Symbols for Concentration

Notice that the notation for molal concentration to this point in our discussion of the Harned and Ehlers paper has been in terms of the variables ni, where x is the species of interest. Do these symbols represent molal analytical concentrations, species, concentrations, or both Explain. Note that the. symbols for concentration in the table adhere to the convention that we have used throughout this book, not the notation of Harned and Ehlers. 

The following symbols for concentration are used in this book ... 

For convenience new dimensionless coordinates are defined using Greek symbols for concentration, degree of advancement, and time normalised by division by the initial concentration qq (called general coordinates) ... 

Note that five symbols for concentration have now been introduced so that concentration variables with different units can be easily distinguished ... 

Figure 24-23 is a sketch of continuous culture with recycle. The symbols for flow rates and organism concentrations are F and X, respec tively Assuming perfect mixing and steady state so that the derivatives can be set to zero, mass balances lead to ... 

Pfiitze,/, pool, puddle, wallow, pH, abbrev. pH, pn (symbol for hydrogen-ion concentration) (pro Hundert) per cent, phagedanisches Wasser. (Pharm.) yellow mercurial lotion. 

Chemists traditionally use m to designate moiaiity, but this symbol easily leads to confusion because m also represents mass. For this reason, we use the symbol Cm (concentration, molal) for molality. 

The right part of equation [4], E = e c d, represents Lambert-Beer s law. E is called the extinction, c is the substance concentration, and d is the thickness of the sample. The E values span from 0 (this is the case when all light is transmitted and no absorption takes place, i.e., 1 = Iq) to inhnity, °o (this is the case of maximal extinction when no incident light is transmitted, i.e., 1 = 0). Realistic E values that can be correctly measured by normal spectrometers range between 0 and 2. Instead of using the E expression for extinction, A for absorbance is often used. E and A are dimensionless values, i.e., numbers without units. Nevertheless, OD, the symbol for optical density, is often added to E and A in order to clarify their meanings. 

Both molarity (Chap. 10) and normality (Chap. 15) are defined in terms of a volume. Since the volume is temperature-dependent, so are the molarity and normality of the solution. Two units of concentration that are independent of temperature are introduced in this chapter. Molality is defined as the number of moles of solute per kilogram of solvent in a solution. The symbol for molality is m. Note the differences between molality and molarity ... 

In the equations describing enzyme kinetics in this chapter, the notation varies a bit from other chapters. Thus v is accepted in the biochemical literature as the symbol for reaction rate while Vmax is used for the maximum rate. Furthermore, for simplification frequently Vmax is truncated to V in complex formulas (see Equations 11.28 and 11.29). Although at first glance inconsistent, these symbols are familiar to students of biochemistry and related areas. The square brackets indicate concentrations. Vmax expresses the upper limit of the rate of the enzyme reaction. It is the product of the rate constant k3, also called the turnover number, and the total enzyme concentration, [E]o. The case u, = Vmax corresponds to complete saturation of all active sites. The other kinetic limit, = (Vmax/KM)[S], corresponds to Km >> [S], in other words Vmax/KM is the first order rate constant found when the substrate concentration approaches zero ... 

This reaction occurs at a constant temperature. The reactant formulas are represented hy A and B. The stoichiometric coefficients are represented by a and b. In this section, you will study reaction rates that are not affected by the concentrations of the products. Therefore, you do not need to use symbols for the products. 

In a solution of a weak acid, only a very small proportion of the original acid molecules dissociate into ions and therefore [HA] is taken to be the same as the original concentration of the unionised acid molecules and is given the symbol c for concentration. 

Figure 1.30. Evolution of the water phase viscosity rjc as a function of the shear rate and alginate concentration (filled symbols). For the sake of comparison, the viscosity rja of the inverted emulsion at 0, = 75 wt% is reported in the same graph (open symbols). (Adapted from [162].)...

The threshold concentration above which a free amphi-phile will self-assemble and spontaneously form micelles. Below this concentration, no micelles are detectable. Note that micelle formation is not equivalent to a phase separation For most systems, the concentration range associated with the monomer-to-micelle transition is fairly narrow, and c.m.c. values can be obtained from graphical procedures. The symbol for c.m.c. is Cm. Whenever c.m.c. values are reported, the method for the determination should be clearly stated, because different physical techniques may be more or less sensitive to changes in the amphiphile s aggregation state. See Micelle Formation... 

Symbol for the product of the H+ concentration (or, H3O+ concentration) and the OH concentration of an aqueous solution the autoprotolysis constant. See Water, Temperature Effects of pK, of... 

Symbol for the temperature coefficient, a quotient equal to Vt+wIvt, where Vr+io and Vj are the rates of a process (e.g., an enzyme-catalyzed reaction) at two temperatures differing by 10°C. This parameter is usually evaluated at saturating concentrations of substrate(s), so that temperature-dependent changes in Michaelis constant(s) are inconsequential. The <2io value is a characteristic property of a particular enzyme from a specific organism and cell type. For example, one cannot use the Qio value for one hexokinase from yeast to infer the temperature dependence of another hexokinase, say from rat brain. Likewise, the Qio value need not remain the same for a mutant form and a wild-type enzyme. 

Fio. 11. Concentration profiles as measured with the equipment depicted in Fig. 10 (open symbols) and by GC analysis (closed symbols) for an esterification reaction between octanol and hexanoic acid. Conditions 200 ml, of reactant, 0.4mol/L of octanol, 0.4mol/L of hexanoic acid, l.Og Nafion resin/ silica, 447 K. The profiles were constructed from signals at 1720 and 1745 cm , and the spectra were corrected for solvent, octanol, and catalyst (74). 

For this mechanism, a differential equation may be written for the rate of change of each ring form, letting the symbols A, B, and E stand for concentrations ... 

Table 1 Kinetic and thermodynamic parameters determined for various tautomeric equilibria in aqueous solution at 25°C. The symbols for the rate constants k and the equilibrium constants K are explained in the text (first paragraph of section Examples ). Acidity constants are concentration quotients of ionization at ionic strength 7=0.1 m... 

Figure I. Surfactant sorption isotherms on kaolinite (pH 4.6, I S. = 0.1 M). Error bars for some data points are smaller than the symbols. Kaolinite concentrations were 100 g/L (SDS, Tween 80) or 250 g/L (SDS). Adapted from Ko et al. (1998b).

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