Using Equilibrium Constants

16 Write the equilibrium constant expression for each of the reactions in Problem 13.14. 

17 What is the numerical value of for the following reaction if the equilibrium mixture contains 0.030 M N2O4 and 0.21 M NO2  

When A gq is known, the equilibrium concentration of a substance can be calculated if you know the concentrations of all other reactants and products. The following example problem shows you how to determine an equilibrium concentration. 

Solving Problems A Chemistry Handbook Chemistry Matter and Change 183 

An extra digit is retained here for accuracy, but the final answer will be rounded to three digits. 

A chemist studying the equilibrium N204(g) 2N02(g) controls the temperature so that = 0.028. At one equilibrium position, the concentration of N2O4 is 1.5 times greater than the concentration of NO2. Find the concentrations of the two gases in mol/L. (Hint Let x = [NO2] and 1.5x = [N2O4] in the equilibrium constant expression.) 

The coefficient of is 1, and the coefficient of OH is 2, so the following is the solubility product constant expression. 

When a reaction has a large the products are favored at equilibrium. That means that the equilibrium mixture contains more products than reactants. Conversely, when a reaction has a small K, the reactants are favored at equilibrium, which means that the equilibrium mixture contains more reactants than products. Knowing the size of the equilibrium constant can help a chemist decide whether a reaction is practical for making a particular product. 

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. 

Suppose the industrial chemist that you read about earlier knows that at 1200 K, Kgq equals 3.933 for the reaction that forms methane from H2 and CO. How much methane would actually be produced If the concentrations of H2, CO, and H2O are known, the concentration of CH4 can be calculated. 

The first thing the chemist would do is write the equilibrium constant expression. 

The equation can be solved for the unknown [CH4] by multiplying both sides of the equation by [CO][H2] and dividing both sides by [H2O]. 

Real-World Reading Link If you have ever tried to squeeze yourself into the backseat of a car already occupied by several of your friends, you know there is a limit to how many people the seat can hold. An ionic compound encounters a similar situation when being dissolved in a solution. 

Calculating Equilibrium Concentrations At 1405 K, hydrogen sulfide, which has a foul odor resembling rotten eggs, decomposes to form hydrogen and a diatomic sulfur molecule, 2. The equilibrium constant for the reaction is 2.27 X 10-3. 

You have been given /(eq and two of the three variables in the equilibrium constant expression. The equilibrium expression can be solved for [H2]. / eq is less than one, so more reactants than products are in the equilibrium mixture. Thus, you can predict that [H2] will be less than 0.184 mol/L, the concentration of the reactant H2S. 

Multiply both sides by [H2S]. Divide both sides by [S2]. 

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Carbon dioxide fugacity fcOi- CO2 fugacity (/coa) of ore fluids is estimated based on CO2 concentration of fluid inclusions analyzed. By using equilibrium constant of the reaction, C02(g) + H2O = H2CO3, and assuming uh20 to be unity, /CO2 can be estimated. 

In this expression, K is the thermodynamic equilibrium constant, which can be multiplied by Na/p (with Na equal to Avogadro s number) to obtain the commonly used equilibrium constants based on the molar bulk concentration reference state. It is important to note that the exponential term in the right-hand side of Equations 2.20 and 2.21 is an activity coefficient term. This term depends on the interaction field n z), which is nonlocal and therefore it couples with all the interactions and chemical equilibria in all regions of the film. 

Marine chemists have developed two approaches to handling nonspecific effects. The easiest one, which we will adopt in this book, is to use equilibrium constants appropriate for the temperature, pressure, and salinity of seawater. (Since most of the ionic... 

It is to be noticed that both of these equilibrium constants are protonation constants, since they apply to the addition of a proton (H+) to a given species. The pH values for which these reactions occur can be determined using equilibrium constant expressions and the appropriate equilibrium constant, K. Recall that equilibrium expressions take the general form of ... 

The choice of equilibrium constant for measuring the stability of a carbocation depends partly on experimental accessibility and partly on the choice of solvent. A desire to relate measurements to the majority of existing equilibrium constants implies the use of water as solvent. Water has the advantage and disadvantage that it reacts with carbocations. It follows that the most widely used equilibrium constant is that for the hydration reaction shown in Equation (1), which is denoted KR (or pAR). A simple interpretation of AR is that it measures the ratio of concentrations of unionized alcohol to carbocation in an (ideal) solution of aqueous acid of concentration 1 M. 

Although Ksp values and other equilibrium constants can be calculated this way, widely used equilibrium constants are often listed in tables, such as Table 2.9. Equilibrium constants are, however, temperature dependent. If a constant is required for a reaction occurring at temperatures other than that listed (usually 25 °C), but between 10 and 40 °C, the van t Hoff equation is used to calculate the equilibrium constant at the desired temperature (Langmuir, 1997), 21. The equation states ... 

Later this table was also calculated using equilibrium constants (Alberty, 1997). A third way to calculate this table is to use the properties of H2C03(ao), HCOJ(ao), and C03 (ao) directly from the NBS Tables (Alberty, 1998b). The reason is that when only dilute aqueous solutions are considered, the thermodynamic properties of TotC02 are independent of the value of Kb. 

The relative proportions of the different carbonic acid system species can be calculated using equilibrium constants. If thermodynamic constants are used, activities must be employed instead of concentrations. The activity of the ith dissolved species (a,) is related to its concentration (mj) by an activity coefficient... 

In some cases, the reaction rates are very fast and a pseudoequilibrium approach is used to model the system (4.30). This approach consists of assuming that the concentration of species is always close to the equilibrium conditions and hence, they can be calculated using equilibrium constants from the values of other species present in the reaction system. This approach is especially important for the modeling processes in which the reaction rates are fast and when the kinetic rates are ill-defined (because of a large number of species or a lack of experimental data that makes difficult the kinetic analysis)... 

A simpler desaiption of the system is desired and it can be obtained using equilibrium constants that describe aU eqnilibria in the systan obviously only a thermodynamic equilibrium constant must be made use of since, as discussed above, at variance with stoichiometric constants, they account for all the molecular level interactions in a very simple way, and notably, their chromatographic and non-chromatographic estimates can be compared to validate the retention mechanism they describe. 

To use equilibrium constants to determine the concentrations of reactants and products in a system at equilibrium... 

To use equilibrium constants for acids with more than one ionizable hydrogen atom... 

Calculation of Bubble-Point Pressure and Dew-Point Pressure Using Equilibrium Constants. Since the total pressure P

bubble-point and dew-point pressure as was done in the case of ideal solutions. A method will now be presented for calculating the bubble-point pressure and the dew-point pressure, which is applicable to both binary and multicomponent systems which are non-ideal. At the bubble point the system is entirely in the liquid state except for an infinitesimal amount of vapor. Consequently, since ti, = 0 and n — n% equation 19 becomes... 

To calculate the dew-point pressure using equilibrium constants a similar procedure is carried out. At the dew point the system is entirely in the vapor state except for an infinitesimal amount of liquid. Consequently, since ni = 0 and n = equation 18 becomes... 

A hydrocarbon mixture is made up of 5 pound-moles of n-hezane and 5 pound-moles of iso-butane. It exists at 200 psia and 200° F. Calculate the amount and composition of liquid recovery per mole of starting material if it is separated at 60 psia and 200° F. Calculate the same quantities if it is separated at 90 psia and 200° F and then if the liquid is again separated at 60 psia and 200° F. Use equilibrium constants. 

A system contains 25 mole per cent propane, 30 mole per cent pentane and 45 mole per cent heptane at 150° F. Using equilibrium constants calculate the composition of the liquid and vapor at 20 psia. Hint Assume Wj = 0.46 per mole of starting material.) What is the weight of liquid obtained per mole of starting material ... 

Using equilibrium constants calculate the bubble-point and dew-point pressures at 120° F for the hydrocarbon system described in Problem 9. Answer BPP = 48 psia. 

Figure 2.8 depicts the dependence of AG° = -RT In K on both pressure and temperature. The plot is schematic. The equilibrium constants of aqueous reactions are, in general influenced by both pressure and temperature. The range of temperatures experienced at the surface of the earth is appreciable. Temperature over the range from 5 C to 45°C or greater needs to be considered in using equilibrium constant data for many reactions of interest. The influence... 

Results from two field investigations illustrate this point. Kent et al. (1995) modeled adsorption of Cr(VI) in the presence of S(VI) by natural aquifer solids using equilibrium constants that were 1.75 Log K units lower than those used to model adsorption by ferrihydrite (Dzombak and Morel, 1990). To model competitive adsorption of Mo(Vl) and P(V) by these same aquifer solids, Stollenwerk (1995) decreased the Dzombak and Morel (1990) equilibrium constants for both anions by 1.2 Log K units. Results from both of these studies indicate that the dominant adsorbents had lower affinities for adsorption of anions than pure ferrihydrite. 

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