Using the Equilibrium Constant

When one of the elements is solid, as in tire case of carbon in the calculation of the partial pressures of tire gaseous species in the reaction between methane and air, CO(g) can be used as a basic element together widr hydrogen and oxygen molecules, and thus the calculation of the final partial pressure of methane must be evaluated using the equilibrium constant for CH4 formation... 

As pointed out earlier, the equilibrium constant of a system changes with temperature. The form of the equation relating K to T is a familiar one, similar to the Clausius-Clapeyron equation (Chapter 9) and the Arrhenius equation (Chapter 11). This one is called the van t Hoff equation, honoring Jacobus van t Hoff (1852-1911), who was the first to use the equilibrium constant, K. Coincidentally, van t Hoff was a good friend of Arrhenius. The equation is... 

Using the equilibrium constants in Table 13.2, rank the following 0.1 Af aqueous solutions in order of increasing Xj,... 

The following example shows how to use the equilibrium constant to calculate an equilibrium concentration. 

Step 4 Use the equilibrium constant to determine the value of x, the unknown change in molar concentration or partial pressure. 

Because conjugate acids and bases are in equilibrium in solution, we use the equilibrium constant for proton transfer between the solute and the solvent as an indicator of the strength of an acid or a base. For example, for acetic acid in water,... 

Up to this point, we have focused on aqueous equilibria involving proton transfer. Now we apply the same principles to the equilibrium that exists between a solid salt and its dissolved ions in a saturated solution. We can use the equilibrium constant for the dissolution of a substance to predict the solubility of a salt and to control precipitate formation. These methods are used in the laboratory to separate and analyze mixtures of salts. They also have important practical applications in municipal wastewater treatment, the extraction of minerals from seawater, the formation and loss of bones and teeth, and the global carbon cycle. 

Using the equilibrium constants below, calculate the concentrations of free (uncomplexed) cadmium ion in a freshwater with a chloride concentration of 15 mg/L, and in seawater containing 17 000 mg/L chloride. Ignore com-plexation with other ions. 

The second main type of equilibrium problem asks for values of equilibrium concentrations. We also use concentration tables for this type of problem, with one additional feature. In such problems, we need to assign a variable x to one unknown concentration, and then we use the equilibrium constant to find the value of x by standard algebraic techniques. Examples 16-11 and 16-12 illustrate this use and manipulation of unknowns. 

Using the equilibrium constant for (2-5) and (2-9), the relationship between pH and Cl concentration can be derived as shown in Fig. 2.7. The line shown in Fig. 2.7 has a slope of approximately —1, indicating that the pH of the geothermal waters decreases with increasing Cl concentration. 

EXAMPLE 20.7. Calculate the hydronium ion concentration of a 0.200 M solution of acetic acid, using the equilibrium constant of Example 20.6. 

Equations 5.1.5, 5.1.6, and 5.1.8 are alternative methods of characterizing the progress of the reaction in time. However, for use in the analysis of kinetic data, they require an a priori knowledge of the ratio of kx to k x. To determine the individual rate constants, one must either carry out initial rate studies on both the forward and reverse reactions or know the equilibrium constant for the reaction. In the latter connection it is useful to indicate some alternative forms in which the integrated rate expressions may be rewritten using the equilibrium constant, the equilibrium extent of reaction, or equilibrium species concentrations. 

You learned about acids and bases in your previous chemistry course. In this chapter, you will extend your knowledge to learn how the structure of a compound determines whether it is an acid or a base. You will use the equilibrium constant of the reaction of an acid or base with water to determine whether the acid or base is strong or weak. You will apply your understanding of dissociation and pH to investigate buffer solutions solutions that resist changes in pH. Finally, you will examine acid-base titrations that involve combinations of strong and weak acids and bases. 

Calculate the standard free-eneigy changes of the following metabolically important enzyme-catalyzed reactions at 25 °C and pH 7.0, using the equilibrium constants given. 

Once we know ZnY2 and [EDTA], we can use the equilibrium constant to find [Zn2+] ... 

To emphasize that partial pressures are being used, the equilibrium constant is often denoted KP. 

Step 4 Use the equilibrium constant to determine the value of x, the unknown molar concentration or partial pressure at equilibrium. A good habit is to check the answer by substituting the concentrations or pressures into the expression for K. 

Explain what is wrong with the following statements, (a) Once a reaction has reached equilibrium, all reaction stops, (b) If more reactant is used, the equilibrium constant will have a larger value. 

The actual arithmetic involved in the calculations may be done easily by starting with the general expression for electroneutrality and substituting equilibrium expressions (9). Using the equilibrium constants of Table I and assuming that activities equal concentrations, we obtain for 5°C. and an invariant condition (model No. 1) the following data ... 

We mentioned that biochemists usually define the standard state of protons as 10-7 m and report values of free energy and equilibrium constants for solutions at pH 7. These values are designated by a prime and written as AG°, AG and K q. Unprimed symbols are used to designate values based on a standard state of 1 m for protons (pH 0). For a reaction that releases one proton, the relationship between K eq and K q is K eq = 107/feq. In evaluating the standard free energies AG° and AG°, it is critical to use the equilibrium constants K eq and Keq, respectively, because these can be very different quantities. 

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.)... 

Use the Equilibrium Constant for Acids activity (eChapter 15.9) to experiment with the dissociation of a weak acid. What would be the hydronium ion concentration and pH of 0.10 M solutions of weak acids with Ka = 1 X 10"5 Ka= IX 10"10 and Ka = IX 10"15 Describe the relationship between the pH and the strength of an acid for acids at equal concentrations. 

Using the equilibrium constants estimated by Guthrie (12) for hemi-orthoamide tetrahedral intermediates (derived from N,N-dimethylformamide and N,N-di-methylacetamide) and the activation parameters described in Table 2, it was possible to obtain the free energy of activation for the breakdown UG ieav) and for conformational change (aG onf) of the tetrahedral interme.-diates derived from the N-benzyl-N-methyl derivatives of formamide, acetamide and propionamide. These values are the following. 

The distribution (or partition) coefficient, Ka, of a metal cation between an aqueous (aq) and organic (org) phase may also be used to assess the selectivity of a given host for a range of metal cations under standard conditions, using the equilibrium constants (K) for the following processes (Equations 1.17-1.20) (for metal picrate (Pic) salt, water (aq) and water-saturated chloroform (org) phases, 25 °C). 

Use the equilibrium constants in equations 7.3-2 and 7.3-3 to calculate the further transformed Gibbs energies of formation of the forms of the dimer of hemoglobin and of the pseudoisomer group at [02] = 5 xlO"6, 10"5, and 2 xlO"5M. Make a table with the last three columns and first four rows of Table 7.3. 

Calculate the fractional saturation YT of the tetramer of human hemoglobin with molecular oxygen using the equilibrium constants determined by Mills, Johnson, and Akers (1976) at 21.5 °C, 1 bar, pH 7.4, [Cl"] = 0.2 M and 0.2 M ionic strength. Make the calculation with the Adair equation and also by using the binding polymomial YT. 

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