The equilibrium constant is more than just a simple number. From it, we can infer some important information about a system of reversible reactions. In this article, we'll focus on the magnitude of the equilibrium constant and what it tells us about a reaction at equilibrium.
- This article is about the magnitude of the equilibrium constant in chemistry.
- We'll look at how the magnitude of the equilibrium constant reflects the relative amounts of products and reactants in a system at equilibrium.
- You'll be able to use the equilibrium constant to describe the position of the equilibrium and how far the forward reaction goes to completion.
What is the magnitude of the equilibrium constant?
Let's take a moment to consider the equilibrium constant.
The equilibrium constant, Keq, is a value that tells us the relative amounts of reactants and products in a system at equilibrium.
We tend to focus on two equilibrium constants in particular:
Check out "Equilibrium Constant" to find out more about Kc and Kp.
The magnitude of the equilibrium constant is its absolute value - or in other words, its distance from 0. For example, both -4 and 4 have a magnitude of 4. But equilibrium constants are always greater or equal to 0, and so their magnitude is simply their value itself.
Why can't the equilibrium constant be less than 0? As you'll see in just a second, we calculate the equilibrium constant using either concentration or partial pressure. A negative equilibrium constant would require one of these values to be less than 0, which isn't possible - you can't have a negative concentration or partial pressure!
Magnitude of the equilibrium constant expression
As we mentioned above, the magnitude of the equilibrium constant, be it Kc or Kp, is just its value. To work out its magnitude, we simply calculate the equilibrium constant itself. This is done using formulae based on the reaction's balanced chemical equation. For example, take the reaction \(aA(g)+bB(g) \rightleftharpoons cC(g)+dD(g)\). To find Kc and Kp, we'd use the following expressions: $$K_c=\frac{{[C]_{eqm}}^c\space {[D]_{eqm}}^d}{{[A]_{eqm}}^a\space {[B]_{eqm}}^b}\qquad K_p=\frac{{{(P_C)}_{eqm}}^c\space {{(P_D)}_{eqm}}^d}{{{(P_A)}_{eqm}}^a\space {{(P_B)}_{eqm}}^b}$$
Equilibrium Constant will explain these expressions in more detail, so if you aren't sure what they mean, feel free to head over there now.
Discuss the magnitude of the equilibrium constant
So, we now know that the equilibrium constant Keq, be it in the form of Kc or Kp, tells us about the relative amounts of products and reactants in a system at equilibrium. We'll now look at three different scenarios:
- When the magnitude of Keq is less than 1.
- When the magnitude of Keqequals 1.
- When the magnitude of Keq is greater than 1.
Keq < 1
For Keq to be less than 1, the numerator of the equilibrium constant expression must be smaller than the denominator. This typically means that the relative amount of products is less than the relative amount of reactants at equilibrium.
Here's an example to help you understand the concept a little better. We'll use Kc to illustrate our point.
Imagine a system at equilibrium. It has a volume of 1 cubic liter and contains 5 moles of A and 1 mole of B. A and B are related using the equation \(A(g)\rightleftharpoons B(g)\). From the diagram below, it is fairly easy to see that we have a much smaller amount of the products than the reactants:
A system at equilibrium. Here, the relative amount of products is less than the relative amount of reactants.Vaia Originals
In this case, the equilibrium concentration [A]eqm is (5 ÷ 1) = 5 M, whilst the equilibrium concentration [B]eqm is (1 ÷ 1) = 1 M. If we substitute this into the expression for Kc, we get the following:
$$K_c=\frac{(1)}{(5)}=0.2$$
Here, the equilibrium constant is less than 1. If Keq < 1, then the relative amount of the products is typically less than the relative amount of the reactants at equilibrium. In other words, the reactants are favored.
Why have we included the word typically in our explanation? It is because this rule, and the other general rules you will learn in the article, don't always stand up. They only apply 100% of the time if there is an equal number of moles of species in the relevant states on each side of the equation, depending on the equilibrium constant you use. For example, when looking at the magnitude of Kc, there must be the same number of aqueous or gaseous species on the left-hand side of the equation as on the right. When looking at Kp, there must be the same number of gaseous species on each side of the equation.
We'll show you some examples of when the rule doesn't hold later on. However, it is a good starting point, and it is what you need to know for your exams.
Keq = 1
For Keq to equal 1, the numerator of the equilibrium constant expression must equal the denominator. This typically means that the relative amount of products is exactly the same as the relative amount of reactants at equilibrium.
Let's go back to our example from earlier. The system has the same volume, but this time it contains 3 moles of A and 3 moles of B at equilibrium:
A system at equilibrium. Here, the relative amount of products is the same as the relative amount of reactants. Vaia Originals
The equilibrium concentration of A is now (3 ÷ 1) = 3 M. The equilibrium concentration of B is also (3 ÷ 1) = 3 M. We get the following value for Kc:
$$K_c=\frac{(3)}{(3)}=1$$
Here, the equilibrium constant is equal to 1. If Keq = 1, then the relative amount of the products is typically the same as the relative amount of the reactants at equilibrium. In other words, both reactants and products are favored equally.
Keq > 1
For Keq to be greater than 1, the numerator of the equilibrium constant expression must be larger than the denominator. This typically means that the relative amount of products is greater than the relative amount of reactants at equilibrium.
Consider our equilibrium system again. This time, there is just 1 mole of A but 5 moles of B:
A system at equilibrium. Here, the relative amount of products is greater than the relative amount of reactants. Vaia Originals
In this case, the equilibrium concentration of A is (1 ÷ 1) = 1 M whilst the equilibrium concentration of B is also (3 ÷ 1) = 3 M.
For Kc, we get the following:
$$K_c=\frac{(5)}{(1)}=5$$Here, the equilibrium constant is greater than 1. If Keq > 1, then the relative amount of the products is typically greater than the relative amount of the reactants at equilibrium. In other words, products are favored.
Consider the following reaction:
$$CO_2+H_2\rightleftharpoons H_2O+CO\qquad K_c=0.010$$
What can you infer about the relative concentrations of reactants and products at equilibrium?
Well, note that the equilibrium constant Kc is significantly less than 1. That means the relative amount of the products is much smaller than the relative amount of the reactant in the system in equilibrium.
Learn the three main points above about the magnitude of Keq and you'll soar through your exams. But if you go on to study chemistry at a higher level, you might find some examples where the general rules don't hold up. This can happen if we have different numbers of moles of species on each side of the equilibrium equation. Look at the following case as an example.
A reaction has the equation \(A(g)\rightleftharpoons 3B(g)\) . At equilibrium, the system contains 0.3 M of A and 0.4 M of B. Calculate Kc.
We can see that there is a greater concentration of products than reactants at equilibrium. Using the general rules for the magnitude of Keq that we learned above, we would expect Kc to be greater than 1. However, this isn't true:
$$K_c=\frac{{[B]}^3}{[A]}$$ $$K_c=\frac{{(0.4)}^3}{(0.3)}$$ $$K_c=0.213$$
Here, Kc is actually less than 1.
Significance of the magnitude of the equilibrium constant
The magnitude of the equilibrium constant also tells us something else about the reaction. It provides information about the position of the equilibrium and how far the forward reaction goes to completion.
Like before, these are general rules. They only apply 100% of the time when both sides of the equation feature the same number of moles in the relevant states. For Kc, that means aqueous or gaseous species; for Kp, that means just gaseous species.
Keq < 1
In our first example, we had much more of the reactants than the products in our system at equilibrium and ended up with a value of Keq that was less than 1. In this reaction, the reactants predominate. It means that the position of the equilibrium lies to the left and in fact, the forward reaction barely progresses at all.
If the word reaction is used on its own when talking about Keq, it generally means the forward reaction. However, we find it much clearer to simply specify that it is the forward reaction we are referring to!
Keq = 1
In our second example, we had the same relative amounts of reactants and products in our system at equilibrium, which gave us a value of Keq that was exactly equal to 1. In this reaction, neither reactants nor products predominate. The position of the equilibrium lies in the middle and the forward reaction goes halfway to completion.
Keq > 1
Finally, in our third example, we had much more of the products than the reactants in our system at equilibrium. This resulted in a value of Keq that was greater than 1. In this reaction, the products predominate. The position of the equilibrium lies to the right and the forward reaction goes almost to completion.
Consider the following reaction:
$$2NO_2\rightleftharpoons N_2+O_2\qquad K_c=9019$$
What can you infer about the position of the equilibrium and the extent of the forward reaction?
Well, notice that Kc is very large. That means that we have much more of the products than reactants in the system at equilibrium. The products predominate; the position of the equilibrium lies to the right and the forward reaction goes almost to completion.
Order of magnitude of the equilibrium constant
It's hard to come up with fixed rules when it comes to dynamic equilibria. However, scientists like to be able to generalize such reactions. To help with that, there are a few general guidelines that we use to categorize systems in equilibrium, when it comes to their order of magnitude:
- If Keq is less than 10-2, we consider the backward reaction to be irreversible. The relative amount of products in the system at equilibrium is so small that it is practically insignificant.
- If Keq is between 10-2 and 102, we consider the overall reaction to be reversible. There are significant amounts of both products and reactants in the system at equilibrium.
- If Keq is greater than 102, we consider the forward reaction to be irreversible. The relative amount of reactants in the system at equilibrium is so small that it is practically insignificant.
These guidelines are just that - merely guidelines. For reactions in certain fields of chemistry, a very small value for Kc is still extremely significant! For your AP exam, you won't be asked to comment on the magnitude of the equilibrium constant beyond predicting the relative amounts of reactants and products in a system at equilibrium.
Summarizing the magnitude of the equilibrium constant
Hopefully, you now feel confident interpreting the magnitude of the equilibrium constant. To help consolidate your learning, we've created a handy table summarizing all of the information that the magnitude of the equilibrium constant tells us.
A table summarizing the magnitude of the equilibrium constant.Vaia Originals
That's the end of this article. By now, you should be able to use the magnitude of the equilibrium constant to describe the relative amounts of products and reactants in a system at equilibrium. You should also be able to use it to describe the position of the equilibrium and how far the forward reaction goes to completion.
Magnitude of equilibrium constant - Key takeaways
- The magnitude of the equilibrium constant is its distance from 0. Because equilibrium constants are always greater than or equal to 0, this is simply the constant's value.
- The magnitude of the equilibrium constant can be found by working out the equilibrium constant. This uses the following formulae: $$K_c=\frac{{[C]_{eqm}}^c\space {[D]_{eqm}}^d}{{[A]_{eqm}}^a\space {[B]_{eqm}}^b}$$ $$K_p=\frac{{{(P_C)}_{eqm}}^c\space {{(P_D)}_{eqm}}^d}{{{(P_A)}_{eqm}}^a\space {{(P_B)}_{eqm}}^b}$$
- If Keq < 1, then the reactants are typically favored at equilibrium. The position of the equilibrium lies on the left and the forward reaction barely progresses.
- If Keq = 1, both reactants and products are typically favored equally at equilibrium. The position of the equilibrium lies in the middle and the forward reaction goes halfway to completion.
- If Keq > 1, then the products are typically favored at equilibrium. The position of the equilibrium lies on the right and the forward reaction goes almost to completion.
- If Keq < 10-2, then we generally consider the backward reaction to be irreversible.
- If Keq > 102, then we generally consider the forward reaction to be irreversible.
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