CHM 1046

CHM 1046
General Chemistry II
Dr. Michael Blaber

Chemical Equilibrium

The Equilibrium Constant

The Haber Process

Human agriculture requires a whole bunch of ammonia-based fertilizer. Natural deposits of nitrate compounds, and bird and bat guano (i.e. poop) have been rich sources of nitrogen from which to produce ammonia based fertilizer (and also, nitrogen based explosives).

Although the atmosphere is about 70% nitrogen, it was not until the early 1900's that a chemical method was developed to allow the chemical production of ammonia from nitrogen gas. This method was developed by Fritz Haber in Germany in 1912, a method known as the Haber Process:

In the Haber Process, N₂ and H₂ are placed together in a high-pressure tank (at several hundred atmospheres pressure), and at a temperature of several hundred °C (and in the presence of a catalyst also).
Under these conditions the two gases react to produce ammonia:

N₂(g) + 3H₂(g) -> 2NH₃(g)

Extreme conditions are required because we have to break the N-N bond in N₂ and this bond is a (strong) triple bond

When the N₂(g) and H₂(g) are combined in the Haber process, the reaction proceeds and ammonia, NH₃(g) is produced

The reaction seems to stop at a certain point, and some N₂(g) and H₂(g) remain in the sample (along with the ammonia that is produced)

Another way of saying the reaction appears to stop, is to say that at some point in time the concentrations of H₂, N₂ and NH₃ reach a steady state (i.e. they don't appear to change)

Curiously enough, the same equilibrium concentrations of H₂, N₂ and NH₃ were observed even when the reaction was started with the vat containing only pure NH₃ (i.e. pure product!)

The same equilibrium condition for the concentrations of reactants and products was reached from either direction (i.e. starting from either pure reactants, or pure product)

For a simple A->B unimolecular reaction

Forward Rate = Reverse Rate

k_f [A] = k_r [B]

This equation can be rearranged to relate the concentration of A to B at equilibrium:

A similar equation relates the concentrations of H₂, N₂ and NH₃ at equilibrium in the Haber reaction

The Law of Mass Action

In 1864 Guldberg and Waage postulated the Law of Mass Action which expresses the relationship between the concentrations of reactants and products at equilibrium in any reaction
Given the following general equilibrium equation

According to the Law of Mass Action, the equilibrium condition is expressed by the equation:

Where the brackets indicate molar concentration of the reactants and products at dynamic equilibrium.

This expression is called the equilibrium expression for the reaction
K_c is called the equilibrium constant. Its value is what we get when we put in the observed concentrations of the reactants and products, at equilibrium, into the equilibrium expression.
The numerator (the stuff on top) of the equilibrium expression is the product of all concentrations of products raised to their coefficients in the balanced equation. The denominator (the stuff on the bottom) of the equilibrium expression is the product of all concentrations of reactants raised to their coefficients in the balanced equation.

Back to Fritz Haber and his famous process to make ammonia from N₂ and H₂:

From the Law of Mass Action, the equilibrium expression would be based upon the balanced equation:

N₂(g) + 3H₂(g) -> 2NH₃(g)

Note that once we have a balanced equation, although we may not know the reaction mechanism (i.e. underlying elementary steps or reaction intermediates), we can determine the equilibrium expression. Thus, the equilibrium expression depends only upon the balanced equation and is independent of the reaction mechanism

Yet another note: The convention is to write equilibrium constants as dimensionless values
Expressing Equilibrium Constants in Terms of Pressure, K_p

Kc indicates that the equilibrium constant is in terms of concentration (in molar units)
When reactants and products in a reaction are all gases we can use partial pressures in the equilibrium equation

The Magnitude of Equilibrium Constants

Given the following general equation for a reaction, and the associated equilibrium expression

What can we conclude about an equilibrium constant that is LARGE?

The value of the numerator (the stuff on top) must be larger than the value of the denominator (stuff on bottom)
This will happen if the equilibrium concentrations of the products are larger than the reactants

Thus, for a reaction with a large equilibrium constant, the equilibrium "lies to the right", meaning that the equilibrium mixture comprises mostly product

What can we conclude about an equilibrium constant that is SMALL?

The value of the numerator (the stuff on top) must be smaller than the value of the denominator (stuff on the bottom)
This will happen if the equilibrium concentrations of the reactants are larger than the products

Thus, for a reaction with a small equilibrium constant, the equilibrium "lies to the left", meaning that the equilibrium mixture comprises mostly reactants

To summarize the interpretation for the magnitude of the equilibrium constant:

K >> 1 Products favored

K << 1 Reactants favored

The Direction of the Chemical Equation and K

By definition, equilibrium implies that we have both a "forward" and a "backward" reaction in a balanced chemical equation.

"Forward" and "backward" are thus relative terms

Consider the following reaction:

Experimentally, the value of K_c for this expression equals 0.212 (@100°C)

We could, however, just as equally valid, consider the reaction to be the following:

The equilibrium expression in this case would be:

The value of Kc in this case would be (1/0.212) = 4.72

The equilibrium expression for a reaction written in one direction is the reciprocal of the one for the reaction written in the reverse direction

Therefore, an equilibrium constant, in the absence of information about the direction of the reaction, is ambiguous (i.e. meaningless)