System at Equilibrium Calculations

We can use equilibrium constants to calculate new equilibrium concentrations that result from adding species to, or removing species from, a system at equilibrium. 

Some hydrogen and iodine are mixed at 22TC in a 1.00-liter container. When equilibrium is established, the foUowing concentrations are present [HI] = 0.490 M, [H2] = 0.080 M, and [I2] = 0.060 M. If an additional 0.300 mol of HI is then added, what concentrations will be present when the new equihbrium is established  

We use the original equihbrium concentrations to calculate the value of Kc- Then we determine the new concentrations after some HI has been added and calculate Q. Comparing the value oiQtoKc tehs us which reaction is favored. Then we can represent the new equihbrium concentrations. We substitute these representations into the IQ expression and solve for the new equihbrium concentrations. 

Calculate the value of IQ from the first set of equilibrium concentrations. 

Unless othewise noted, all content on this page is Cengage Learning. 

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Example 9.4 deals with a system at equilibrium, but suppose the reaction mixture has arbitrary concentrations. How can we tell whether it will have a tendency to form more products or to decompose into reactants To answer this question, we first need the equilibrium constant. We may have to determine it experimentally or calculate it from standard Gibbs free energy data. Then we calculate the reaction quotient, Q, from the actual composition of the reaction mixture, as described in Section 9.3. To predict whether a particular mixture of reactants and products will rend to produce more products or more reactants, we compare Q with K ... 

Cyclohexane (C) and methylcyclopentane (M) are isomers with the chemical formula C6H12. The equilibrium constant for the rearrangement C M in solution is 0.140 at 25°C. (a) A solution of 0.0200 mol-L 1 cyclohexane and 0.100 mol-I. 1 methylcyclopentane is prepared. Is the system at equilibrium If not, will it will form more reactants or more products (b) What are the concentrations of cyclohexane and methylcyclohexane at equilibrium (c) If the temperature is raised to 50.°C, the concentration of cyclohexane becomes 0.100 mol-L 1 when equilibrium is reestablished. Calculate the new equilibrium constant, (d) Is the reaction exothermic or endothermic at 25°C Explain your conclusion. 

Sometimes the calculation predicts that the fluid as initially constrained is supersaturated with respect to one or more minerals, and hence, is in a metastable equilibrium. If the supersaturated minerals are not suppressed, the model proceeds to calculate the equilibrium state, which it needs to find if it is to follow a reaction path. By allowing supersaturated minerals to precipitate, accounting for any minerals that dissolve as others precipitate, the model determines the stable mineral assemblage and corresponding fluid composition. The model output contains the calculated results for the supersaturated system as well as those for the system at equilibrium. 

Such a method has seldom been used with systems containing an aqueous fluid, probably because the complexity of the solution s free energy surface and the wide range in aqueous solubilities of the elements complicate the numerics of the calculation (e.g., Harvie el al., 1987). Instead, most models employ a procedure of elimination. If the calculation described fails to predict a system at equilibrium, the mineral assemblage is changed to swap undersaturated minerals out of the basis or supersaturated minerals into it, following the steps in the previous chapter the calculation is then repeated. 

For a system at equilibrium AG° = -RTIn K = -2.303 RTlog K Know how to apply this equation to calculate equilibrium constants. 

Since thermodynamics deals with systems at equilibrium, time is not a thermodynamic coordinate. One can calculate, for example, that if benzene(equilibrium with hydrogen(g) and carbon(s) at 298.15 K, then there would be very little benzene present since the equilibrium constant for the formation of benzene is 1.67 x 10-22. The equilibrium constant for the formation of diamond(s) from carbon(s, graphite) at 298.15 K is 0.310 that is, graphite is more stable than diamond. As a final example, the equilibrium constant for the following reaction at 298.15 K is 2.24 x 10-37 ... 

Thus, when values of (A/if - A/if) are plotted as a function of xt, the area between the best smooth curve drawn through the points and the composition axis must be zero within the experimental accuracy. This test concerns the thermodynamic consistency of the data as a whole rather than that of each individual set of experimental values. It also applies strictly to the liquid solution at the arbitrary pressure P0 and only to the two-phase system at equilibrium through the calculation of A fi [ and A /if from the experimental data. 

The criterion of spontaneous change and equilibrium for a nonreaction system is dG < 0 at constant T, P, and n , but the criterion for a system involving chemical reactions is dG 0 at constant T, P, and nci. Therefore, to calculate the composition of a reaction system at equilibrium, it is necessary to specify the amounts of components. This can be done by specifying the initial composition because the initial reactants obviously contain all the components, but this is more information than necessary, as we will see in the chapter on matrices. 

Equilibrium models provide information about the chemistry of the system at equilibrium but will not tell you anything about the kinetics with which the system reached equilibrium state. The basic objectives in using equilibrium models in estuarine/aquatic chemistry is to calculate equilibrium compositions in natural waters, to determine the amount of energy needed to make certain reactions occur, and to ascertain how far a system may be from equilibrium. 

Before we begin considering shifts in an equilibrium system, we need a quantitative way to describe the state of the system at any time, whether it has established equilibrium or not. In Chapter 13, you learned about the reaction quotient, Q, which was used to describe equilibrium systems. In solubility equilibria, we re not really dealing with a quotient—-just a product. Because the expression is the product of the concentrations of two different ions, the equilibrium expression that describes solubility equilibria is known as the ion product. Q is calculated in the same way as K, except it does not necessarily describe a system at equilibrium. Referring to our initial example, for the equilibrium shown below... 

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

In this chapter we will discuss how and why a chemical system comes to equilibrium and the characteristics of a system at equilibrium. In particular, we will discuss how to calculate the concentrations of the reactants and products present for a given system at equilibrium. 

Distinguish between intensive and extensive variables, giving examples of each. Use the Gibbs phase rule to determine the number of degrees of freedom for a multicomponent multiphase system at equilibrium, and state the meaning of the value you calculate in terms of the system s intensive variables. Specify a feasible set of intensive variables that will enable the remaining intensive variables to be calculated. 

Note that even though K is a constant in Eqs. (3.18) and (3.19), the individual activities of D, E, B, and C can vary. The major advantage of these equations is that the K for any balanced chemical reaction can he directly calculated from AG , which in turn can be determined by plugging AG values from thermodynamic tables into Eq. (3.14). In a chemical system at equilibrium the individual activities of reactants and products are closely constrained hy this equation. 

In principle, Boltzmann s equation enables us to calculate all the properties of the system at equilibrium and in particular the mean values of all functions (u1 . . . , Uff) of the configurations of the system. However, in practice, it is impossible to perform the calculation and approximations have to be made. The most classical one consist in choosing a priori a simpler trial probability PT ui, , Uff-, a ) depending on parameters a1 . .., ap. This trial... 

The standard entropy of reaction, AS°xn, is calculated from S° values. When the amount (mol) of gas (AOgas) increases in a reaction, usually ASfxn > 0- The value of ASsurr is related directly to AH ys and inversely to the T at which the change occurs. In a spontaneous change, the entropy of the system can decrease only if the entropy of the surroundings increases even more. For a system at equilibrium, ASuniv = 0-... 

Pursued to their logical conclusions, these statements provide us with an understanding of the behavior of chemical systems at equilibrium and of the circumstances under which chemical change will occur. For example, they allow us to calculate the equilibrium constants of reactions that have never been carried out and show how these equilibrium constants vary with the temperature. 

These technical problems were overcome by the development of a group of methods known as relaxation methods, the pioneer worker in this field being the German physical chemist Manfred Eigen. These methods differ fundamentally from conventional kinetic methods in that we start with the system at equilibrium under a given set of conditions. We then change these conditions very rapidly the system is then no longer at equilibrium, and it relaxes to a new state of equilibrium. The speed with which it relaxes can be measured, usually by spectrophotometry, and we can then calculate the rate constants. 

This appendix contains a computer program called EQBRM written in FORTRAN which calculates the concentrations of all aqueous species in a system at equilibrium. The algorithm and some of the theory are outlined in Chapter 19. We describe here how to use the program, using a. simple calculation as an example. 

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