Temperature half-reaction

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]. 

If the T values of Table I are first fitted against EA values, without first fitting with EE(v) values, poor linea correlations result. For example, for tKe one-hour half-life temperatures of reactions 1 and 4, the squares of the correlation coefficients for these linear regression analyses are only 0.51 and 0.55, respectively. 

Fig. 22.6. Redox potentials (mV) of various half-cell reactions during mixing of fluid from a subsea hydrothermal vent with seawater, as a function of the temperature of the mixture. Since the model is calculated assuming 02(aq) and H2(aq) remain in equilibrium, the potential for electron acceptance by dioxygen is the same as that for donation by dihydrogen. Dotted line shows currently recognized upper temperature limit (121 °C) for microbial life in hydrothermal systems. A redox reaction is favored thermodynamically when the redox potential for the electron-donating half-cell reaction falls below that of the accepting half-reaction.

In the discussion of the Daniell cell, we indicated that this cell produces a voltage of 1.10 V. This voltage is really the difference in potential between the two half-cells. The cell potential (really the half-cell potentials) is dependent upon concentration and temperature, but initially we ll simply look at the half-cell potentials at the standard state of 298 K (25°C) and all components in their standard states (1M concentration of all solutions, 1 atm pressure for any gases and pure solid electrodes). Half-cell potentials appear in tables as the reduction potentials, that is, the potentials associated with the reduction reaction. We define the hydrogen half-reaction (2H+(aq) + 2e - H2(g)) as the standard and has been given a value of exactly 0.00 V. We measure all the other half-reactions relative to it some are positive and some are negative. Find the table of standard reduction potentials in your textbook. 

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. 

To understand potentiometric methods, those that measure electrical potentials and determine analyte concentrations from these potentials, it is necessary that numerical values for these tendencies be known under conventional standard modes and conditions. What are these modes and conditions First, all halfreactions must be written as either reductions or oxidations. Scientists have decided to write them as reductions. Second, the tendencies for half-reactions to proceed depend on the temperature, the concentrations of the chemical species involved, and, if gases are involved, the pressure in the half-cell. Scientists have defined standard conditions to be a temperature of 25°C, a concentration of exactly 1 M for all dissolved chemical species involved, and a pressure of exactly 1 atm. Third, because every cell consists of two half-cells, it is not possible to measure the value directly. However, if we were to assign the tendency of a certain half-reaction to be zero, then the tendencies of all other half-reactions can be determined relative to this reference half-reaction. 

If any species involved is a gas, the partial pressure of the gas is substituted for the concentration. If the temperature is different from 25°C, the constant 0.0592 changes. The number of electrons, n, in Equation (14.4) is the total number of electrons transferred, as discovered after equalizing the electrons in the two half-reactions in step 3 of the scheme for determining E, in Section 14.3. 

Consequently, a wealth of information on the energetics of electron transfer for individual redox couples ("half-reactions") can be extracted from measurements of reversible cell potentials and electrochemical rate constant-overpotential relationships, both studied as a function of temperature. Such electrochemical measurements can, therefore, provide information on the contributions of each redox couple to the energetics of the bimolecular homogeneous reactions which is unobtainable from ordinary chemical thermodynamic and kinetic measurements. 

The external source of electricity forces electrons onto one electrode. As a result, this electrode becomes negative relative to the other electrode. The positive sodium ions move toward the negative electrode, where they gain electrons and are reduced to the element sodium. At this temperature, sodium metal is produced as a liquid. The negative chloride ions move toward the positive electrode, where they lose electrons and are oxidized to the element chlorine, a gas. As in a galvanic cell, reduction occurs at the cathode, and oxidation occurs at the anode of an electrolytic cell. The half-reactions for this electrolytic cell are as follows. 

Since in experiments such as the one we have just discussed, it is only possible to determine potential differences between two electrodes (and not the absolute potential of each half cell), it is now useful to choose a reference system to which all measured potential differences may be related. In accord with the IUPAC 1953 Stockholm convention, the standard hydrogen electrode (SHE) is commonly selected as the reference electrode to which we arbitrarily assign a zero value of electrical potential. This is equivalent to assigning (arbitrarily) a standard free energy change, ArG°, of zero at all temperatures to the half reaction ... 

For modest temperature excursions away from 25°C, the change in E° for a half-reaction can be written in the form... 

All species are aqueous unless otherwise indicated. The reference state for amalgams is an infinitely dilute solution of the element in Hg. The temperature coefficient, dE°/dT, allows us to calculate the standard potential, E°(T), at temperature T E°(T) — Ec + (dE°/dT)AT. where A T is T — 298.15 K. Note the units mVIK for dE°ldT. Once you know E° for a net cell reaction at temperature T, you can find the equilibrium constant, K, for the reaction from the formula K — lOnFE°,RTln w, where n is the number of electrons in each half-reaction, F is the Faraday constant, and R is the gas constant. 

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