Chemistry Lab/Equilibrium

This page is related to the 2013 focus on Equilibrium for Chem Lab.

Basic Information
The term "equilibrium" in chemistry refers to the ability of a reaction to proceed in either direction. When a balance between reactants and products is met, the equation is said to be in equilibrium. Although many reactions are simplified by assuming they run to completion, in reality, this is not the case. In equilibrium, the forward (reactants --> products) and reverse (products --> reactants) are occurring at equal but opposite rates (hence, equilibrium). The ratio of reactants to products at equilibrium can be defined as a constant, generally k.

The standard example of chemical equilibrium given in most textbooks is the decomposition of N2O4 (g) to 2NO2 (g) (probably because the color changes, making it easy to see changes in equilibrium). Because of its simplicity, this example will be used to introduce calculation of the equilibrium constant.

The Equilibrium Constant
K, the equilibrium constant, is derived from chemical kinetics. It can be defined as the concentration of the products to the power of their coefficients divided by the concentration of the reactants to the power of their coefficients. To use the example given earlier:

K for the decomposition of N2O4 (g) to yield 2NO2 (g) is given as follows: $$[NO2]^2/[N2O4]$$. Because the coefficient of NO2 is 2, the concentration of this gas is squared. To make this easier to understand, suppose the concentration of NO2 at equilibrium (not initially) is 0.0172 M and the concentration of N2O4 at equilibrium is 0.00140 M. To calculate the equilibrium constant, square the concentration of NO2 and divide it by the concentration of N2O4:

$$(0.0172)^2/(0.001400) = 0.211$$

Notice the lack of units because the M in the numerator and the M in the denominator cancel.

For a slightly more complex example, we can use the Haber process of synthesizing ammonia at high temperatures and pressures from nitrogen and hydrogen gas. The equation for this reaction is N2 (g) + 3H2 (g) --> 2NH3 (g). To calculate this equilibrium constant, take the concentration of N2 times the concentration of hydrogen cubed divided by the concentration of ammonia squared, like so:

$$[N2][H2]^3/[NH3]^2$$.

Heterogenous Equilibia
Notice all of the reactants and products in the above examples were gases. This is because when calculating an equilibrium constant, solids and liquids are not taken into account (aqueous reactants or products, however, are). This is because the concentrations of solids and liquids remain constant, unlike the concentrations of gases (if you double the mass of a solid, its volume is also doubled). For example, if calculating the equilibrium constant for the dissocation of PbCl2 in water (PbCl2 (s) --> Pb2+ (aq) + 2Cl- (aq)), the solid lead chloride will not be factored into the calculation. The expression then becomes $$[Pb2+][Cl-]^2$$.

LeChatelier's Principle
LeChatelier's principle says that changes in the system that an equilibrium reaction occurs in will cause a change in the overall equilibrium. That is, if a stress is applied to a system, the system will react in such a way as to minimize or counter the stress. Examples of these changes or stresses can include volume, temperature, pressure, or concentration.

Volume
If the volume of a system is reduced, the system will react by shifting in the direction that reduces the number of moles of gas. To return to the example of N2O4 and NO2, if the volume of this system is reduced, the reaction will be driven toward N2O4. Recall the equation: $$N2O4 (g) --> 2NO2 (g)$$. Because there are fewer moles of N2O4 than there are moles of NO2, if the volume decreases, the reaction will shift toward N2O4, converting more products into reactants than reactants into products. The opposite is also true: if the volume is increased, the reaction will shift toward NO2 because there will be more moles of gas to occupy the larger volume.

Application to Acids and Bases
When weak acids and/or bases are combined, the reaction that results is an equilibrium reaction. Through a process called titration, you can find the equilibrium constant of the weak substances.