Concentration, molar scales

In the case of pure solids such as Ag and AgCl the chemical potential is identical to the standard chemical potential at 25°C and 1 bar pressure. For solutions, the standard state of the solute is unit activity at the same temperature and pressure. In the case of electrolytes as solutes, the activity is defined on the concentration (molarity) scale, and the standard state is the hypothetical ideal state of unit molarity for which the activity coefficient ye is unity. Under these circumstances, the activity of the solvent, which does not appear explicitly in equation (9.2.9), is also unity to a good approximation when the solvent is water. For gases the standard state is a pressure of 1 bar (10 Pa) at 25°C. In the older literature the standard pressure was 1 atm (101,325 Pa). In data compilations appearing after 1982, the standard state of 1 bar and 25°C is always used for gases [G3]. 

The activation parameters from transition state theory are thermodynamic functions of state. To emphasize that, they are sometimes designated A H (or AH%) and A. 3 4 These values are the standard changes in enthalpy or entropy accompanying the transformation of one mole of the reactants, each at a concentration of 1 M, to one mole of the transition state, also at 1 M. A reference state of 1 mole per liter pertains because the rate constants are expressed with concentrations on the molar scale. Were some other unit of concentration used, say the millimolar scale, values of AS would be different for other than a first-order rate constant. 

This form assumes that the effect of pressure on the molar volume of the solvent, which accelerates reactions of order > 1 by increasing the concentrations when they are expressed on the molar scale, has been allowed for. This effect is usually small, ignored but in the most precise work. Equation (7-41) shows that In k will vary linearly with pressure. We shall refer to this graph as the pressure profile. The value of A V is easily calculated from its slope. The values of A V may be nearly zero, positive, or negative. In the first case, the reaction rate shows little if any pressure dependence in the second and third, the applied hydrostatic pressure will cause k to decrease or increase, respectively. A positive value of the volume of activation means that the molar volume of the transition state is larger than the combined molar volume of the reactant(s), and vice versa. 

A literature procedure whereby bromopyrimidine is oxidised by excess peroxy-acetic acid in acetone, with sulfuric acid catalysis, was being scaled up. The crude product from the fourth batch at two molar scale was filtered out and allowed to dry to dry in the sintered glass funnel over the weekend. An explosion occurred when it was scraped out to complete purification on the Monday. This was considered due to acetone peroxides, which had probably concentrated locally by wicking or sublimation. 

Tbe discussion of the semi-chlute properties remains confined mainly to the osmotic modulus which in good solvents describes the repulsive interaction among the macromolecules as a function of concentration. After scaling the concentration by the overlap concentration c = A2M.Yf) and normalizing the osmotic modulus by the molar mass, universal masteS" curves are obtained. These master curves differ characteristically for the various macromolecular architectures. The branched materials form curves which lie, as expected, in the range between hard spheres and flexible linear chains. 

Here, p and m are the standard chemical potential and concentration (molal scale) of the /-component (z = 1 for solvent, z = 2 for biopolymer) A2 is the second virial coefficient (in molal scale units of cm /mol, i.e., taking the polymer molar mass into account) and m° is the standard-state molality for the polymer. 

At this point let us address the problem of expressing abundance of compounds in a bulk phase. In environmental chemistry, the most common way to express concentrations is not by mole fraction, but by the number of molecules per unit volume, for example, as moles per liter of solution (mol L, M). This molar concentration scale is sometimes not optimal (volumes are, for example, dependent on Tandp, whereas masses are not hence, the use of concentration data normalized per kilogram of seawater is often seen in the oceanographic literature). However, the molar scale is widely used. We can convert mole fractions to molar concentrations by ... 

Ionic strength ranges are applicable for the equations Yi yL where and y, are the activity coefficients on the mole fraction and molarity concentration/activity scales, respectively. The parameter A depends on T(K) according to the equation A = 1.92 x 106 (sT) 3/2 where e is the temperature-dependent dielectric constant of water B = 50.3 (eT) 1,2. For water at 298 K (25°C), A = 0.51 and B = 0.33. Applicable ionic strength range obtained from Stumm and Morgan (1981). 

Concentration is expressed on the molar scale in terms of mol L of solvent or on the molal scale in terms of mol kg of solvent. The molal scale gives concentrations that are independent of temperature and pressure. In this chapter, the molar scale will be used on the basis that molarity and molality are almost identical for the low ionic strengths commonly associated with freshwaters. 

For concentrations (activities of HA and A ) in a molal — molar scale, pATha is commonly referred to as pATa. 

The acidity constants given here are based on the convention H2O = 1 for the solvent water. H (aq), HA, and A are on a moial molar concentration scale. In order to compare the acidity of water with that of the other acids, we must express the Biyinsted acid water on a molal (or molar scale) accordingly, the ion product of water has to be divided by H2O = 55.4 = 15.74. 

In many cases, it is more convenient to use activity coefficients on the molarity scale. Not only is molarity more commonly used as a concentration unit in chemistry but values of are more directly related to the results of statistical mechanical theories of electrolyte solutions discussed later in this chapter. For a given molality, m, one must calculate the corresponding molarity, c, using the relationship... 

In the first series solutions of silver nitrate and sodium selenite were mixed to the total concentrations 5.0 x 10 and 48.0 x 10 M, respectively. The pH was adjusted by addition of HCIO4 or NaOH to values between 1.2 and 13.1 (53 experimental points). After equilibration for 6 days, the phases were separated. The pH and pAg were obtained from potentiometric measurements with a glass and a silver electrode. The latter electrode was calibrated on the concentration scale. The following equilibrium constants were evaluated from the data on the molar scale ... 

Here, cs denotes the concentration in mol/kg (molality scale), and [s] is the concentration in mol/liter (molarity scale). Both units are related in that [s] = pwcs where pw= 1 kg/dm3 is the density of water. Its variation with temperature causes the molarity scale to depend on temperature, whereas the molality scale does not. In the temperature range 0-25°C, however, the density of water differs from unity by less than 0.3%, so that [s] = cs with reasonable accuracy. Most Henry coefficients are less well known. From the definitions in Eqs. (8-7) and (8-8), the coefficients involved are related by... 

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