Reduction to standard states

It is observed in table 7.2 that the most important terms in the reduction to standard states are the decomposition of aqueous nitric acid (AU (,), the compression of the initial gaseous phase (02+H20) from a negligibly small pressure to the initial pressure (A 6/7), the decompression of the final gaseous phase (02 + N2 + C02 + H20) from the final pressure to a negligibly small pressure (Af/19), and the evaporation of C02 from the final aqueous phase (AU o). The terms relative to the vaporization and condensation of liquid water (A f/3 — AIJ24) almost cancel out. 

The standard molar internal energy of eombustion, Ac(/°(7 ref), is calculated. This calculation is called reduction to standard states. 

Figure 7.4 Reduction of combustion calorimetric results to standard states.

C. E. Vanderzee. Reduction of Experimental Results to Standard State Quantities. In Experimental Thermodynamics, vol. 4 Solution Calorimetry K. N. Marsh, P. A. G. O Hare, Eds. Blackwell Scientific Publications Oxford, 1994 chapter 2. 

Since the potential for a single half-reaction cannot be measured, a reference halfreaction is arbitrarily assigned a standard-state potential of zero. All other reduction potentials are reported relative to this reference. The standard half-reaction is... 

Appendix 3D contains a listing of the standard-state reduction potentials for selected species. The more positive the standard-state reduction potential, the more favorable the reduction reaction will be under standard-state conditions. Thus, under standard-state conditions, the reduction of Cu + to Cu E° = -1-0.3419) is more favorable than the reduction of Zn + to Zn (E° = -0.7618). 

Consequently, solutions of Fe + and Fe + are buffered to a potential near the standard-state reduction potential for Fe +. 

To provide basic geographic units for the air-pollution control program, the United States was divided into 247 air quahty control regions (AQCRs). By a standard rollback approach, the total quantity of pollution in a region was estimated, the quantity of pollution that could be tolerated without exceeding standards was then calculated, and the degree of reduction called tor was determined. States were required by EPA to develop state implementation plans (SIPs) to achieve comphance. 

We have already noted that the standard free energy change for a reaction, AG°, does not reflect the actual conditions in a ceil, where reactants and products are not at standard-state concentrations (1 M). Equation 3.12 was introduced to permit calculations of actual free energy changes under non-standard-state conditions. Similarly, standard reduction potentials for redox couples must be modified to account for the actual concentrations of the oxidized and reduced species. For any redox couple. 

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. 

The obtained A 7 a() value and the energy equivalent of the calorimeter, e, are then used to calculate the energy change associated with the isothermal bomb process, AE/mp. Conversion of AE/ibp to the standard state, and subtraction from A f/jgp of the thermal corrections due to secondary reactions, finally yield Ac f/°(298.15 K). The energy equivalent of the calorimeter, e, is obtained by electrical calibration or, most commonly, by combustion of benzoic acid in oxygen [110,111,113]. The reduction of fluorine bomb calorimetric data to the standard state was discussed by Hubbard and co-workers [110,111]. 

C. E. Vanderzee. Reduction of Results to the Isothermal Calorimetric Process and to the Standard-State Process in Solution-Reaction Calorimetry. J. Chem. 

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 reduction potentials used to calculate E ceii for the decomposition of water apply only to reactants and products in their standard states. However, in pure water at 25°C, the hydrogen ions and hydroxide ions each have concentrations of 1 x 10 mol/L. This is not the standard state value of 1 mol/L. The reduction potential values for the non-standard conditions in pure water are given below. The superscript zero is now omitted from the E symbol, because the values are no longer standard. 

The two half reactions of any redox reaction together make up an electrochemical cell. This cell has a standard potential difference, E , which is the voltage of the reaction at 25 °C when all substances involved are at unit activity. E refers to the potential difference when the substances are not in the standard state. E for a particular reaction can be found by subtracting one half cell reaction from the other and also subtracting the corresponding voltages. For example for reduction of Fe to Fe by H2, E° = 0.77 - 0 = 0.77 V. A further example is the oxidation of Fe " by solid Mn02 in acid solution. The half cell reactions are. 

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