Equilibrium constant worked examples

The electrical method of measuring A is thus a very convenient way of obtaining the equilibrium constant Working out the above example, we see that—... 

We will use two useful relationships when working with equilibrium constants. First, if we reverse a reaction s direction, the equilibrium constant for the new reaction is simply the inverse of that for the original reaction. For example, the equilibrium constant for the reaction... 

When R = H, in all the known examples, the 3-substituted tautomer (129a) predominates, with the possible exception of 3(5)-methylpyrazole (R = Me, R = H) in which the 5-methyl tautomer slightly predominates in HMPT solution at -17 °C (54%) (77JOC659) (Section 4.04.1.3.4). For the general case when R = or a dependence of the form logjRTT = <2 Za.s cTi + b Xa.s (Tr, with a>0,b <0 and a> b, has been proposed for solutions in dipolar aprotic solvents (790MR( 12)587). The equation predicts that the 5-trimethylsilyl tautomer is more stable than the 3-trimethylsilylpyrazole, since experimental work has to be done to understand the influence of the substituents on the equilibrium constant which is solvent dependent (78T2259). There is no problem with indazole since the IH tautomer is always the more stable (83H(20)1713). 

The direction chosen for the equilibrium reaction Is determined by convenience. A scientist interested in producing ammonia from N2 and H2 would use f. On the other hand, someone studying the decomposition of ammonia on a metal surface would use eq,r Either choice works as long as the products of the net reaction appear in the numerator of the equilibrium constant expression and the reactants appear in the denominator. Example applies this reasoning to the iodine-triiodide reaction. 

Worked Example 4.15 The isomerization of 1-butene (X) to form frans-2-butene (XI). The equilibrium constants of reaction are given below. Determine the enthalpy of reaction AH using a suitable graphical method. 

Worked Example 8.18 Consider the reaction between pyridine and heptyl bromide, to make 1-heptylpyridinium bromide. It is an equilibrium reaction with an equilibrium constant K = 40. What is the rate constant of back reaction k if the value of the forward rate constant k = 2.4 x 103 dm3 mol 1 s ... 

Worked Example 8.19 The data below relate to the first-order isomerization of 2-hexene at 340 K, a reaction for which the equilibrium constant is known from other studies to be 10.0. What are the rate constants k and k i ... 

One of the most basic requirements in analytical chemistry is the ability to make up solutions to the required strength, and to be able to interpret the various ways of defining concentration in solution and solids. For solution-based methods, it is vital to be able to accurately prepare known-strength solutions in order to calibrate analytical instruments. By way of background to this, we introduce some elementary chemical thermodynamics - the equilibrium constant of a reversible reaction, and the solubility and solubility product of compounds. More information, and considerably more detail, on this topic can be found in Garrels and Christ (1965), as well as many more recent geochemistry texts. We then give some worked examples to show how... 

The purpose of this Preamble is to remind the reader that when we attempt to explain a change of rate brought about, for example, by dilution with a solvent that may be more or less polar than the monomer, we are attempting to visualize and rationalize the resulting changes in the physico-chemical circumstances and the consequent changes in the population of the propagators, and in the equilibrium constants and rate constants involved. That is what this paper is about. (In this work the term population is shorthand for nature and concentration .)... 

We illustrate the nomenclature introduced above in an example taken from coordination chemistry. In fact, equilibrium species of interesting complexity are commonly encountered in coordination chemistry and to a large extent coordination chemists have developed the principles of equilibrium studies. Consider the interaction of a metal ion M (e.g. Cu2+) with a bidentate ligand L (e.g. ethylenediamine, en) in aqueous solution. For work in aqueous solution the pH also plays an important role and thus, the proton concentration H (=[ff+]), as well as several differently protonated species, need to be taken into account. Using the nomenclature commonly employed in coordination chemistry, there are three components, M, L, and H. In aqueous solution they interact to form the following species, HL, H2L, ML, Mia, ML3, MLH, MLH1 and OH. (In fact, more species are formed, e.g. ML2H 1, but the above selection will suffice now.) The water molecules are usually not defined as additional components. The concentration of water is constant and its value is taken into the equilibrium constants. 

The usual way to work with this equation is in terms of an equilibrium constant for a reaction. For example, consider a reversible gas-phase reaction of A to form B at a specific rate kj and B reacting back to A at a specific reaction rate The stoichiometry of the reaction is such that v moles of A react to form Vj moles of B. 

This example illustrates a case of considerable analytical importance, especially for the determination of complex formation constants for hydrophilic complexes, as discussed in section 4.12, when the equilibrium constants for the stepwise metal-organic complexes are of secondary interest. values are tabulated in several reference works. is a conditional constant and only valid provided no other species are formed besides the extracted one. 

As shown by Turner et fluorescence experiments using a 5 -pyrenylated oligonucleotides have aided the determination of rate constants and equilibrium constants that define (a) the initial base-pairing step in substrate binding, (b) the so-called docking step that reflects a substrate-induced conformational step, and (c) the bond cleavage step per se. The scheme shown in Fig. 3 represents a beautiful example of Koshland s induced-fit model at work in ribozyme action. 

Using the Equilibrium Constant activity (eChapter 13.2), compare the reactions A B and A 2 B in Worked Key Concept Example 13.4 (page 534). (Each picture represents the contents of a 1.00 x 10-24 L vessel.)... 

The stability of a complex ion is measured by its formation constant Kf (or stability constant), the equilibrium constant for formation of the complex ion from the hydrated metal cation. The large value of Kf for Ag(NH3)2+ means that this complex ion is quite stable, and nearly all the Ag+ ion in an aqueous ammonia solution is therefore present in the form of Ag(NH3)2+ (see Worked Example 16.12). 

Calculate E° for the reaction from standard reduction potentials, as in Worked Example 18.5. Then use the equation log K = nE°/0.0592 V to determine the equilibrium constant. 

The characteristic features of parameter estimation in a molecular model of adsorption are illustrated in Table 9.9, taking the simple example of the constant-capacitance model as applied to the acid-base reactions on a hydroxylated mineral surface. (It is instructive to work out the correspondence between equation (9.2) and the two reactions in Table 9.9.) Given the assumption of an average surface hydroxyl, there are just two chemical reactions involved (the background electrolyte is not considered). The constraint equations prescribe mass and charge balance (in terms of mole fractions, x) and two complex stability constants. Parameter estimation then requires the determination of the two equilibrium constants and the capacitance density simultaneously from experimental data on the species mole fractions as functions of pH. 

A good deal of work will have to be done to extract species information from the apparent equilibrium constants that have been reported for about 500 reactions. Beyond that, use can be made of analogies with known reactions for example, the various ribonucleotide phosphates (AMP, GMP, CMP, UMP, and dTMP) are believed to have the same hydrolysis constants and pKs. Beyond that, the group additivity method (Alberty, 1998c) can be used to estimate thermodynamic properties. 

There is an equilibrium between the different sites that determines the observed distribution. For example, the ratio of the sites with the cation vacancy nearby to those with the vacancy distant will depend upon the concentration of vacancies by the law of mass action. One can write the conventional equilibrium relationships given by mass action considerations for equilibria between vacancies and probe ion sites with local and distant vacancy compensation. The equilibrium constant will depend on the temperature under which the equilibrium was established. Since all of the sites can be observed by site selective laser spectroscopy, one can measure the equilibrium distributions directly. We find that the sites and their distributions are described excellently by the mass action relationships of conventional equilibria. This work is described in more detail elsewhere (5,6). 

Sections 3.3.1 and 4.2.1 dealt with Bronsted acid/base equilibria in which the solvent itself is involved in the chemical reaction as either an acid or a base. This Section describes some examples of solvent effects on proton-transfer (PT) reactions in which the solvent does not intervene directly as a reaction partner. New interest in the investigation of such acid/base equilibria in non-aqueous solvents has been generated by the pioneering work of Barrow et al. [164]. He studied the acid/base reactions between carboxylic acids and amines in tetra- and trichloromethane. A more recent compilation of Bronsted acid/base equilibrium constants, determined in up to twelve dipolar aprotic solvents, demonstrates the appreciable solvent influence on acid ionization constants [264]. For example, the p.Ka value of benzoic acid varies from 4.2 in water, 11.0 in dimethyl sulfoxide, 12.3 in A,A-dimethylformamide, up to 20.7 in acetonitrile, that is by about 16 powers of ten [264]. 

Because the potential of an electrochemical cell depends on the concentrations of the participating ions, the observed potential can be used as a sensitive method for measuring ion concentrations in solution. We have already mentioned the ion-selective electrodes that work by this principle. Another application of the relationship between cell potential and concentration is the determination of equilibrium constants for reactions that are not redox reactions. For example, consider a modified version of the silver concentration cell shown in Fig. 11.11. If the 0.10 M AgN03 solution in the left-hand compartment is replaced by 1.0 M NaCl and an excess of solid AgCl is added to the cell, the observed cell potential can be used to determine the concentration of Ag+ in equilibrium with the AgCl(s). In other words, at 25°C we can write the Nernst equation as... 

A fine example of tliis type of work is the determination of Z)q(I2) from vapour density measurements at high temperatures by Perlman and Rollefson 8 8 These workers were interested in obtaining very accurate values of the equilibrium constant to see whether they exhibited any trend which would indicate the presence of 13 and incidentally in obtaining an accurate value of Dq(12) for comparison with the spectroscopically derived result. They introduced highly purified iodine into a silica bulb of known volume contained in a furnace controlled at temperatures between 723° K and 1,274° K, measured the pressure, and then removed the iodine and weighed it. Gas imperfection for molecular iodine was taken into account, but atomic iodine was assumed to be a perfect gas. 

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