Half reactions combining

Strategy We search the alphabetical listing in Appendix 2B for half-reac- tions that can be combined to give the desired half-reaction. Combine these i half-reactions and their free energies of reaction. Convert to standard potentials by using Eq. 3 and then simplify the resulting expressions. 

To illustrate, we can use two different combinations of half-reactions combined in hypothetical half-cells to arrive at the reaction... 

Half-reactions, one oxidation and one reduction, are exactly that one-half of a complete reaction. The two half-reactions combine to produce the complete reaction. Note that the electrons cancel in the electron transfer process, no free electrons remain. 

A redox reaction must involve an oxidation half-reaction combined with a reduction half-reaction. Therefore, one reactant in an overall redox reaction must come from the left side of a table of reduction half-reactions (i.e., the reduced form in the half-equation) and one reactant must come from the right side of the table (i.e., the oxidized form in the half-equation). Such combinations could be of two types (a) those for which the oxidized form lies below the reduced form (e.g., 03(g) and Ag(s) - see Table 6.2), and (b) those for which the oxidized form lies above the reduced form (e.g., Fe (aq) and H2(g) -see Table 6.2). Under standard conditions, type (a) combinations produce significant redox reactions in the forward direction (because ccii = x + ed is positive). For type (b) combinations the redox reaction is not significant in the forward direction under standard conditions (because en is negative). Stated in another way Under standard conditions the reduced form of any couple [e,g., Li(s)for the... 

A connnon approach has been to measure the equilibrium constant, K, for these reactions as a fiinction of temperature with the use of a variable temperature high pressure ion source (see section (Bl.7.2)1. The ion concentrations are approximated by their abundance in the mass spectrum, while the neutral concentrations are known from the sample mlet pressure. A van t Hoff plot of In K versus /T should yield a straight Ime with slope equal to the reaction enthalpy (figure B1.7.11). Combining the PA with a value for basicityG at one temperature yields a value for A.S for the half-reaction involving addition of a proton to a species. While quadnipoles have been tire instruments of choice for many of these studies, other mass spectrometers can act as suitable detectors [19, 20]. 

Eeq by combining the two Nernst equations. To do so we recognize that the potentials for the two half-reactions are the same thus,... 

The half-reactions, when combined, express the overall, or net, reaction. 

Each zinc atom loses two electrons in changing to a zinc ion, therefore zinc is oxidized. Each hydrogen ion gains an electron, changing to a hydrogen atom, therefore hydrogen is reduced. (After reduction, two hydrogen atoms combine to form molecular H2.) As before, reaction (7) can be separated into two half-reactions ... 

The value of this list is obvious. Any half-reaction can be combined with the reverse of another half-reaction (in the proportion for which electrons gained is equal to electrons lost) to give a possible chemical reaction. Our list permits us to predict whether equilibrium favors reactants or products. We would like to expand our list and to make it more quantitative. Electrochemical cells help us do this. 

We would like to measure the contribution each half-reaction makes to the voltage of a cell. Yet every cell involves two half-reactions and every cell voltage measures a difference between their half-cell potentials. We can never isolate one half-reaction to measure its E°. An easy escape is to assign an arbitrary value to the potential of some selected half-reaction. Then we can combine all other half-reactions in turn with this reference half-reaction and find values for them relative to our reference. The handiest arbitrary value to assign is zero and chemists have decided to give it to the half-reaction... 

Similarly, if we combine a Cu-Cu+2 half-cell in its standard state with a standard Hj-2H+ halfcell, the voltage (potential) we measure (0.34 volt) is the value assigned to the half-reaction ... 

When balancing redox equations, we consider the gain of electrons (reduction) separately from the loss of electrons (oxidation), express each of these processes as a halfreaction, and then balance both atoms and charge in each of the two half-reactions. When we combine the halfreactions, the number of electrons released in the oxidation must equal the number used in the reduction. 

Finally, simplify the appearance of the equation by canceling species that appear on both sides of the arrow and check to make sure that charges as well as numbers of atoms balance. In some cases it is possible to simplify the half-reactions before they are combined. 

In some cases, we find that available tables of data do not contain the standard potential that we need but do contain closely related values for the same element for instance, we might require the standard potential of the Ce4+/Ce couple, whereas we know only the values for the Ce3+/Ce and Ce4+/Ce3+ couples. In such cases, the potential of a couple cannot be determined by adding or subtracting the standard potentials directly. Instead, we calculate the values of AG° for each half-reaction and combine them into the AC° for the desired half-reaction. We then convert that value of AG° into the corresponding standard potential by using Eq. 2. 

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 ... 

Then find two reduction half-reactions in Appendix 2B that combine to give that equation. Reverse one of the half-reactions and add them together. 

One combination of electrodes that could be used to determine pH is a hydrogen electrode connected through a salt bridge to a calomel electrode. The reduction half-reaction for the calomel electrode is... 

The mechanism of the first half-reaction has been studied by a combination of reductive titrations with CO and sodium dithionite and pre-steady-state kinetic studies by rapid freeze quench EPR spectroscopy (FQ-EPR) and stopped-flow kinetics 159). These combined studies have led to the following mechanism. The resting enzyme is assumed to have a metal-bound hydroxide nucleophile. Evidence for this species is based on the similarities between the pH dependence of the EPR spectrum of Cluster C and the for the for CO, deter-... 

After oxidation and reduction half-reactions are balanced, they can be combined to give the balanced chemical equation for the overall redox process. Although electrons are reactants in reduction half-reactions and products in oxidation half-reactions, they must cancel in the overall redox equation. To accomplish this, multiply each half-reaction by an appropriate integer that makes the number of electrons in the reduction half-reaction equal to the number of electrons in the oxidation half-reaction. The entire half-reaction must be multiplied by the integer to maintain charge balance. Example illustrates this procedure. 

The balanced half-reactions appear in Example. Balance the overall equation by combining the half-reactions in such a way that electrons cancel. 

The half-reaction for iron contains one electron on the right, whereas the half-reaction for chromium contains six electrons on the left. To combine these half-reactions so that the electrons cancel, multiply the iron half-reaction by 6 and add it to the chromium half-reaction ... 

When half-reactions are combined, there is often a duplication of some chemical species, particularly H2 0 and H3 O or OH. The overall equation is cleaned up by combining species that appear twice on the same side. Also, when a species appears on both sides of the balanced equation, equal numbers of the species are subtracted from each side. 

Step 4 Recombine the half-reactions, and simpiify by combining and canceling dupiicated species. 

Divide the reaction into half-reactions, balance each using the stepwise procedure, combine the half-reactions, and then clean up the result to eliminate duplicated species. 

A table giving the cell potentials of all possible redox reactions would be immense. Instead, chemists use the fact that any redox reaction can be broken into two distinct half-reactions, an oxidation and a reduction. They assign a potential to every half-reaction and tabulate E ° values for all half-reactions. The standard cell potential for any redox reaction can then be obtained by combining the potentials for its two half-reactions. 

They are the basis of many products and processes, from batteries to photosynthesis and respiration. You know redox reactions involve an oxidation half-reaction in which electrons are lost and a reduction half-reaction in which electrons are gained. In order to use the chemistry of redox reactions, we need to know about the tendency of the ions involved in the half-reactions to gain electrons. This tendency is called the reduction potential. Tables of standard reduction potentials exist that provide quantitative information on electron movement in redox half-reactions. In this lab, you will use reduction potentials combined with gravimetric analysis to determine oxidation numbers of the involved substances. 

In the ion-electron method of balancing redox equations, an equation for the oxidation half-reaction and one for the reduction half-reaction are written and balanced separately. Only when each of these is complete and balanced are the two combined into one complete equation for the reaction as a whole. It is worthwhile to balance the half-reactions separately since the two half-reactions can be carried out in separate vessels if they are suitably connected electrically. (See Chap. 14.) In general, net ionic equations are used in this process certainly some ions are required in each half-reaction. In the equations for the two half-reactions, electrons appear explicitly in the equation for the complete reaction—the combination of the two half-reactions—no electrons are included. 

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 ... 

Combining half-reactions (1) and (3) would give the greatest voltage ... 

In general, the number of electrons in each half must be the same when ionic half-equations are combined. To do this, one or both half-reactions may have to be multiplied by an integer. 

A half-reaction is either the oxidation reaction or the reduction reaction of a cell. On the other hand, the net reaction is an oxidation-reduction reaction, the combination of two half-reactions. 

If we examine the reactant, we find that the compound, KF, is an ionic compound containing potassium ions and fluoride ions. For this reason, we could replace the KF(1) in the original equation with K+(l) + F (l). These two ions, either alone or in combination, are the only substances, other than electrons, that can appear on the reactant side of the half-reactions. One of these ions, the fluoride ion, appears in the fluorine half-reaction. Since KF, and therefore F, is a reactant, we must reverse the fluorine half-reaction to place the fluoride ion on the reactant side. The original KF has no F2, so F2 cannot be a reactant. 

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