Magnitude of Equilibrium Constant

Q: What is the likely magnitude of the equilibrium constant Keq?

For a reversible reaction, Keq is usually between 10-2 and 102. This means that there are significant amounts of both products and reactants at equilibrium. If Keq is less than 10-2, we consider the backward reaction to be irreversible. If Keq is greater than 102, we consider the forward reaction to be irreversible.

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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, K_eq, 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:

K_c measures the Concentration of aqueous or gaseous species in a Reversible Reaction at equilibrium.
K_p measures the Partial Pressure ofgaseous species in a Reversible Reaction at equilibrium.

Check out "Equilibrium Constant" to find out more about K_c and K_p.

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 K_c or K_p, 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 K_c and K_p, 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 K_eq, be it in the form of K_c or K_p, 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 K_eq is less than 1.
When the magnitude of K_eqequals 1.
When the magnitude of K_eq is greater than 1.

K_eq < 1

For K_eq 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 K_c 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:

Magnitude of Equilibrium Constant Kc<1 StudySmarter A system at equilibrium. Here, the relative amount of products is less than the relative amount of reactants.StudySmarter 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 K_c, we get the following:

$$K_c=\frac{(1)}{(5)}=0.2$$

Here, the equilibrium constant is less than 1. If K_eq < 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 K_c, 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 K_p, 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.

K_eq = 1

For K_eq 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:

Magnitude of Equilibrium Constant Keq=1 StudySmarter A system at equilibrium. Here, the relative amount of products is the same as the relative amount of reactants. StudySmarter 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 K_c:

$$K_c=\frac{(3)}{(3)}=1$$

Here, the equilibrium constant is equal to 1. If K_eq = 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.

K_eq > 1

For K_eq 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:

Magnitude of Equilibrium Constant Keq=1 StudySmarter A system at equilibrium. Here, the relative amount of products is greater than the relative amount of reactants. StudySmarter 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 K_c, we get the following:

$$K_c=\frac{(5)}{(1)}=5$$Here, the equilibrium constant is greater than 1. If K_eq > 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 K_c 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 K_eq 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 K_c.

We can see that there is a greater concentration of products than reactants at equilibrium. Using the general rules for the magnitude of K_eq that we learned above, we would expect K_c 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, K_c 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 K_c, that means aqueous or gaseous species; for K_p, that means just gaseous species.