Molarity concentrations defined

We may easily rewrite the important quantities in (2.472) to molar basis as the partial mass and partial molar variables of species s are simply related by the molecular weight. We start by changing the thermodynamic quantities within the two first terms on the RHS of (2.455) using molar concentrations defined by = M Cs-... 

Consider now a solution made up of i species. The two basic concentration units used are the mass concentration [density] and molar concentration., defined, respectively, by... 

Plan We know from the balanced equation that when x mol of COCI2 deconqtoses, x mol of CO and x mol of CI2 form We use the volume (10.0 L) to convert amount (5.00 mol or 0.100 mol) to molar concentration, define x and set up the reaction table, and substitute the values into Q,.. Before using the quadratic formula, we assume that x is negligibly small. After solving for x, we check the assumption and find the equilibrium concentrations. If the assumption is not justified, we use the quadratic formula to find x. 

The true thermodynamic equilibrium constant is a function of activity rather than concentration. The activity of a species, a, is defined as the product of its molar concentration, [A], and a solution-dependent activity coefficient, Ya. 

Traditional chemical kinetics uses notation that is most satisfactory in two cases all components are gases with or without an inert buffer gas, or all components are solutes in a Hquid solvent. In these cases, molar concentrations represented by brackets, are defined, which are either constant throughout the system or at least locally meaningful. The reaction quotient Z is defined as... 

Define fC = Xm/XaXb and = c /caCb, convert molar concentrations to mole fractions using the dilute solution limit, Eq. (6-25), thus obtaining Using Eqs. (6-21) and (6-22) yields... 

To be preci.se in physical chemical terms, the activities of tire various components, not their molar concentration.s,. should be u.sed in the.se equations. The activity ( z) of a. solute component is defined as the product of its molar concentration, c, and an activity coefficient, 7 a = [c]y. Mo.st biochemical work involves dilute solutions, and die u.se of acdvides instead of molar concentration.s is usually neglected. However, the concentration of certain solutes may be very high in living cells. 

In Chapter 4, molarity was the concentration unit of choice in dealing with solution stoichiometry. You will recall that molarity is defined as... 

FIGURE 3.6 Classical model of agonism. Ordinates response as a fraction of the system maximal response. Abscissae logarithms of molar concentrations of agonist, (a) Effect of changing efficacy as defined by Stephenson [24], Stimulus-response coupling defined by hyperbolic function Response = stimulus/(stimulus-F 0.1). (b) Dose-response curves for agonist of e = 1 and various values for Ka. 

The equilibrium constant in Eq. 2 is defined in terms of activities, and the activities are interpreted in terms of the partial pressures or concentrations. Gases always appear in K as the numerical values of their partial pressures and solutes always appear as the numerical values of their molarities. Often, however, we want to discuss gas-phase equilibria in terms of molar concentrations (the amount of gas molecules in moles divided by the volume of the container, [I] = j/V), not partial pressures. To do so, we introduce the equilibrium constant Kt., which for reaction E is defined as... 

To set up expressions for the instantaneous rate of a reaction, we consider At to be very small so that t and t + At are close together we determine the concentration of a reactant or product at those times and find the average rate from Eq. 1. Then we decrease the interval and repeat the calculation. We can imagine continuing the process until the interval At has become infinitely small (denoted d/) and the change in molar concentration of a reactant R has become infinitesimal (denoted d R]). Then we define the instantaneous rate as... 

Some Chemical Considerations Relevant to the Mouse Bioassay. Net toxicity, determined by mouse bioassay, has served as a traditional measure of toxin quantity and, despite the development of HPLC and other detection methods for the saxi-toxins, continues to be used. In this assay, as in most others, the molar specific potencies of the various saxitoxins differ, thus, net toxicity of a toxin sample with an undefined mixture of the saxitoxins can provide only a rough approximation of the net molar concentration. Still, to the extent that limits can be placed on variation in toxin composition, the mouse assay can in principle provide useful data on trends in net toxin concentration. However, the somewhat protean chemistry of the saxitoxins makes it difficult to define conditions under which the composition of a mixture of toxins will remain constant thus, attaining a reproducible level of mouse bioassay toxicity is difficult. It is therefore useful to review briefly some of the chemical factors that should be considered when employing the mouse bioassay for the saxitoxins or when interpreting results. Similar concepts will apply to other assays. 

The inlet methanol molar concentration was determined by the mass of catalyst, S/C ratio, and W/F ratio. Here, steam-to-carbon (S/C) ratio is defined as the ratio of steam molecules per carbon atom in the reactant feed and W/F ratio as the amount of catalyst loading into the channel divided by the amount of methanol molar flow rate. For more information on the design parameters, physical properties, and operating conditions, refer to Jung et al. [12]. 

Perhaps the most useful measure of concentration is molarity. Molarity is defined as the number of moles of solute per liter of solution ... 

Relationship 23 provides a method for evaluating the parameter "a" that is defined by Equation 2A. The cumulative molar concentration of polymeric species PT0T was numerically evaluated via integration of population density distributions. The contribution of network molecules to the zeroth moment of the distribution is negligible. Results are presented by Figure A and show that... 

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... 

Normalization may be by means of the system volume V. This converts nA into a volumetric molar concentration (molarity) of A, cA, defined by ... 

Absorptivity is defined as A = ebC where A = absorbance, 8 = molar absorptivity (L/mol/cm), b = path length of radiation through sample (cm), and C = molar concentration. 

Activity coefficient vary with the concentration especially in the presence of added electrolyte. Lewis and Randall introduced the quantity called ionic strength which is a measure of the intensity of the electric field due to the ions in a solution. It is defined as the sum of the terms obtained by multiplying the molarity (concentration) of each ion present in solution by the square of its valence... 

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). 

Because of the difficulties in measuring the amount of enzyme in the conventional units of mass or molar concentration, the accepted unit of enzyme activity is defined in terms of reaction rate. The International Unit (IU) is defined as that amount of enzyme which will result in the conversion of 1 /nmol of substrate to product in 1 minute under specified conditions. The SI unit of activity, which is becoming more acceptable, is the katal and is defined as that amount of enzyme which will result in the conversion of 1 mol of substrate to product in 1 second. A convenient sub-unit is the nanokatal, which is equal to 0.06 International Units. 

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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