standard conditions, can be measured in a galvanic cell.
When setting up a galvanic cell, it is vital to choose the right materials to use for each the anode and the cathode. An important property to know is the standard reduction potential (E°), which is the potential of the species to be reduced under standard conditions. The standard conditions are 1 atm pressure, 298 K (25°C), and 1 M concentration of products and reactants. Standard reduction potential is measured in volts (V) or millivolts (mV). Standard reduction potentials of various species can be determined experimentally using a standard hydrogen electrode (SHE), a platinum electrode in 1 M H+ (aq) solution with bubbled hydrogen gas at 1 atm of pressure. Hydrogen has a reduction potential of zero, so any electrons transferred using a SHE are because of the reduction potential of the experimental electrode.

#### Standard Hydrogen Electrode

Thus, by making one half-cell of a galvanic cell a SHE and attaching a voltmeter to the wire connecting the half-cells, E° can be measured for any species. It is also possible to determine whether the experimental species is an oxidant or reductant because the SHE has a standard reduction potential of zero. If the reading on the voltmeter is positive, the electrons are flowing toward the SHE. This means the experimental species is being oxidized and thus is the reducing agent. If the reading on the voltmeter is negative, the electrons are flowing toward the experimental species. This means the experimental species is being reduced and thus is the oxidizing agent.

#### Standard Reduction Potential Cell

Once for both species is known, the standard cell potential can be calculated. The standard cell potential is the potential difference between the cathode and the anode under standard conditions. It can be written as ${E^\circ}_{\rm{cell}}={E^\circ}_{\rm{cathode}}-{E^\circ}_{\rm{anode}}$. This measures the electrical work of the cell, that is, the voltage between two points when a charged particle is moved between them.

### The Nernst Equation

The Nernst equation allows for the calculation of cell potential, which can be used to find the change in Gibbs free energy and determine whether a reaction is spontaneous.

Cell potential is related to Gibbs free energy (G), which is an indicator of the spontaneity of a reaction. The equation relating cell potential and Gibbs free energy is $\Delta G=-nFE$ where n is the number of electrons transferred in the balanced redox reaction; F is the Faraday constant, the charge of one mole of electrons (96,485 C/mol); and E is the cell potential. A positive $\Delta G$ indicates a nonspontaneous reaction, while a negative $\Delta G$ indicates a spontaneous one.

Standard cell potential is taken under standard conditions, but in real life, conditions are not always standard. The Nernst equation, can be used to find the cell potential under conditions that are not standard.
$E=E^\circ-\frac{RT}{nF}\ln{Q}$
In this equation, $E^\circ$ is the standard cell potential, R is the ideal gas constant (8.314 J/K·mol), T is the temperature in Kelvin, n is the number of moles of electrons transferred in the balanced redox reaction, and Q is the reaction quotient, equal to the concentrations of the products of the reaction divided by the concentrations of the reactants. The Nernst equation is derived from the change in Gibbs free energy in a reaction of gas mixtures, which can be written as $\Delta G=\Delta {G}^\circ+RT\ln Q$.
The electrochemical potential, E, is defined as the decrease in Gibbs free energy per unit of charge transferred. In this equation, $-\Delta{G}$ is the decrease in Gibbs free energy, F is the Faraday constant, and n is the number of transferred electrons.
$E=-\frac{\Delta{G}}{nF}$
This relation can be rearranged to solve for the change in Gibbs free energy.
$\Delta{G}=-nFE$
Substitute this expression in the equation for Gibbs free energy.
$-nFE=-nFE^\circ+RT\ln{Q}$
Divide all terms by –nF to derive the Nernst equation.
$E=E^\circ-\frac{RT}{nF}\ln{Q}$
Step-By-Step Example
Use the Nernst Equation to Calculate Cell Potential
Consider the galvanic cell ${\rm{Cu}}\vert{\rm{Cu}}^{2+}(0.15\;{\rm{M}})\parallel{\rm{Ag}}^+(0.020\;{\rm{M}})\vert{\rm{Ag}}$ at 298 K. What is the cell potential?
Step 1
Begin by writing the half-reactions and their standard reduction potentials.
\begin{aligned}{\rm{Cu}}\rightarrow{\rm{Cu}}^{2+}+2{\rm{e}}^-&&E^\circ=-0.34\;{\rm{V}}\\{\rm{Ag}}^{+}+{\rm{e}}^-\rightarrow{\rm{Ag}}\;&&E^\circ=+0.80\;{\rm{V}}\end{aligned}
Step 2
Balance the redox reaction, and determine the standard cell potential.
${\rm{Cu}}(s)+2{\rm{Ag}}^+(aq)\rightarrow{\rm{Cu}}^{2+}(aq)+2{\rm{Ag}}(s)\;\;\;\;\;\;\;\;\;\;E^\circ=+0.46\;{\rm{V}}$
Solution
Use the Nernst equation to find E. Recall that Q is the reaction quotient, equal to the concentration of the products of the reaction divided by the concentration of the reactants.
\begin{aligned}E&=E^\circ-\frac{RT}{nF}\ln{Q}\\&=+0.46\;{\text{V}}-\frac{(8.314\;{\rm{J/K}}\!\cdot\!{\rm{mol)}}(298\;{\rm{K}})}{2(96{\rm{,}}485\;{\rm{C/mol)}}}\ln\left(\frac{0.15\;{\rm{M}}}{(0.020\;{\rm{M}})^2}\right)\\&=0.38\;{\rm{V}}\end{aligned}
When E has been calculated, it can be used to solve for $\Delta G$. For a cell potential of 0.38 V, for example, with two transferred electrons:
\begin{aligned}\Delta G&=-nFE\\&=-(2\;{\rm{mol}})(96{\rm{,}}485\;{\rm{J/V}}\!\cdot\!{\rm{mol}})(0.38\;{\rm{V}})\\&=-73{\rm{,}}329\;{\rm{J}}\\&=-73\;{\rm{kJ}}\end{aligned}
Notice that F could be expressed in joules per volt (J/V) per mol instead of coulombs (C) per mole because 1 C is equal to 1 J/V. In this case, $\Delta G$ is negative, so the reaction is spontaneous.

The Nernst equation and the equation for Gibbs free energy can be used in calculations of the cell potential when the electrodes are different or when they are the same as in a concentration cell.

### Galvanic Cell Applications

Galvanic cells are used as batteries and fuel cells to produce electrical power.
Galvanic cells can produce electricity on demand and have many uses. The galvanic cell most people are familiar with is the battery, a galvanic cell in which the electrical work is used as a source of electrical power. Batteries rely on an electrolyte, an ionic solution that can be decomposed by electricity. A dry cell is a galvanic cell in which the electrolytes exist as pastes. Dry cells are used as batteries because they prevent spilling. The alkaline battery, a dry cell battery in which the electrolyte is potassium hydroxide, is the most common battery.

#### Alkaline Battery

Many electronics, such as cell phones, use a lithium-ion battery, a battery that contains lithium in its electrolyte and electrodes. Lithium-ion batteries can be recharged by adding electricity to make the current flow against the spontaneous direction of the redox reaction. Another rechargeable battery is the nickel-cadmium battery, a battery that uses nickel and cadmium as the electrodes. Nickel-cadmium batteries replace alkaline batteries in many devices and are preferred by many people because they can be recharged. The lead-acid battery is another type of rechargeable battery, which uses lead electrodes and sulfuric acid as the electrolyte. Lead-acid batteries are commonly used in cars and other vehicles.

Another use of a galvanic cell is a fuel cell. A fuel cell is a device that generates electrical power through the ionization of hydrogen or another molecule. A fuel cell is different than a battery. In a fuel cell, fuel is being continually consumed to produce electricity, and the fuel cell functions as long as fuel is available. Batteries are limited by the mass of electrodes they contain. Fuel cells are used in many industrial applications and have begun to be introduced as power for vehicles.

Hydrogen fuel cells are the most common type of fuel cell. In a hydrogen fuel cell, oxygen reacts at the cathode and hydrogen reacts at the anode. The electrons given off when hydrogen is ionized are used as the fuel. In some hydrogen fuel cells, hydrogen travels through the electrolyte to meet the oxygen at the cathode. In others, oxygen travels through the electrolyte to meet the hydrogen at the anode. In both types, when the oxygen and hydrogen meet, they form water, which is the only exhaust given off. Because of this, hydrogen fuel cells are considered clean energy. However, they are not yet in widespread use because they are very expensive and inefficient compared to other methods of electricity generation.