Equilibrium constant expression calculation using

As shown, the equilibrium constants are calculated using the activity. In simple language, activity is a measure of the effectiveness of a given species in its participation in a reaction. It is proportional to concentration it is an effective or active concentration and has units of concentrations. Because activity bears a relationship to concentration, its value may be obtained using the value of the corresponding concentration. This relationship is expressed as follows ... 

Write equilibrium-constant expressions and use these expressions to calculate equilibrium constants. 

When concentrations and pressures are used in equilibrium constant expression calculations, K is not exactly constant with varying concentrations and pressures it is an approximate equilibrium constant that applies only to limited conditions. Thermodynamic equilibrium constants are more exact forms derived from thermodynamic data that make use of activities in place of concentrations. At a specified temperature, the value of a thermodynamic equilibrium constant is applicable over a wide concentration range. The activity of a species, commonly denoted as ax for species X, expresses how effectively it interacts with its surroundings, such as other solutes or electrodes in solution. Activities approach concentrations at low values of concentration. The thermodynamic equilibrium constant expression for Reaction 19.15 is expressed as the following in terms of activities ... 

Guides to Writing the Equilibrium Constant Expression, Calculating the Value, Using the Equilibrium Constant, Calculating and Calculating Molar Solubility from Ksp have been updated and rewritten. 

This is the equation (or equations) that we must use to complete the calculations. The equilibrium constant expression for LiF dissolving in water is. eq [Li" ]eq [F ]gg... 

As the LiF example illustrates, the most direct way to determine the value of an equilibrium constant is to mix substances that can undergo a chemical reaction, wait until the system reaches equilibrium, and measure the concentrations of the species present once equilibrium is established. Although the calculation of an equilibrium constant requires knowledge of the equilibrium concentrations of all species whose concentrations appear in the equilibrium constant expression, stoichiometric analysis often can be used to deduce the concentration of one... 

The weak acid curves can also be calculated. This involves the use of the equilibrium constant expression for a weak monoprotic acid ionization ... 

It is also worthwhile to make some distinctions between methods of calculating phase equilibrium. For many years, equilibrium constants have been used to express the abundance of certain species in terms of the amounts of other arbitrarily chosen species, see for example Brinkley (1946,1947), Kandliner and Brinkley (1950) and Krieger and White (1948). Such calculations suffer significant disadvantages in that some prior knowledge of potential reactions is often necessary, and it is difficult to analyse the effect of complex reactions involving many species on a particular equilibrium reaction. Furthermore, unless equilibrium constants are defined for all possible chemical reactions, a true equilibrium calculation caiuiot be made and, in the case of a reaction with 50 or 60 substances present, the number of possible reactions is massive. 

The equilibrium constant expression for the first step is used to calculate an expression for [A] ... 

A most useful characteristic of chemical equilibrium is that all equilibria are satisfied simultaneously. If we know the concentration of I, we can calculate the concentration of Pb2+ by substituting this value into the equilibrium constant expression for Reaction 6-11, regardless of whether there are other reactions involving Pb2+. The concentration of Pb2 that satisfies any one equilibrium must satisfy all equilibria. There can be only one concentration of Pb2 in the solution. 

This expression is plotted in Figure 11.18 as flux as a function of feed pressure for different values of the equilibrium constant, K. In this example, at an equilibrium constant K of 0.01 atm-1, very little of carrier R reacts with permeant A even at a feed pressure of 10 atm, so the flux is low. As the equilibrium constant increases, the fraction of carrier reacting with permeant at the feed side of the membrane increases, so the flux increases. This result would suggest that, to achieve the maximum flux, a carrier with the highest possible equilibrium constant should be used. For example, the calculations shown in Figure 11.18 indicate a carrier with an equilibrium constant of 10 atm-1 or more. 

In performing a calculation based on an acid or base ionization constant expression such as Eqs. (13-7) or (13-8), there are often many unknowns. Remember that in an algebraic problem involving multiple unknowns, one needs as many equations as there are unknowns. The equilibrium constant expression itself is one equation, and the Kw expression is always available. Two other types of equation are often useful equations expressing... 

With a weak acid, the calculations are a bit more complex. We begin by computing the initial pH, using the method of Example 1, pH = 2.79. At the equivalence point, we have 50.0 mL of 0.060 M sodium acetate. Since acetate is the base conjugate to a weak acid, the solution is basic and we must compute the pH. From eq (13-12) for acetate ion, Kb = KyKa =5.62 x 10 10, and the equilibrium constant expression is... 

Calculating the pH of weak acids and bases is more challenging, because they do not ionize completely. So, in a 0.10 M solution of acetic acid, the [H+] concentration is not 0.10 M. We must use the equilibrium constant expression to find the pH of weak acid solutions. So, what is the pH of a 0.10 M solution of acetic acid The K of acetic acid is 1.8 x 10"5. 

The second variation is to determine either the pH or the hydrogen ion concentration of a solution when given the hydroxide ion concentration, [OH-], for the solution. To solve these problems you need to utilize the equilibrium constant expression for the self-ionization of water (Kw). This expression will allow you to convert from the hydroxide ion concentration, [OH-], to the hydrogen ion concentration, [H+], The [H+] can then be used to calculate pH if necessary. One of the free-response questions on the 1999 test required this calculation. 

At this point, the calculation becomes a little different. Because the benzoate ion is a base, the equilibrium constant expression must be the base ionization constant, Kb. You haven t been given the value of Kb, however, so you will have to generate it using Equation 13.8 ... 

Quantitative calculations can be made for systems at equilibrium using the equilibrium constant expression. For the general reaction... 

One way to recognize the significance of this equation is to remember that the ultimate objective of chemical thermodynamics is to calculate the equilibrium composition of a system of reactions. A chemical reaction system has R independent equilibrium constant expressions and C conservation equations, and this is just enough information to calculate the equilibrium concentrations of N species. Equation 7.1-9 is useful because it makes it possible to calculate a conservation matrix from a stoichiometric number matrix. In doing this with the operation NullSpace we will see again that it yields a basis for the conservation matrix. 

The equilibrium constant expression can be useful in another way. Knowing the equilibrium constant expression, a chemist can calculate the equilibrium concentration of any substance involved in a reaction if the concentrations of all other reactants and products are known. 

The value of is in the range that favors products. Solving the equilibrium constant expression requires the evaluation of the cube root of the concentration of H2. Use the/ key on your calculator. 

The reactions used in analytical chemistry never result in complete conversion of reactants to products. Instead, they proceed to a state of chemical equilibrium in which the ratio of concentrations of reactants and products is constant. Equilibrium-constant expressions are algebraic equations that describe the concentration relationships existing among reactants and products at equilibrium. Among other things, equilibrium-constant expressions permit calculation of the error in an analysis resulting from the quantity of unreacted analyte that remains when equilibrium has been reached. 

Equation 9-7 is only an approximate form of a thermodynamic equilibrium constant expression. The exact form is given by Equation 9-8 (in the margin). Generally, we use the approximate form of this equation because it is less tedious and time consuming. In Section lOB, we show when the use of Equation 9-7 is likely to lead to serious errors in equilibrium calculations and how Equation 9-8 is modified in these cases. 

If we wish to calculate the solubility of barium sulfate in a system containing hydronium and acetate ions, we must take into account not only the solubility equilibrium but also the other three equilibria. We find, however, that using four equilibrium-constant expressions to calculate solubility is much more difficult and complex than the simple procedure illustrated in Examples 9-4, 9-5, and 9-6. To solve this type of problem, the systematic approach described in Section llA is helpful. We then use this approach to illustrate the effect of pH and complex fonna-tion on the solubility of typical analytical precipitates. In later chapters, we use this same systematic method for solution of problems involving multiple equilibria of several types. 

We have used the subscript eq to emphasize that the concentrations in the equilibrium constant expression are those at equilibrium. For the remainder of this text, we shall omit these subscripts, remembering that calculations with K,. values always involve equilibrium values of concentrations. 

We first write equations for the two reversible reactions and their equilibrium constant expressions. We note that [OH ] appears in both equilibrium constant expressions. From the statement of the problem we know the concentration of Mg +. We use the Xj, expression for aqueous NH3 to find [OH ], Then we calculate for Mg(OH)2 and compare it with its K. ... 

We have the same reactions and equilibrium constant expressions as in Example 20-10. We are given [Mg ], and so we use the expression of Mg(OH)2 to calculate the [OH ] necessary to initiate precipitation. Then we find the molarity of aqueous NHj solution that would furnish the desired [OH ]. 

The treatment of diprotic and polyprotic acids is more involved than that of mono-protic acids because these substances may yield more than one hydrogen ion per molecule. These acids ionize in a stepwise manner that is, they lose one proton at a time. An ionization constant expression can be written for each ionization stage. Consequently, two or more equilibrium constant expressions must often be used to calculate the concentrations of species in the acid solution. For example, for carbonic acid, H2CO3, we write... 

Using a few mathematical maneuvers we can turn this equilibrium-constant expression into one that will allow us to calculate the pH of the buffer if we know how much acid (acetic acid) and salt (sodium acetate) are present in a known volume of the solution. 

A buffer solution can be described by an equilibrium-constant expression. The equilibrium-constant expression for an acidic system can be rearranged and solved for [H3O+]. In that way, the pH of a buffer solution can be obtained, if the composition of the solution is known. Alternatively, the Henderson-Hasselbalch equation, derived from the equilibrium constant expression, may be used to calculate the pH of a buffer solution. 

If we wish to calculate j8q> the fraction of Ag", then we can use the equilibrium constant expressions in Equation 9.1 and 9.2 to substitute in Equation 9.16 to obtain an expression containing only [Ag" ] as the silver species. From Equation 9.1,... 

We may solve the multiple equilibrium problem as well by using the systematic The systematic approach is well approaches described in Chapter 6, using the equilibrium constant expressions, the suited for competing equilibria mass balance expressions, and the charge balance expression. calculations. 

Before we discuss redox titration curves based on reduction-oxidation potentials, we need to learn how to calculate equilibrium constants for redox reactions from the half-reaction potentials. The reaction equilibrium constant is used in calculating equilibrium concentrations at the equivalence point, in order to calculate the equivalence point potential. Recall from Chapter 12 that since a cell voltage is zero at reaction equilibrium, the difference between the two half-reaction potentials is zero (or the two potentials are equal), and the Nemst equations for the halfreactions can be equated. When the equations are combined, the log term is that of the equilibrium constant expression for the reaction (see Equation 12.20), and a numerical value can be calculated for the equilibrium constant. This is a consequence of the relationship between the free energy and the equilibrium constant of a reaction. Recall from Equation 6.10 that AG° = —RT In K. Since AG° = —nFE° for the reaction, then... 

Quadratic equations are frequently encountered in calculation of equilibrium concentrations of ionized species using equilibrium constant expressions. Hence, an equation of the following type might require solving ... 

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