Standard cell potential calculations, 246

To calculate the open circuit voltage of the lead—acid battery, an accurate value for the standard cell potential, which is consistent with the activity coefficients of sulfuric acid, must also be known. The standard cell potential for the double sulfate reaction is 2.048 V at 25 °C. This value is calculated from the standard electrode potentials for the (Pt)H2 H2S04(yw) PbS04 Pb02(Pt) electrode 1.690 V (14), for the Pb(Hg) PbS04 H2S04(yw) H2(Pt) electrode 0.3526 V (19), and for the Pb Pb2+ Pb(Hg) 0.0057 V (21). 

The aluminum-air fuel cell is used as a reserve battery in remote locations. In this cell aluminum reacts with the oxygen in air in basic solution, (a) Write the oxidation and reduction half-reactions for this cell, (b) Calculate the standard cell potential. See Box 12.1. 

Calculate the standard cell potential for the reaction between silicon and water in a cell that also produces hydrogen from water and write the balanced equation for the cell reaction. See Box 12.1. 

The calculation o E° for this cell illustrates an important feature of cell potentials. A standard cell potential is the difference between two standard reduction potentials. This difference does not change when one half-reaction is multiplied by 2 to cancel electrons in the overall redox reaction. 

EXAMPLE 14.5. Calculate the standard cell potential of the Danicll cell, shown in Fig. 14-l. 

We can use this table of standard reduction potentials to write the overall cell reaction and to calculate the standard cell potential, the potential (voltage) associated with the cell at standard conditions. There are a couple of things to remember when using these standard reduction potentials to generate the cell reaction and cell potential ... 

Since oxidation occurs at the anode and reduction at the cathode, the standard cell potential can be calculated from the standard reduction potentials of the two half-reactions involved in the overall reaction by using the equation ... 

Once you have calculated the standard cell potential, then the reaction can be written by reversing the half-reaction associated with the anode (show it as oxidation) and adding the two half-reactions. 

Thus far, we have based all of our calculations on the standard cell potential or standard half-cell potentials—that is, standard state conditions. However, many times the cell is not at standard conditions—commonly the concentrations are not 1 M. We may calculate the actual cell potential, Ecell, by using the Nemst equation ... 

Because one half-reaction must involve oxidation, one of the half-reactions shown in the table of reduction potentials must be reversed to indicate the oxidation. If the half-reaction is reversed, the sign of the standard reduction potential must be reversed. However, this is not necessary to calculate the standard cell potential. 

Experiments involving the Nernst equation are primarily concerned with concentrations. One or more of the concentrations in the Q portion of the Nernst equation are calculated by measuring the nonstandard cell potential and comparing this to the standard cell potential. Remember, you calculate the concentration from a measured voltage. Once the concentration is determined, it may be combined with other concentrations and used to calculate an equilibrium constant. 

The standard cell potential can also be used to calculate the equilibrium constant for a nE°... 

You can use Table 11.1 to calculate the standard cell potential of the familiar Daniell cell. This cell has its standard potential when the solution concentrations are 1 mol/L, as shown in the shorthand representation below. 

One method to calculate the standard cell potential is to subtract the standard reduction potential of the anode from the standard reduction potential of the cathode. 

This calculation of the standard cell potential for the Daniell cell used the mathematical concept that the subtraction of a negative number is equivalent to the addition of its positive value. You saw that 0.342 V - (-0.762 V) = 0.342 V + 0.762 V... 

To summarize, the standard cell potential can also be calculated as the sum of a standard reduction potential and a standard oxidation potential. 

The calculation of the standard cell potential using these standard half-reaction potentials is as follows. 

Calculating a Standard Cell Potential, Given a Net Ionic Equation... 

Calculate the standard cell potential for the galvanic cell in which the following reaction occurs. 

A standard cell potential depends only on the identities of the reactants and products in their standard states. As you will see in the next Sample Problem, you do not need to consider the amounts of reactants or products present, or the reaction stoichiometry, when calculating a standard cell potential. Since you have just completed a similar Sample Problem, only a brief solution using the subtraction method is given here. Check that you can solve this problem by adding a reduction potential and an oxidation potential. 

The standard cell potential is 1.883 V. The Problem Tip on this page illustrates this calculation. 

Use the given standard reduction potentials to calculate the standard cell potentials for the following redox reactions. 

In this section, you learned that you can calculate cell potentials by using tables of half-cell potentials. The half-cell potential for a reduction half-reaction is called a reduction potential. The half-cell potential for an oxidation half-reaction is called an oxidation potential. Standard half-cell potentials are written as reduction potentials. The values of standard reduction potentials for half-reactions are relative to the reduction potential of the standard hydrogen electrode. You used standard reduction potentials to calculate standard cell potentials for galvanic cells. You learned two methods of calculating standard cell potentials. One method is to subtract the standard reduction potential of the anode from the standard reduction potential of the cathode. The other method is to add the standard reduction potential of the cathode and the standard oxidation potential of the anode. In the next section, you will learn about a different type of cell, called an electrolytic cell. 

Calculate a standard cell potential using a table of standard reduction potentials. 

Write the half-reactions and calculate the standard cell potential for each reaction. Identify each reaction as spontaneous or non-spontaneous. 

Calculate the standard cell potential of a cell constructed with nickel (Ni) and copper (Cu) electrodes. 

Calculate the standard cell potentials (emf) for the following cells ... 

The energy available from spontaneous cell reactions can be used to power vehicles or generate electricity (Box 12.2). To calculate the standard cell potential for a spontaneous process, we must combine the standard potential of the cathode half-reaction (reduction) with that of the anode half-reaction (oxidation) in such a way as to obtain a positive... 

Calculate the equilibrium constant for a reaction from the standard cell potential, Example 12.7. 

Predict the standard cell potential and calculate the standard free energy for the following galvanic cells (the standard potentials of these cells were obtained in Exercise 12.19). 

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