Concentration reciprocal

The units on [CH3CeH4S02H] are inverse molarity. Reciprocal concentrations are often cited in the chemical kinetics literature for second-order reactions. Confirm that second-order kinetics provide a good fit and determine the rate constant. 

A common observation arising with trivalent metal ions in aqueous solution is the occurrence of the conjugate base species, [M(0H)(H20)5] " (1). At low pH values the water exchange rates, kf,, observed experimentally by 0 NMR, depend linearly on the reciprocal concentration of Has shown by Eq. (20),... 

Since r p is dimensionless, [q] has units of reciprocal concentration (e.g., 1/g or dl/g). Hence in viscosity measurements the concentration units must always be stated. 

The effect of a competitive inhibitor can also be expressed as an inhibitor affinity constant K,) by plotting the inhibitor concentration versus the reciprocal of the reaction velocity, or versus the reciprocal concentration of a labeled ligand (the isotopically radiolabeled agonist that is displaced by the antagonist). The intersect of the lines so generated is -K,. 

The dependence of IjG of the formation of products 56 and 19, plotted against the reciprocal concentration of 55, are differently curved, i.e., the ratio of the yields of 56 and 19 changes with the concentration of 55. This points out that at least two different excited states of the donor (benzene) are transferred, differing in k /k, values (km — rate constant of energy transfer from an excited benzene molecule to 55, kq = over-all constant of deactivation of excited benzene molecule by other pathways) which influence the reactions of the acceptor 55 in different ways. 

Fig. 2. Plots of reciprocal energy transfer efficiency (y) against the concentration of benzene (B) and against reciprocal concentration of acetanilide (A) by the photo-rearrangement of acetanilide in cyclohexane, (o) 2-Aminoacetophenone ( ) 4-amino-acetophenone.

Solution Since refractive index is dimensionless, dn/dc has reciprocal concentration units. In Equation (20) the factors [/7(dn/dc)]2c/(d7r/dc) have the units pressure-1 since the units of c s cancel. The product r2X4 in Equation (20) has the units length6 or volume2 therefore, the denominator of Equation (20) has the units pressure volume2. The product kBT in the numerator... 

The value of K is given by the ratio mlb according to Equation (77). For this (hypothetical) system, K = (769)/(0.0700) = 1.10 104 liter (mole B) 1. These reciprocal concentration units are appropriate for K of Equation (66) since the activity of the bulk solvent has been absorbed into the definition of K. ... 

This mechanism is fully compatible with the observed linear relationship between the 46/47 product ratio and the reciprocal concentration of the alcohol, since the initial product ratio should be represented by the following equation ... 

From the above expressions it can be seen that reduced and intrinsic viscosities have the unit of reciprocal concentration. When one considers particle shape and solvation, however, concentration is generally expressed in terms of the volume fraction of the particles (i.e. volume of particles/total volume) and the corresponding reduced and intrinsic viscosities are, therefore, dimensionless. 

Fig. 5. Lineweaver-Burk plot of the Orpinomyces BglA on hydrolysis of cellobiose (0.04-16 mM). The release of glucose was measured. Reciprocal initial velocities (mg/U) are plotted against the reciprocal concentrations of substrates (1 mM). The inset is a plot of initial velocities (U/mg) against the log cellobiose concentrations (mM).

Figure 8. Relationship between the number of carbons in sugar alcohols and the reciprocal concentration which elicited a 50% response (CRsc). Bars indicate 95% confidence interval. Ethylene glycol (2C, 0, N = 5) glycerol (3C, 0, N —...

For the reaction A + A — P, we can write —dAJdt = k(A)(A) = k A2. In this case, the rate involves a higher power of the concentration (n = 1 + 1 = 2) and the reaction is second-order. For the reaction A -I- B —> P, the rate is proportional to the first power of each reactant and —d(A)(B)/dt = k(A)(B). The reaction is first-order with respect to A or B, but the overall reaction is second-order, because the right-hand side of the equation contains the product of two concentrations. The value of tV2 will depend on the initial reactant concentration(s), and the second-order rate constants have the dimensions of reciprocal concentration times time. Reactions of higher order, such as third order, are relatively rare, and their rates are proportional to the product of three concentration terms. 

Note that the units of this rate constant are reciprocal concentration (in number density units) and reciprocal time (in s-1). Remember that number density is a fancy way of saying molecules per unit volume (usually as molecules/cm3). 

The intrinsic viscosity is also called the limiting viscosity number. Many of these so-called viscosity terms are not viscosities at all. Thus ri, and are actually unitless ratios of viscosities [t ] is a ratio of viscosities divided by a concentration. The units of [ij] are reciprocal concentration and are commonly quoted in cubic centimeters per gram (cmVg) or deciliters per gram (dl/g). [A deciliter (dL) equals lOOcm. ] The units of K inEq. (3-44) must correspond to those of[t ]. 

Figure 5-6 Plot of reciprocal concentration as a function of time.

Figure 9.1. Langmuir adsorption isotherm. From the adsorption isotherm (plotted in accordance with equation 11a or equation 11b), the equilibrium constant and the adsorption capacity, F ax. are obtained by plotting F versus the reciprocal concentration (activity) of the adsorbate (equation 11c).

The ratio of specific viscosity to polymer concentration is the reduced viscosity, Vsp/c, which has units of reciprocal concentration. In the limit of very low concentrations (far below the overlap concentration) the reduced viscosity becomes a very important material property called the intrinsic viscosity (see Section 1.7.3, and in particular Fig. 1.24) ... 

The intrinsic viscosity is the initial slope of specific viscosity as a function of concentration, and has units of reciprocal concentration [see Eq. (1.97)]. 

The rate constant k for this type of reaction has the units of reciprocal concentration-reciprocal time. 

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