Activity concentration and

When environmental chemists measure the amounts of chemical substances, for example in a water sample, they are usually measuring the concentration of that substance, for example the concentration of calcium (Ca) in the water. It is very easy to assume that the analysis has measured all of the free Ca2+ ions in the sample, but in fact it will almost certainly have measured all of the calciumbearing dissolved species, called ion pairs, as well. Ions in solution are often sufficiently close to one another for electrostatic interactions to occur between oppositely charged species. These interactions reduce the availability of the free ion to participate in reactions, thereby reducing the effective concentration of the free ion. Collisions between oppositely charged ions also allow the transient formation of ion pairs, for example  

The formation of these ion pairs (see Box 6.4) further reduces the effective concentration, and the frequency of collisions increases as the total amounts of chemical species in the solution increase. The effective concentration of an ion therefore becomes an important consideration in concentrated and complex 

In order to predict accurately chemical reactions in a concentrated solution, we need to account for this reduction in effective concentration. This is done using a concentration term known as activity that is independent of electrostatic interactions. Activity is the formal thermodynamic representation of concentration and it describes the component of concentration that is free to take part in chemical reactions. Activity is related to concentration by an activity coefficient (y). 

Equation 2.9 shows that units of activity and concentration are proportional in other words y can be regarded as a proportionality constant. These constants, which vary between 0 and 1, can be calculated experimentally or theoretically and are quite well known for some natural solutions. Having said this, measuring y in complex solutions like seawater has proved very difficult. Most importantly for our purposes, as solution strength approaches zero, y approaches 1. In other words, in very dilute solutions (e.g. rainwater), activity and concentration are effectively the same. 

In this book activity is expressed in units of mol 1 1 in the same way as concentration, but activity is denoted by the prefix a in equations. 

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Other generator systems are possible and many have been constmcted, but none thus far has yielded the combination of low cost, high utility, concentration, and activity of the Mo— Tc system. 

The concentration of links, / = 1/Nq, and that of polymers, Np = p/Nq, follow from standard relations between concentrations and activities... 

The addition of strong acids or neutral salts, such as NH4F, to the hydrofluoric acid solution was recommended in order to increase the concentrations and activities of fluorine and hydrogen ions [451]. 

The fact that the experimentally determined exponent of h0 in Scheme 3-25 is not an integer ( — 2), as expected for the mechanism discussed here, is due to the complexity of concentrations and activities in highly acidic solutions. In 66-74% H2S04 the rate is propotional to ho2A. Concerning the subscript 6, see the footnote explaining this point for Schemes 3-12 to 3-14. 

It should be noted again that ISEs sense the activity, rather than the concentration of ions in solution. The term activity is used to denote the effective (active) concentration of the ion. The difference between concentration and activity arises because of ionic interactions (with oppositely charged ions) that reduce the effective concentration of the ion. The activity of an ion i in solution is related to its concentration, c by... 

In the case considered in this section of a joint action of concentration and activation polarization, in the polarization equation (6.10) we must take into account the concentration changes of the rectants near the electrode surface ... 

Application of electrochemical methods as analytical tools for the detection as well as the concentration and activity determination of biologically active compounds in bioanalysis and medicine ... 

This equation is not particularly useful in practice, smce it is difficult to quantify the relationship between concentration and activity. The Elory-Huggins theory does not work well with the crosslinked semicrystalline polymers that comprise an important class of pervaporation membranes. Neel (in Noble and Stern, op. cit., pp. 169-176) reviews modifications of the Stefan-Maxwell approach and other equations of state appropriate for the process. 

Altered removal of a neurotransmitter from the synaptic cleft. The third mechanism by which drugs may alter synaptic activity involves changes in neurotransmitter reuptake or degradation. A very well known example of a drug in this category is Prozac (fluoxetine), which is used to treat depression. The complete etiology is unknown, but it is widely accepted that depression involves a deficiency of monoamine neurotransmitters (e.g., norepinephrine and serotonin) in the CNS. Prozac, a selective serotonin reuptake inhibitor, prevents removal of serotonin from the synaptic cleft. As a result, the concentration and activity of serotonin are enhanced. 

Kinetic theory indicates that equation (32) should apply to this mechanism. Since the extent of protonation as well as the rate constant will vary with the acidity, the sum of protonated and unprotonated substrate concentrations, (Cs + Csh+), must be used. The observed reaction rate will be pseudo-first-order, rate constant k, since the acid medium is in vast excess compared to the substrate. The medium-independent rate constant is k(), and the activity coefficient of the transition state, /, has to be included to allow equation of concentrations and activities.145 We can use the antilogarithmic definition of h0 in equation (33) and the definition of Ksh+ in equation (34) ... 

TABLE 7.1. Trap Concentration and Activation Energy of Each Trap Measured by DLTS... 

Bowling, A. C., Barkowski, E. E., McKenna-Yasek, D. et al. Superoxide dismutase concentration and activity in familial amyotrophic lateral sclerosis. /. Neurochem. 64 2366-2369, 1995. 

The resulting species distribution (Table 6.7), as would be expected, differs sharply from that in seawater (Table 6.4). Species approach millimolal instead of molal concentrations and activity coefficients differ less from unity. In the Amazon River water, the most abundant cation and anion are Ca++ and HCOJ in seawater, in contrast, Na+ and Cl- predominate. Seawater, clearly, is not simply concentrated river water. 

Figure 8.7 shows how concentrations and activities of the calcium and sulfate species vary with NaCl concentration. In the B-dot model, there are three ion pairs (CaCl+, NaSO, and CaS04) in addition to the free ions Ca++ and SO4 . 

For simplicity, we assume that the concentration and activity of silver nitrate are the same, i.e. a(Ag+, = 10-3. We also assume that the silver is pure, so its activity is unity. 

This expression has been written in terms of concentration if activity coefficients sue known or estimated, then a thermodynamically ideal solubility product may be obtained from the Emalogous product of ionic activities. As the concentration of ions in solutions of lanthanide fluorides is low, the concentration and activity solubility products will not differ markedly, although activity coefficients for these salts of 3 + cations are significantly less than unity even in such dilute solutions (4a). 

To a first approximation, the concentration and activity of the water molecules do not change during dissolution so nH2Q can be neglected. 

Equations (7), (8), (9a) thus permit the basicity constants to be determined if the concentrations and activity coefficients of the ions and neutral molecules present in the solution are known. 

Note here how we have assumed that concentration and activity are the same thing this assumption is why the units of concentration have been omitted - see Section 3.4.)... 

A third (and usually more profound) cause of error lies in the way that the Nemst equation is formulated in terms of activities rather than concentration. Even if the emf and E are correct, the proportionality constant between concentration and activity (the mean ionic activity coefficient y ) is usually wholly unknown. Errors borne of ignoring activity coefficients (i.e. caused by ionic interactions) are discussed in Sections 3.4 and 3.6.3. 

Note how we have assumed throughout this calculation that concentration and activity can be employed interchangeably. 

If measurements are to be carried out at low activities (for example in studying complexation equilibria), standard solutions cannot be prepared by simple dilution to the required value because the activities would irreproducibly vary as a result of adsorption effects, hydrolysis and other side reactions. Then it is useful to use well-defined complexation reactions to maintain the required metal activity value [14, 50, 132]. EDTA and related compounds are very well suited for this purpose, because they form stable 1 1 complexes with metal ions, whose dissociation can be controlled by varying the pH of the solution. Such systems are often termed metal-ion buffers [50] (cf. also p. 77) and permit adjustment of metal ion activities down to about 10 ° m. (Strictly speaking, these systems are defined in terms of the concentration, but from the point of view of the experimental precision, the difference between the concentration and activity at this level is unimportant.)... 

In Example 5.1, again, we found that for this solution is 0.248 V when ion-ion interaction is neglected. The difference between calculated with concentration and activity is 4 mV. ... 

Example 11.1 illustrates the point that in a solution containing simple salts of zinc and copper, the ion concentration and activity values are so close together that the large difference between the Eq values for copper and for zinc will make alloy deposition virtually impossible. 

The equilibrium constant of an enzyme-catalyzed reaction can depend greatly on reaction conditions. Because most substrates, products, and effectors are ionic species, the concentration and activity of each species is usually pH-dependent. This is particularly true for nucleotide-dependent enzymes which utilize substrates having pi a values near the pH value of the reaction. For example, both ATP" and HATP may be the nucleotide substrate for a phosphotransferase, albeit with different values. Thus, the equilibrium constant with ATP may be significantly different than that of HATP . In addition, most phosphotransferases do not utilize free nucleotides as the substrate but use the metal ion complexes. Both ATP" and HATP have different stability constants for Mg +. If the buffer (or any other constituent of the reaction mixture) also binds the metal ion, the buffer (or that other constituent) can also alter the observed equilibrium constant . ... 

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