E - The Equilibrium Condition (Lesson)
The Equilibrium Condition
Defining Chemical Equilibrium
Up to this point, most chemical and physical processes that have been studied proceed to completion. In other words, reactants are mixed together and the reaction proceeds until the limiting reactant is consumed to form new products. There are numerous reactions, however, that do not proceed in this fashion. Consider the example shown below:
N2O4 (g) ⇌ 2 NO2 (g)
In this process, dinitrogen tetroxide (N2O4) decomposes to form nitrogen dioxide (NO2). However, at a certain point an interesting phenomenon occurs: the products begin reacting with one another to reform the reactants. This can also be considered by looking at the reaction from the standpoints of changes in both concentration and reaction rate.
Notice that when considering the changes in concentration as a function of time that the concentrations of each substance involved in the reaction continue to change until a certain point when they remain constant. Likewise, when analyzing the reaction from the viewpoint of reaction rate, something even more significant occurs. As the reaction proceeds the rate of the forward reaction decreases as N2O4 reacts, while at the same time, the rate of the reverse reaction increases as more NO2 is being produced. Even more significant is the fact that both of these rates approach the same value. By definition, chemical equilibrium is said to have been achieved when these rates are equal. It is also important to note that chemical equilibrium is a dynamic equilibrium as opposed to a static one. Both reactions continue to proceed, but there is no change in the concentrations of all substances involved.
The Equilibrium Expression and Constant
Because the concentrations of all substances are no longer changing once equilibrium has been achieved it is possible to relate these concentrations through what is referred to as an equilibrium expression. In an equilibrium expression, the concentrations of each species can be mathematically related as shown below for any reaction at equilibrium. Please note that the brackets are shorthand notation to describe concentration. Therefore [A] should be read as "the concentration of A".
aA + bB ⇌ cC + dD
K=[C]c[D]d[A]a[B]b
Calculation of the equilibrium constant, K, provides a way to describe the extent to which a reaction proceeds. For example, because the concentration of products is in the numerator, if K > 1 that means that at equilibrium, the system has more products present than reactants. This can be described by saying that products are favored or "the equilibrium lies to the right." Alternatively, K < 1 implies that the denominator is larger, and since it refers to the amount of reactants, such an equilibrium value would be described as favoring the reactants or "the equilibrium lies to the left."
Calculating K
The equilibrium constant for a system can only be calculated by using the concentrations of all species after the reaction has reached equilibrium. Consider the equilibrium shown below.
2 SO3 (g) \(\rightleftharpoons\) 2 SO2 (g) + O2 (g)
Suppose that the concentrations of all species were analyzed at equilibrium and found to be as follows: [SO2] = 0.44 M, [O2] = 0.22 M, [SO3] = 0.11 M. The equilibrium constant could therefore be calculated as shown below:
K=[SO2]2[O2][SO3]2=(0.44)2(0.22)(0.11)2=3.5
Relationships Between Pressure and Concentration
Thus far, equilibria and equilibrium expressions have been expressed in terms of concentration only. While many reactions can be analyzed by studying changes in concentration over time, it is also possible to analyze changes in partial pressure for those reactions that occur in the gas phase. Because of this, it is necessary to differentiate between two different types of equilibrium constants. When dealing with concentration, it is necessary to describe the equilibrium constant by designating it as Kc; however, for those systems studying in the gas phase it is necessary to use Kp. In these two constants, the subscripts c and p refer to concentration and pressure, respectively. While these two constants are describing the same thing, they do not always have the same value. Consider the equilibrium that can be described using either version below as an example:
COCl2 (g) \(\rightleftharpoons\) CO (g) + Cl2 (g)
Kc=[CO][Cl2][COCl2]
As mentioned above, Kp and Kc both may describe the same equilibrium; however, they do not always have the same value, and it is sometimes necessary to convert from one form to another. In order to do this, the relationship shown below is used:
Kp=Kc(RT)Δn
where Δn refers to the change in the number of moles between reactant and product (nf - ni), R is the universal gas constant, and T is temperature expressed in Kelvin.
As an example, the equilibrium below can be examined:
PCl5 (g) ⇌ PCl3 (g) + Cl2 (g)
Let's assume that the numerical value of Kp for this equilibrium is 0.74 at 499 K. Using this information, it is possible to convert this value to Kc.
Kp=Kc(RT)Δn
0.74=Kc[(0.08206)(499)]+1
Kc = 1.8 x 10-2
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