Standard states concentration, 248 pressure

A G° is the free energy difference between products and reactants (each in their standard states at pressure, P° and 298.15 K). This equation does not refer to the actual reaction (41.2) (Frame 41) at equilibrium (except where Kp/po = 1 and A G° = 0). A G refers to the difference in Gibbs energy between products and reactants at other concentrations/pressures not corresponding to equilibrium. 

Because reactions are carried out under a variety of conditions, it is convenient to define a standard state for substances and experimental conditions. The standard state is the form (solid, liquid, or gas) assumed by the pure substance at 1 atm pressure. For substances in aqueous solution, the standard-state concentration is 1 M. Standard-state values are designated by a superscript ° following the thermodynamic symbol as in AG°. 

In this expression ct(X) is the symmetry number of the solute X (the number of indistinguishable orientations of the solute), C° is the standard state concentration of the solute, m is the mass of atom i of the solute, M(X) is the total number of atoms of the solute, P° is the standard pressure. 

The first term, AG°, is the change in Gibb s free energy under standard-state conditions defined as a temperature of 298 K, all gases with partial pressures of 1 atm, all solids and liquids pure, and all solutes present with 1 M concentrations. The second term, which includes the reaction quotient, Q, accounts for nonstandard-state pressures or concentrations. Eor reaction 6.1 the reaction quotient is... 

Only those components which are gases contribute to powers of RT. More fundamentally, the equiUbrium constant should be defined only after standard states are specified, the factors in the equiUbrium constant should be ratios of concentrations or pressures to those of the standard states, the equiUbrium constant should be dimensionless, and all references to pressures or concentrations should really be references to fugacities or activities. Eor reactions involving moderately concentrated ionic species (>1 mM) or moderately large molecules at high pressures (- 1—10 MPa), the activity and fugacity corrections become important in those instances, kineticists do use the proper relations. In some other situations, eg, reactions on a surface, measures of chemical activity must be introduced. Such cases may often be treated by straightforward modifications of the basic approach covered herein. 

II The increment in the free energy, AF, in the reaction of forming the given substance in its standard state from its elements in their standard states. The standard states are for a gas, fugacity (approximately equal to the pressure) of 1 atm for a pure liquid or solid, the substance at a pressure of 1 atm for a substance in aqueous solution, the hyj)othetical solution of unit molahty, which has all the properties of the infinitely dilute solution except the property of concentration. 

Since concentration variations have measurable effects on the cell voltage, a measured voltage cannot be interpreted unless the cell concentrations are specified. Because of this, chemists introduce the idea of standard-state. The standard state for gases is taken as a pressure of one atmosphere at 25°C the standard state for ions is taken as a concentration of 1 M and the standard state of pure substances is taken as the pure substances themselves as they exist at 25°C. The half-cell potential associated with a halfreaction taking place between substances in their standard states is called ° (the superscript zero means standard state). We can rewrite equation (37) to include the specifications of the standard states ... 

We now have the foundation for applying thermodynamics to chemical processes. We have defined the potential that moves mass in a chemical process and have developed the criteria for spontaneity and for equilibrium in terms of this chemical potential. We have defined fugacity and activity in terms of the chemical potential and have derived the equations for determining the effect of pressure and temperature on the fugacity and activity. Finally, we have introduced the concept of a standard state, have described the usual choices of standard states for pure substances (solids, liquids, or gases) and for components in solution, and have seen how these choices of standard states reduce the activity to pressure in gaseous systems in the limits of low pressure, to concentration (mole fraction or molality) in solutions in the limit of low concentration of solute, and to a value near unity for pure solids or pure liquids at pressures near ambient. 

The standard free energy change is a function only of temperature. That is, it is independent of pressure and concentration for a specified standard state. Thus, at a given temperature, the term a1 1 is constant and we can write... 

Alternative forms of the equilibrium constant can be obtained as we express the relationship between activities, and pressures or concentrations. For example, for a gas phase reaction, the standard state we almost always choose is the ideal gas at a pressure of 1 bar (or 105 Pa). Thus... 

An enthalpy of reaction also depends on the conditions (such as the pressure). All the tables in this book list data for reactions in which each reactant and product is in its standard state, its pure form at exactly 1 bar. The standard state of liquid water is pure water at 1 bar. The standard state of ice is pure ice at 1 bar. A solute in a liquid solution is in its standard state when its concentration is 1 mol-L". The standard value of a property X (that is, the value of X for the standard state of the substance) is denoted X°. 

A note on good practice Recall that the standard state of a pure substance is its pure form at a pressure of 1 bar (Section 6.15). For a solute, the standard state is for a concentration of 1 mol-L 1. Pure solids and liquids may always be regarded as being in their standard states provided the pressure is close to 1 bar. 

It is possible to choose a different standard state (after all, molecules don t know what their standard state is) for the pressure or concentration of chemical species. The standard state corresponding to data presented in Appendix 2A is for... 

The Nernst equation is used to calculate electrode potentials or cell potentials when the concentrations and partial pressures are other than standard state values. The Nernst equation using both base 10 and natural logarithms is given by ... 

Electrolytes are solutes that carry an electrical charge. As charged species typically have negligible vapor pressures, it is convenient to introduce yet another standard state for their description.8,9 In general, the same conditions of concentration, temperature, and pressure are assumed as... 

To evaluate the logarithm, we must measure the vapor pressure Pa of A in equilibrium with a solution where its mole fraction is XA in the limit where the solution becomes infinitely dilute. That is, in the limit of infinite dilution where y is 1, the free energy of solvation can be obtained from measurement of the solute vapor pressure (in the appropriate standard state units) over a solution of known concentration. 

For gases and vapors, exposure concentrations are traditionally expressed in parts per million (ppm). The calculation for the ppm of a gas or vapor in an air sample is based on Avogadro s Law, which states that Equal volumes contain equal numbers of molecules under the same temperature and pressure. In other words, under standard temperature and pressure (STP), one gram-molecular weight (mole) of any gas under a pressure of one atmosphere (equivalent to the height of 760 mm mercury) and a temperature of 273 K has the same number of molecules and occupies the same volume of 22.4 liters. However, under ambient conditions, the volume of 22.4 liters has to be corrected to a larger volume based on Charles Law, which states that at constant pressure the volume of gas varies directly with the absolute temperature. Thus, at a room temperature of 25° C, one mole of a gas occupies a volume of 24.5 liters. 

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. 

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