Reaction volume, molar

ArF( ) is the molar reaction volume which is the measure of how strongly the transformation of the substances taking place changes the volume at a particular extent of reaction. The index r refers to reaction and serves to differentiate the molar reaction volume (unit m mol ) from a change of volume AV (unit m ). 

The conditions added to the equation above can be expressed as for the case of molar reaction volume by replacing the A by 3 in the difference quotient and adding the quantities which will be kept constant to the index ... 

J si,o represents the drive of the melting process at the chosen initial state (in this case, a temperature of To and pressure of po). The temperature coefficient aTsi of the drive corresponds to the molar reaction entropy Agi o of the melting process and the pressure coefficient corresponds to the negative molar reaction volume — AsiVo (compare Chap. 9), both at the initial state To, po)- This yields ... 

Oa, Ka, and R Ka and R must be known from independent measurements (e.g., conductance or heat of dilution measurements). Figure 7 shows the apparent molar volume of CdS04 in water and the extrapolation to zero concentration based on Eq. (115). The quantity AVa = Va is the molar reaction volume of ion-pair formation it is related to the pressure derivative of the association constant of Eq. (102) and can also be obtained from the pressure dependence of the association constant of conductance measurements at various pressures, for example, AVA(CdS04) = 9.4 cm mol from density measurements and 11.7 cm mol" from conductance measurements, which is fairly good agreement when the mutual limits of error are taken into account. 

Herein Pa and Pb are the micelle - water partition coefficients of A and B, respectively, defined as ratios of the concentrations in the micellar and aqueous phase [S] is the concentration of surfactant V. ai,s is fhe molar volume of the micellised surfactant and k and k , are the second-order rate constants for the reaction in the micellar pseudophase and in the aqueous phase, respectively. The appearance of the molar volume of the surfactant in this equation is somewhat alarming. It is difficult to identify the volume of the micellar pseudophase that can be regarded as the potential reaction volume. Moreover, the reactants are often not homogeneously distributed throughout the micelle and... 

Herein [5.2]i is the total number of moles of 5.2 present in the reaction mixture, divided by the total reaction volume V is the observed pseudo-first-order rate constant Vmrji,s is an estimate of the molar volume of micellised surfactant S 1 and k , are the second-order rate constants in the aqueous phase and in the micellar pseudophase, respectively (see Figure 5.2) V is the volume of the aqueous phase and Psj is the partition coefficient of 5.2 over the micellar pseudophase and water, expressed as a ratio of concentrations. From the dependence of [5.2]j/lq,fe on the concentration of surfactant, Pj... 

Although many industrial reactions are carried out in flow reactors, this procedure is not often used in mechanistic work. Most experiments in the liquid phase that are carried out for that purpose use a constant-volume batch reactor. Thus, we shall not consider the kinetics of reactions in flow reactors, which only complicate the algebraic treatments. Because the reaction volume in solution reactions is very nearly constant, the rate is expressed as the change in the concentration of a reactant or product per unit time. Reaction rates and derived constants are preferably expressed with the second as the unit of time, even when the working unit in the laboratory is an hour or a microsecond. Molarity (mol L-1 or mol dm"3, sometimes abbreviated M) is the preferred unit of concentration. Therefore, the reaction rate, or velocity, symbolized in this book as v, has the units mol L-1 s-1. 

Use the estimates of molar constant-volume heat capacities given in the text (as multiples of R) to estimate the change in reaction enthalpy of N2(g) + 3 H,(g) —> 2 NH.(g) when the temperature is increased from 300. K to 500. K. Ignore the vibrational contributions to heat capacity. Is the reaction more or less exothermic at the higher temperature ... 

The quantitative aspects of acid-base chemistry obey the principles Introduced earlier in this chapter. The common acid-base reactions that are important in general chemistry take place in aqueous solution, so acid-base stoichiometry uses molarities and volumes extensively. Example Illustrates the essential features of aqueous acid-base stoichiometry. 

Reactions were carried out in liquid phase in a well-stirred (1000 rpm) high-pressure reactor (Parr Instruments, 300 mL) at 30 bar and 150°C with 370 mg catalyst for two hours, unless otherwise specified. The feed consisted of the amine with slight excess of ketone at ketone/amine-group molar ratio of 1.6 while maintaining a reaction volume of about 150 mL. In a typical experiment, 576 mmol of aniline is mixed with 920 mmol of cyclohexanone and 370 mg of BS2 catalyst in the 300 mL reactor. The reactor is closed and then pressure-tested to 50 psi above operating pressure to ensure that the system is leak proof Once pressure-tested, the headspace is replaced... 

Add 500 pi of the peptide solution to 200 pi of carrier protein. For greater reaction volumes, keep the molar ratio of peptide-to-carrier addition the same and proportionally scale up the amount of EDC added in the next step. If the peptide is initially dissolved in DMSO, much less peptide volume compared to protein volume should be used to maintain solubility (see discussion in step 2). 

In Table 2 Diels-Alder reactions are complied showing ratios of activation volume to reaction volume that are smaller than or close to unity (0 = AV /AV < 1) and in Table 3 those that are close to or even larger than unity (0 > 1). Within the scope of transition state theory, the activation volume can be considered to be a measure of the partial molar volume of the transition state [AV = F — F (reactants)]. Accordingly, the transition state volumes of these reactions are close to or even smaller than the... 

For the mechanistic interpretation of activation volume data for nonsymmetrical electron-transfer reactions, it is essential to have information on the overall volume change that can occur during such a process. This can be calculated from the partial molar volumes of reactant and product species, when these are available, or can be determined from density measurements. Efforts have in recent years focused on the electrochemical determination of reaction volume data from the pressure dependence of the redox potential. Tregloan and coworkers (139, 140) have demonstrated how such techniques can reveal information on the magnitude of intrinsic and solvational volume changes associated with electron-transfer reactions of transition... 

Based on experimental results and a model describing the kinetics of the system, it has been found that the temperature has the strongest influence on the performance of the system as it affects both the kinetics of esterification and of pervaporation. The rate of reaction increases with temperature according to Arrhenius law, whereas an increased temperature accelerates the pervaporation process also. Consequently, the water content decreases much faster at a higher temperature. The second important parameter is the initial molar ratio of the reactants involved. It has to be noted, however, that a deviation in the initial molar ratio from the stoichiometric value requires a rather expensive separation step to recover the unreacted component afterwards. The third factor is the ratio of membrane area to reaction volume, at least in the case of a batch reactor. For continuous opera-... 

The pressure dependence of an equilibrium constant K° is determined by the standard reaction volume AV°, which is the change in molar volume of the system as the reaction goes from the initial to the final state, that is, the difference in molar volumes between the products and the reactants ... 

Magnetic quantum number. 19 Magnetic susceptibility mass. 460-463 molar, 461 volume, 460 Maim. J. O.. 70 Map of twist angles, 490 Marcus theory, 571 Mass spectrometry. 239 Maximum multiplicity, 26-27 Mechanisms inner sphere, 565-567 outer sphere. 558-561 of redox reactions. 557-572 of substitution reactions. 545-547. 551-553 Medicinal chemistry, 954-960 Meissner effect, 285 Melting points, and chemical forces. 307-310... 

As described above, the activation volume is the difference in partial molar volume between the transition state and the initial state. From a synthetic point of view this could often be approximated by the difference in the molar volume between the reactant(s) and product(s). Partial molar activation volumes, which can be divided into a structural part and a solvent-dependent part, are of considerable value in speculating about the nature of the transition state. This thermodynamic property has led to many studies on the mechanism of organic reactions. 

The reaction volume may be of interest in itself, and furthermore its determination can provide a route to the volume of activation in the reverse direction if that parameter is not experimentally accessible and when AV for the reaction in the forward direction is known. As indicated above, AV may be determined from the dependence upon pressure of the equilibrium constant. It may also be obtained under certain circumstances from the partial molar volumes of the reactants and products. Density measurements d are made on several solutions of different concentrations of the reactant(s) and the product(s). The following equation is used to obtain the apparent molar volume of each species, tp, at each molar concentration c. 

Molarities and volumes may be used to calculate the numbers of moles involved in chemical reactions (Chapter 10). The conversions used are shown in Figure 11.3, where they have been added to those of Figure 10.2. 

The number of moles of a reactant involved in a reaction can be calculated from molarity and volume that number of moles can then be used to calculate the number... 

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