In this lesson, we will first define and explain the notion of a chemical equilibrium. Then, you'll learn about the equilibrium constant and reaction quotient. Finally, we'll round off the lesson with a couple of examples to solidify what you've learned!
A State of Equilibrium
A balance scale with equal weights on each side, a stalemate during a tug of war, and an equal amount of supply and demand are all examples of a type of equilibrium, a kind of state of balance that's achieved due to opposing forces. Chemistry is subject to a notion of equilibrium as well, and we're going to go over it right now.
Imagine a simple chemical reaction with species A and B, denoted as follows:
A <-> B
The double arrow that's in the middle of A and B means that the reaction is going both ways. That is to say, the reactants are turning into the product species, while products are turning back into the reactant species.
Suppose that the A molecules start turning into the B molecules whenever the temperature rises above room temperature. Inasmuch, imagine placing a test tube with only A molecules into an oven that maintains a constant temperature above room temperature.
Given what I just mentioned, you would expect that some A molecules will start turning into B molecules. As time passes, more and more A molecules will turn into B molecules. However, suppose that there is also a backward tendency for B molecules to turn into A molecules for a large range of temperatures, including the one in the oven.
What will result is a back-and-forth movement between the concentrations of products and reactants, with the possibility of a chemical equilibrium eventually being established. A chemical equilibrium is a state in which the rate of the forward reaction is the same as the rate of the reverse reaction.
In our example, this means that after a certain period of time, the concentrations of species A and B will reach a stable state in which just as many A molecules will be turning into B molecules as B molecules turning into A molecules. In other words, the reaction will reach equilibrium, which could be maintained indefinitely if all factors, such as temperature, remain the same.
The Equilibrium Constant
Knowing this, you can now understand the next part of equilibrium, as it relates to chemistry. There is a numerical value, called the equilibrium constant, which is a value that relates the ratio of the concentrations of products to reactants once the reaction has reached chemical equilibrium.
Going back to our example from the last section, we would be able to calculate this constant by knowing the concentrations of species A and B at chemical equilibrium.
But let's consider a more general reaction to drive the point of an equilibrium constant home. It reads as follows:
aA + bB <-> cC + dD
Here, a, b, c, and d are integers, and A, B, C, and D designate the chemical species in question. The square brackets designate taking the concentration of chemical species; that is, [A] is the concentration of A.
We can calculate the equilibrium constant, denoted as Keq, as follows:
It is important to note that only species in the gas and aqueous state are included in the equilibrium constant calculation (pure solids and liquids are omitted).
The Reaction Quotient
At this point, you may be wondering about what happens when the reaction is not in equilibrium. Meaning, is there a similar number that we can calculate to determine the state of the reaction in such a scenario? Why, yes there is!
When the reaction is not in equilibrium, we can determine its state by calculating the reaction quotient (Q), which relates the concentrations of products to reactants at any time. The reaction quotient is useful in determining the direction in which the reaction is moving - toward or away from chemical equilibrium.
It is calculated in the same way as the equilibrium constant:
When the reaction quotient (Q) is greater than the equilibrium constant (Keq), the reactants are favored and the reaction moves in the reverse direction. When Q equals K, the reaction is in equilibrium and there is no tendency to move either towards the reactants or products. But when Q is less than Keq, the products are favored and the reaction moves in the forward direction.
Okay, now that you've got the theory down, let's put theory to practice with a couple of examples! Let's consider the following reaction with equilibrium concentrations of products and reactants:
2SO2 (g) + O2 (g) <-> 2SO3 (g)
[SO2] = 3.77 * 10-3 mol/L
[O2] = 4.30 * 10-3 mol/L
[SO3] = 4.13 * 10-3 mol/L
Calculating the equilibrium constant:
Now, let's just suppose that at a different temperature you determine the concentrations to be:
[SO2 ] = 2.68 * 10-3 mol/L
[O2 ] = 3.20 * 10-3 mol/L
[SO3 ] = 3.24 * 10-3 mol/L
Note that these concentrations are not equilibrium concentrations. In that case, let's calculate the reaction quotient:
In this specific instance, since Q greater than Keq, the reverse reaction would be favored.
Okay, we've learned a lot here, so let's recap the fundamental parts of our lesson. A chemical equilibrium is a state in which the rate of the forward reaction is the same as the rate of the reverse reaction.
The equilibrium constant is a value that relates the ratio of the concentrations of products to reactants once the reaction has reached chemical equilibrium, and the reaction quotient is useful in determining the direction in which the reaction is moving - toward or away from chemical equilibrium.
There are three possible cases for Q and Keq:
- When Q > Keq, the reaction moves in the reverse direction.
- When Q = K, the reaction is in equilibrium.
- When Q < Keq, the reaction moves in the forward direction.
When you are done, you should be able to:
- Describe a chemical equilibrium and how it is attained
- Recall how to calculate the equilibrium constant
- Recite when and how to calculate the reaction quotient