Half-cell reactions Nernst-equation calculations

From the Nernst equation, calculate the pressure of hydrogen involved if alHsO ) = 0.011, and Eh+,h2 = 0.008 V. Take p = 10 Pa. (Remember from the balanced half-cell reaction that n = 2.)... 

Half-Cell Reactions and Nernst-Equation Calculations... 

Plan The standard half-cell reactions are identical, so °eii is zero, and we calculate Eceii from the Nernst equation. Because half-cell A has a higher [Ag ], Ag ions will be reduced and plate out on electrode A. In half-cell B, Ag will be oxidized and Ag ions will enter the solution. As in all voltaic cells, reduction occurs at the cathode, which is positive. 

Equation (12.11) could also be considered to represent a half-cell reaction, except that the electron is not shown. So evidently we could use the Nernst equation to calculate half-cell potentials if we knew what value to assign the chemical potential of an electron. It turns out, of course, that because the electrons always cancel out in balanced reactions, we could assign any value we like to the electron Gibbs energy and it would make no difference to our calculated cell potentials. The easiest value to assign is zero, and that is what is done. Therefore, the Nernst equation is used to calculate both half-cell and cell potentials. 

R is the ideal gas constant, T is the Kelvin temperature, n is the number of electrons transferred, F is Faraday s constant, and Q is the activity quotient. The second form, involving the log Q, is the more useful form. If you know the cell reaction, the concentrations of ions, and the E°ell, then you can calculate the actual cell potential. Another useful application of the Nernst equation is in the calculation of the concentration of one of the reactants from cell potential measurements. Knowing the actual cell potential and the E°ell, allows you to calculate Q, the activity quotient. Knowing Q and all but one of the concentrations, allows you to calculate the unknown concentration. Another application of the Nernst equation is concentration cells. A concentration cell is an electrochemical cell in which the same chemical species are used in both cell compartments, but differing in concentration. Because the half reactions are the same, the E°ell = 0.00 V. Then simply substituting the appropriate concentrations into the activity quotient allows calculation of the actual cell potential. 

Both half- and overall reaction tendencies change with temperature, pressure (if gases are involved), and concentrations of the ions involved. Thus far, we have only been concerned with standard conditions. Standard conditions, as stated previously, are 25°C, 1 atm pressure, and 1 M ion concentrations. An equation has been derived to calculate the cell potential when conditions other than standard conditions are present. This equation is called the Nernst equation and is used to calculate the true E (cell potential)... 

The Nernst equation applies to both cell reactions and half-reactions. For the conditions specified, calculate the potential for the following half-reactions at 25°C ... 

In voltaic cells, it is possible to carry out the oxidation and reduction halfreactions in different places when suitable provision is made for transporting the electrons over a wire from one half-reaction to the other and to transport ions from each half-reaction to the other in order to preserve electrical neutrality. The chemical reaction produces an electric current in the process. Voltaic cells, also called galvanic cells, are introduced in Section 17.1. The tendency for oxidizing agents and reducing agents to react with each other is measured by their standard cell potentials, presented in Section 17.2. In Section 17.3, the Nernst equation is introduced to allow calculation of potentials of cells that are not in their standard states. 

The Nernst equation can be applied to half-reactions. Calculate the reduction potential at 25°C of each of the following half-cells. 

The method illustrated in Example 21-7, applying the Nernst equation to the overall cell reaction, usually involves less calculation than correcting the separate half-reactions as in Example 21-6. We interpret our results as follows The positive cell potentials in Examples 21-6 and 21-7 tell us that each of these cell reactions is spontaneous in the direc-... 

The overall cell potential can be calculated by applying the Nernst equation to the overall cell reaction. We must first find E, the standard cell potential at standard concentrations because the same electrode and the same type of ions are involved in both half-cells, this is always zero. Thus,... 

To compensate partially for activity effects and errors resulting from side reactions, such as those described in the previous section. Swift proposed substituting a quantity called the formal potential E" in place of the standard electrode potential in oxidation-reduction caleulations. The formal potential, sometimes referred to as the conditional potential, of a system is the potential of the half-cell with respect to tite SI IE when the concentrations of reactants and products are 1. M and the concentrations of any other constituents of the solution are earefully specilted. Thus, for example, the formal potential for the reductionof iron(lll) is +0.732 V in 1 M perchloric acid and +0.7(K) V in 1 M hydrochloric acid. Using these values in place of the standard electrode potential in the Nernst equation will yield heller agreement between calculated and experi-... 

The magnitude of the net cell potential AV° will signify the spontaneity of the oxidation-reduction reaction. However, it does not indicate the rate at which corrosion will occur. As noted before, we apply the superscript 0 to denote that we are considering the Standard Electrode Potentials. Engineers may be required to calculate the potential of a particular half-cell at concentrations and temperatures other than the standard conditions. For this purpose, we shall use the Nernst equation, which allows us to account for non-standard temperatures and solution concentrations. 

This problem defines nonstandard conditions that must be addressed using the Nernst equation. Virtually anytime you are given concentrations of electrolytes present in a cell (other than 1 M), you need this equation. This problem also presents the challenge of identifying the reactions involved. Iron will be the anode, but we will need to scan the table of standard reduction potentials to identify a possible cathode reaction. The most likely suspect is the reduction of to H2. Once we know both half-reactions, we can calculate the standard cell potential to fill in the appropriate values in the Nernst equation. 

This is the Nernst equation, after the physical chemist W. Nernst, who derived it at the end of the nineteenth century. As above, n is the number of electrons transferred in the cell reaction (2 in reaction 12.7), 5 the Faraday of charge, R the gas constant, and T the temperature (in kelvins). The constant 2.302 59 is used to convert from namral to base 10 logs. At 25 the quantity 2.30259 RT/3 has the value 0.05916, which is called the Nernst slope. The importance of (12.14) is that it allows calculation of the potentials of cells having nonstandard state concentrations (i.e., real cells) from tabulated values of standard half-cell values or tabulated standard Gibbs energies. 

Describe the role of non-fVwork in electrochemical systems. Define the roles of the anode, cathode, and electrolyte in an electrochemical cell. Given shorthand notation for an electrochemical cell, identify the oxidation and reduction reactions. Use data for the standard half-cell potential for reduction reactions, E°, to calculate the standard potential of reaction E. Apply the Nernst equation to determine the potential in an electrochemical cell given a reaction and reactant concentrations. 

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