Standard molar concentration

As we saw in Section 9.2, the activity of a solute J in a dilute solution is approximately equal to the molar concentration relative to the standard molar concentration, [JJ/c°, with c° = 1 mol-L, and so a practical form of this expression is... 

The pH values produced by 1 mol dm-3 solutions of HC1 and NaOH, i.e. 0 and 14 respectively, define the practical range in which activity coefficients of H + (aq) and OH-(aq) may be ignored for general purposes, and subsidiary definitions of pH and pOH may be used pH = —logi0[H+] and pOH = —logi0[OH-]. The square brackets indicate the molar concentration of the species enclosed as a ratio to the standard molar concentration of I mol dm-3. 

The preceding sections have used standard molar concentration units for RNA and ions, indicated by brackets or the abbreviation M. Thermodynamic definitions of interaction coefficients are made in terms of molal units, abbreviated m, the moles of solute per kilogram of solvent water. Molal units have the convenient properties that the concentration of water is a constant 55.5 m regardless of the amount ofsolute(s) present, and the molality of one solute is unaffected by addition of a second solute. For dilute solutions, M and m units are interchangeable. We use molal units for the thermodynamic derivations in this section, and indicate later (Section 3.1) the salt concentrations where a correction for molar-molal conversion is required. 

A little similar but another choice of standard state, used e.g. in gas chemical kinetics, see Sect. 4.9, is the pure ideal gas at given temperature and at fixed standard molar concentration Cs (usually unit one, say c, = 1 mol/m ). Therefore, by (4.433), the standard function (/u, in (4.441)) is defined as iif(T) = 4- RTlnCj and... 

We often express the composition of a solution in terms of the molar concentration of the solute, [B], rather than as a mole fraction. The mole fraction and the molar concentration are proportional to each other in dilute solutions, so we write Xb = constant x [B]/c, where c = 1 mol dm is introduced to ensure that the constant is dimensionless. We shall call c the standard molar concentration. Then eqn 3.15 becomes... 

In the absence of Fe +, the membrane is colorless, but when immersed in a solution of Fe + and C, the membrane develops a red color as a result of the formation of a Fe +-bathophenanthroline complex. A calibration curve determined using a set of external standards with known molar concentrations of Fe + gave a standardization relationship of... 

Determine the molar concentration of V (V) in the sample of sea water, assuming that the standard additions result in a negligible change in the sample s volume. 

The numerical values of AG and A5 depend upon the choice of standard states in solution kinetics the molar concentration scale is usually used. Notice (Eq. 5-43) that in transition state theory the temperature dependence of the rate constant is accounted for principally by the temperature dependence of an equilibrium constant. 

The standard state chosen for the calculation of controls its magnitude and even its sign. The standard state is established when the concentration scale is selected. For most solution kinetic work the molar concentration scale is used, so A values reported by different workers are usually comparable. Nevertheless, an important chemical question is implied Because the sign of AS may depend upon the concentration scale used for the evaluation of the rate constant, which concentration scale should be used when A is to serve as a mechanistic criterion The same question appears in studies of equilibria. The answer (if there is a single answer) is not known, though some analyses of the problem have been made. Further discussion of this issue is given in Section 6.1. 

As a result standard solutions are now commonly expressed in terms of molar concentrations or molarity (AT). Such standard solutions are specified in terms of the number of moles of solute dissolved in 1 litre of solution for any solution,... 

What Do We Need to Know Already The concepts of chemical equilibrium are related to those of physical equilibrium (Sections 8.1-8.3). Because chemical equilibrium depends on the thermodynamics of chemical reactions, we need to know about the Gibbs free energy of reaction (Section 7.13) and standard enthalpies of formation (Section 6.18). Ghemical equilibrium calculations require a thorough knowledge of molar concentration (Section G), reaction stoichiometry (Section L), and the gas laws (Ghapter 4). 

We use a different measure of concentration when writing expressions for the equilibrium constants of reactions that involve species other than gases. Thus, for a species J that forms an ideal solution in a liquid solvent, the partial pressure in the expression for K is replaced by the molarity fjl relative to the standard molarity c° = 1 mol-L 1. Although K should be written in terms of the dimensionless ratio UJ/c°, it is common practice to write K in terms of [J] alone and to interpret each [JJ as the molarity with the units struck out. It has been found empirically, and is justified by thermodynamics, that pure liquids or solids should not appear in K. So, even though CaC03(s) and CaO(s) occur in the equilibrium... 

C. A silver electrode is immersed in this solution, and its potential is measured relative to a standard hydrogen electrode. A total of 16.7 mL of KI(aq) was required to reach the stoichiometric point, when the potential was 0.325 V. (a) What is the molar concentration of Ag+ in the solution ... 

The Gibbs free energy (computed in the harmonic approximation) were converted from the 1 atm standard state into the standard state of molar concentration (ideal mixture at 1 molL-1 and 1 atm). 

Note, in using Equations 50 and 53 above, that tabulations of thermodynamic data for electrolytes tend to employ a 1 molar ess concentration for all species in solution. For situations defined to have a standard-state pH value different from 0 (which corresponds to a 1 molar concentration of solvated protons), the standard-state chemical potentials for anions and cations are determined as... 

TABLE 2.1 Redox Potentials Important for Selected Microbiological Processes (Madigan et a ., 2000). The Potentials are given under Standard Conditions, i.e., at pH = 7, 25°C, 1 atm and 1 Molar Concentration of Relevant Components... 

Fig. 14.2 Population of the bound state of a complex as a function of the (molar) concentration of the unobserved substance for different KD values. The concentrations of the observed substance are 100 pM (cryo probe, panel A) and ImM (standard equipment, panel B), corresponding to typical experimental situations. The KD areas shaded in...

Enthalpies of reaction can also be calculated from individual enthalpies of formation (or heats of formation), AHf, for the reactants and products. Because the temperature, pressure, and state of the substance will cause these enthalpies to vary, it is common to use a standard state convention. For gases, the standard state is 1 atm pressure. For a substance in an aqueous solution, the standard state is 1 molar concentration. And for a pure substance (compound or element), the standard state is the most stable form at 1 atm pressure and 25°C. A degree symbol to the right of the H indicates a standard state, AH°. The standard enthalpy of formation of a substance (AHf) is the change in enthalpy when 1 mol of the substance is formed from its elements when all substances are in their standard states. These values are then tabulated and can be used in determining A//°rxn. 

However, the equilibrium constant must still be considered as pure and dimensionless numbers (according to the classical relation —AG° = RT In Ks). All molar concentrations in the expression of Ks should thus be interpreted as molar concentrations relative to a standard state of 1 mol dm-3 i.e. they are the numerical values of the molar concentrations5 . If the solution is not dilute enough, the equilibrium constants can still be written with concentrations but they must be considered as apparent stability constants. 

The standard electrode potential of an element is defined as its electrical potential when it is in contact with a molar solution of its ions. For redox systems, the standard redox potential is that developed by a solution containing molar concentrations of both ionic forms. Any half-cell will be able to oxidize (i.e. accept electrons from) any other half-cell which has a lower electrode potential (Table 4.1). 

For fixed time assays this most frequently involves the use of standards and a calibration graph. Some methods, e.g. the use of the molar absorbance coefficient in spectrophotometry, do not requite standards and giiNometric methods permit the calculation of molar concentration from the volume of gas (1 gram mole of gas occupies 22.4 litres at standard temperature and pressure, STP). 

The procedure called titration can be used to standardize a solution of a base, which means determine its molar concentration. To standardize a base, a solution of the base with unknown molarity is gradually added to a solution containing a known mass of an acid. The procedure enables you to determine when the number of moles of added OH- ions from the base equals the number of moles of H+ ion from the acid. 

The standard free energy change is the value obtained when the reactants and products (including H+) are at molar concentration and gasses (if present) are at 1 atmosphere of pressure. Such conditions are quite unphysiological, especially the proton concentration, as 1 molar H+ concentration gives a pH 0 biochemical reactions occur at a pH of between 5 and 8, mostly around pH 7. So a third term, AG°, is introduced to indicate that the reaction is occurring at pH 7. 

Equation A1.3 shows that isotope effects calculated from standard state free energy differences, and this includes theoretical calculations of isotope effects from the partition functions, are not directly proportional to the measured (or predicted) isotope effects on the logarithm of the isotopic pressure ratios. Rather they must be corrected by the isotopic ratio of activity coefficients. At elevated pressures the correction term can be significant, and in the critical region it may even predominate. Similar considerations apply in the condensed phase except the fugacity ratios which define Kf are replaced by activity ratios, a = Y X and a = y C , for the mole fraction or molar concentration scales respectively. In either case corrections for nonideality, II (Yi)Vi, arising from isotope effects on the activity coefficients can be considerable. Further details are found in standard thermodynamic texts and in Chapter 5. 

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