Introduction

In the last decade of the 18th Century, Luigi Galvani discovered that the nerves of frogs were capable of harboring electrical activity. Shocked by his discovery, Galvani rationalized that such activity could only be found in living tissues. Boy was he wrong! A few years later, a man by the name of Alessandro Volta scientifically refuted Galvani’s claim when he observed that electricity could also be produced through inorganic means. By using small metal sheets of copper and zinc separated by pieces of cloth soaked in acidic solution, Volta constructed what is believed to be the first apparatus capable of producing electricity. Through centuries of research and technological advances, electricity is now a crucial part of our everyday lives, an aspect so vital that it has its own chemical course of study—electrochemistry.

Electrochemistry

Electrochemistry is simply referred to as the study of the exchange between electrical and chemical energy. Over time, reactions of this sort have been coined redox reactions as they utilize two unique processes to transfer electrons, and therefore generate electricity. The processes to which we are referring are termed oxidation and reduction. In greater detail, oxidation involves the loss of one or more electrons from a chemical species, while reduction refers to the gain of electrons by the chemical species. These two definitions are easily remembered by the mnemonic “OIL RIG" (Oxidation is Loss, Reduction is Gain).

When an oxidation and a reduction reaction are paired together in a redox reaction, electrons can flow from the oxidized species to the reduced species. Aside, the oxidized species can also be referred to as the reducing agent or the reductant, while the reduced species is also known as the oxidizing agent or oxidant. This flow of electrons can be observed when an electrochemical cell is constructed. Specifically, the two types of cells are a galvanic cell, (also known as a voltaic cell), where a spontaneous reaction drives the electron flow, and an electrolytic cell, where an outside source of current is imposed on the cell to drive a chemical reaction.

Electrochemical Cells

When discussing an electrochemical cell, there are several new terms you must learn. Specifically, these are: the standard reduction potential (E^o_red); a half-cell; an electrode; an anode; and the cathode. The first and most important term here is the standard reduction potential (E^o_red), which is a numerical value of a half-reaction for the reduction of a particular metal. In a more scientific sense, the standard reduction potential is a quantitative measure (in Volts) of a particular substance’s tendency to accept electrons under the standard conditions of 1.0 atm and 1.0 mol/L. A table of standard reduction potentials you will use in this experiment is provided here.

Observing the table, you will notice that the series of half-reactions is listed in descending order from the most positive value to the most negative value. The general rule for these values is that the more positive the standard reduction potential is for a particular substance, the stronger its tendency is to be reduced, or gain electrons. On the other hand, the standard oxidation potential (E^o_ox), is used to measure the tendency of a particular substance to lose electrons, or become oxidized. Specifically, the value of E^o_ox is equal in value, but opposite in sign, to the standard reduction potential. For example, the dichromate ion (Cr₂O₇^2-) has a standard reduction potential of +1.33V, meaning that under standard conditions the ion will have a standard oxidation potential of -1.33 V.

The remaining terms deal entirely with electrochemical cells, and are critical components of its construction. Recalling that galvanic cells utilize a spontaneous redox reaction to ‘pump’ electrons, the system is specifically composed of two parts commonly referred to as half-cells. A half-cellis the part of the electrochemical cell that houses the electrode. In greater detail, the electrode, as described by Faraday, can be either an anode, the electrode where oxidation occurs, or a cathode, the electrode where reduction takes place. For a clear diagram of what we have just describe please carefully note the figure below.

 

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Calculating Cell Potentials

A term left unmentioned in the previous section was the overall cell potential (E^o_cell), which in brief is simply the sum of the standard reduction potential (E^o_red) and the standard oxidation potential (E^o_ox). Mathematically, the overall cell potential is expressed as:

Using our diagram above, let’s make a reasonable hypothesis as to what we believe our overall potential will be for a cell formed between zinc and copper. In the figure, select a 1.0 M solution of zinc nitrate and zinc metal as the anode (black) and copper nitrate and copper metal as the cathode (red). Look at the table provided of the half reaction E^o's of the metals we find:

Using the equation above for the overall cell potential we can arrive at the estimated value:

If you turn on the voltmeter in the diagram above, the value we have just calculated should be confirmed. However, when you construct this cell in the lab the reading from your voltmeter may not be exactly +1.10 V. But remember, you are not working at standard conditions. Still, this is not the most important thing that needs to be considered—the most important condition that needs to be met is that the ratio of concentrations of the corresponding salts is 1:1. If this ratio is met, any differences in the readings could be rationalized to stem from other sources such as resistance in the salt bridge or lack of calibration of the voltmeter. What we have just described will be applied in the first part of this experiment as each student will be constructing their his or her own galvanic cell from 6 possible metals.

Free Energy and The Nernst Equation

The value of ∆G for a reaction at any moment in time tells us two things. The sign of ∆G tells us in what direction the reaction has to shift to reach equilibrium. The magnitude of ∆G tells us how far the reaction is from equilibrium at that moment.

The potential of an electrochemical cell is a measure of how far an oxidation-reduction reaction is from equilibrium. The Nernst equation describes the relationship between the cell potential at any moment in time and the standard-state cell potential.

Let's rearrange this equation as follows.

We can now compare it with the equation used to describe the relationship between the free energy of reaction at any moment in time and the standard-state free energy of reaction.

These equations are similar because the Nernst equation is a special case of the more general free energy relationship. We can convert one of these equations to the other by taking advantage of the following relationships between the free energy of a reaction and the cell potential of the reaction when it is run as an electrochemical cell.

In the second portion of this experiment you will be measuring the overall cell potential of your galvanic cell at various temperatures, data which will give far more information about a particular reaction that you may be studying. As with any other type of chemical reaction, redox reactions are subject to changes in equilibrium brought about by changes in the overall temperature of the system. However, before we obtain the particular equilibrium constant (K) for our reaction, we need the change in Gibb’s free energy (∆G). Overall, the Gibb’s free energy (∆G) of a particular reaction is a measure of the spontaneity of the reaction process, and is defined mathematically by the equation we just derived:

Within this equation, the variables are as follows: n is the number of moles of electrons transferred; is Faraday’s constant; and E^o_Cell is the observed overall cell potential. For our example, the setup would be as follows:

In this particular reaction the ∆G^o is ~ -212 kJ, meaning that our example reaction is highly spontaneous when both products and reactants are in there standard states.

Now, with an approximate value for ∆G^o known, we can calculate the reaction’s equilibrium constant from the relationship shown below.

For this equation, the value of ∆G^o is already known, R is the ideal gas constant, and T is the temperature in Kelvin. Realizing we performed our experiment at room temperature (~ 27^oC) we can quickly calculate the corresponding equilibrium constant.

Thus, for our particular example run at room temperature, we get an approximate value of K = 8.2 x 10³⁶ !! In other words, this reaction is driven to entirety at room temperature.

In summary, the second part of the experiment is aimed towards furthering your understanding of how temperature can affect the Gibb’s free energy of a reaction as well as its equilibrium. Specifically, you will be asked to utilize your knowledge of the following equation to construct a graph of ∆G^o versus temperature:

Using only simple algebra, this equation can quickly be converted into y = mx + b form making your task a tad more bearable. Entropy and enthalpy are then easily derived from the slope and intercept of the resulting line, respectively.