Spontaneous half-reactions

In a spontaneous reaction, electrons are donated by (flow away from) the half-reaction with the more negative reduction potential and are accepted by (flow toward) the half-reaction with the more positive reduction potential. Thus, in the present case, isocitrate donates electrons and NAD accepts electrons. The convention defines as... 

Coupling the half-reactions (3) and (4) gives the reaction (5) [i.e.(4) — (3)) which, because AC is negative, proceeds spontaneously from left to right as written ... 

One of the most important characteristics of a cell is its voltage, which is a measure of reaction spontaneity. Cell voltages depend on the nature of the half-reactions occurring at the electrodes (Section 18.2) and on the concentrations of species involved (Section 18.4). From the voltage measured at standard concentrations, it is possible to calculate the standard free energy change and the equilibrium constant (Section 18.3) of the reaction involved. 

As expected, decreasing the concentration of H+ makes the half-reaction less spontaneous and hence makes red less positive. 

For lithium metal in 1 Af HC1, the observed facts are that the metal dissolves spontaneously and a gas bubbles out of the solution. From Appendix 3 we select the two half-reactions (notice that the half-reactions are already balanced in both charge and number of atoms) ... 

We can use the electrochemical series to predict the thermodynamic tendency for a reaction to take place under standard conditions. A cell reaction that is spontaneous under standard conditions (that is, has K > 1) has AG° < 0 and therefore the corresponding cell has E° > 0. The standard emf is positive when ER° > Et that is, when the standard potential for the reduction half-reaction is more positive than that for the oxidation half-reaction. 

STRATEGY Find the standard potentials of the two reduction half-reactions in Appendix 2B. The couple with the more positive potential will act as an oxidizing agent (and be the site of reduction). That couple will be the right-hand electrode in the cell diagram corresponding to the spontaneous cell reaction. To calculate the standard emf of the cell, subtract the standard potential of the oxidation half-reaction (the one with the less-positive standard potential) from that of the reduction half-reaction. To write the cell reaction, follow the procedure in Toolbox 12.2. 

The half-reaction with the more positive value of E° occurs at the cathode in a spontaneous reaction. 

To construct the spontaneous cell reaction, combine the two half-reactions, leaving the permanganate half-reaction as a reduction and reversing the dichromate half-reaction. To match numbers of electrons, multiply the manganese half-reaction by 6 and the chromium half-reaction by 5 ... 

The fact that we can calculate E° from standard potentials allows us to calculate equilibrium constants for any reaction that can be expressed as two half-reactions. The reaction does not need to be spontaneous nor does it have to be a redox reaction. Toolbox 12.3 summarizes the steps and Example 12.8 shows the steps in action. 

The spontaneous redox reaction shown in Figure 19-7 takes place at the surfaces of metal plates, where electrons are gained and lost by metal atoms and Ions. These metal plates are examples of electrodes. At an electrode, redox reactions transfer electrons between the aqueous phase and the external circuit. An oxidation half-reaction releases electrons to the external circuit at one electrode. A reduction half-reaction withdraws electrons from the external circuit at the other electrode. The electrode where oxidation occurs is the anode, and the electrode where reduction occurs is the cathode. 

We need to determine which reaction occurs as reduction and which occurs as oxidation when this battery is operating in its spontaneous direction. Then we can use Equation to determine E ° for the nickel half-reaction. 

We can combine the half-cell potentials for any two half-reactions in the table to get a complete cell potential. The chemical reaction may proceed spontaneously if the complete cell potential is positive. Otherwise, the opposite reaction may proceed spontaneously. We combine half-cells by adding the chemical reactions and by adding the corresponding half-cell potentials. We must first get the correct chemical reactions and corresponding half-cell potentials for the half-reactions, as follows ... 

If the sign of the standard reduction potential, E°, of a half-reaction is positive, the half-reaction is the cathodic (reduction) reaction when connected to the standard hydrogen electrode (SHE). Half-reactions with more positive E° values have greater tendencies to occur in the forward direction. Hence, the magnitude of a halfcell potential measures the spontaneity of the forward reaction. 

Since the overall cell potential is positive, this step is spontaneous. The next step involves oxidation of Fe2+(aq) back to Fe3+(aq), (i.e. the reverse of reaction (i) and the reduction of H202(aq) to H20(l) in acidic solution, for which the half-reaction is... 

In step 1, if °(d is less than 0.695 V, the overall voltage for the first step will be negative and hence non-spontaneous. In step 2, if the oxidation half-reaction has a potential that is more negative than -1.763 V, the overall potential for this step will be negative, and hence non-spontaneous. Consequently, E°( ) must fall between 0.695 V and 1.763 V in order for both steps to be spontaneous. On this basis we find that... 

One easily demonstrated electrical characteristic of moist soil is seen in the production of electricity when two different metals, namely, copper and zinc, are inserted into it. This is not unexpected because any salt-containing solution adsorbed in media, such as paper or cloth, and placed between these same two electrodes will cause a spontaneous reaction that produces electricity. The source of this flow of electrons is an oxidation-reduction reaction, represented as two half-reactions as shown in Figure 9.1 for copper and zinc. 

When using the Nernst equation on a cell reaction in which the overall reaction is not supplied, only the half-reactions and concentrations, there are two equivalent methods to work the problem. The first way is to write the overall redox reaction based upon E° values and then apply the Nernst equation. If the Ecell turns out to be negative, it indicates that the reaction is not a spontaneous one (an electrolytic cell) or that the reaction is written backwards if it is supposed to be a galvanic cell. If it is supposed to be a galvanic cell, then all you need to... 

We must narrow the options. There will be only one cathode reaction and only one anode reaction. How do we pick the correct half-reactions If one of the half-reactions were spontaneous (positive), we would pick it for that electrode. (If more than were spontaneous, we would pick the largest positive value.) All four half-reactions in this case are nonspontaneous (negative). This is typical for electrolysis, because you are using electrical energy to force a nonspontaneous process to take place. 

Use the following two half-reactions to write balanced net ionic equations for one spontaneous reaction and one non-spontaneous reaction. State the standard cell potential for each reaction. 

Consider a cell made up of two half cells, where one contains the Fe , Fe couple and the other the Cu, Cu couple. By looking up the respective values of the standard electrode potentials E given in Appendix 3, deduce the spontaneous cell reaction that would occur if the leads connecting the two half cells were allowed to short by touching. 

Tabulated E values can be used to calculate the for any reaction, as illustrated in Table 7.2 for the Zn/Cu galvanic cell. The redox reaction is spontaneous when the half-reaction (Cu /Cu) with the larger reduction (+0.34V) acts as the oxidizing agent. In this case, the other half-reaction (Zn /Zn) proceeds as an oxidation. The halfcell potential for this reduction is +0.76 V as it represents the reverse of the half-cell reduction potential as listed in Table 7.2. The sum of the oxidation and reduction half reactions is +0.34V + 0.76 V = +1.10 V. Thus for the galvanic Zn/Cu cell is +1.10V. 

When two conjugate redox pairs are together in solution, electron transfer from the electron donor of one pair to the electron acceptor of the other may proceed spontaneously. The tendency for such a reaction depends on the relative affinity of the electron acceptor of each redox pair for electrons. The standard reduction potential, E°, a measure (in volts) of this affinity, can be determined in an experiment such as that described in Figure 13-14. Electrochemists have chosen as a standard of reference the half-reaction... 

An electron-transfer reaction will occur spontaneously only if the reducing half-reaction lies above the oxidizing half-reaction in a table such as Table 17-1. This results in a positiveE°eU, a negative AG°, and Ke > 1. 

The reaction is spontaneous because, in Table 17-1, the redudng half-reaction... 

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... 

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