# Equilibrium Constants

Imagine you have a mix of two things that can react with each other and make a reversible reaction. If you leave them alone, they'll eventually reach a state of balance called dynamic equilibrium. There are two things to remember about this: the forward reaction rate and backward reaction rate are equal, and the amounts of the products and reactants stay the same. But how can you figure out what's in the mixture? If you try to measure it, you might change the balance. Instead, we use something called the equilibrium constant, or Kc, which tells us how much of each thing is in the mix at equilibrium. In this article, we will go through what Kc is, how to calculate it, and examples. We'll also cover exam questions and what can affect the value of Kc.

## What is the equilibrium constant Kc?

Remember that the equilibrium constant, Kc, is a value that shows how much of the reactants and products are in a mixture at equilibrium. Kc relates to the concentration of the reactants and products in a reversible reaction. Here are two things to keep in mind about Kc:

- The bigger the Kc value, the more products you have compared to reactants at equilibrium.
- The Kc value for a specific reaction at a given temperature will always be the same, no matter how much of the products or reactants you begin with.

## What is the equation for the equilibrium constant Kc?

Great! Now that we have a general understanding of what Kc is and how to write its equation, let's consider an example to demonstrate how we can use Kc to calculate the equilibrium concentrations of the reactants and products.

Suppose we have a reaction where 2 moles of hydrogen gas (H2) and 1 mole of nitrogen gas (N2) react to form 2 moles of ammonia gas (NH3) at 400 K. The equation for this reaction is:

N2(g) + 3H2(g) ⇌ 2NH3(g)

To calculate the value of Kc for this reaction, we need to determine the concentrations of the reactants and products at equilibrium. Let's assume that the initial concentrations of N2 and H2 are 0.1 mol/L each, and the initial concentration of NH3 is 0 mol/L.

At equilibrium, let's say the concentrations of N2, H2, and NH3 are x, y, and z mol/L, respectively. Using the stoichiometric coefficients from the balanced equation, we can write the equilibrium concentrations in terms of x and y:

[N2]eq = (0.1 - x) mol/L

[H2]eq = (0.1 - y) mol/L

[NH3]eq = z mol/L

Now, we can substitute these concentrations into the Kc equation:

Kc = [NH3]eq^2 / ([N2]eq * [H2]eq^3)

Kc = z^2 / [(0.1 - x)(0.1 - y)^3]

At equilibrium, Kc has a fixed value of 4.34 x 10^-3 at 400 K for this reaction. Using this value of Kc, we can solve for x, y, and z, which represent the equilibrium concentrations of the reactants and products:

z^2 = Kc(0.1 - x)(0.1 - y)^3

Substituting the values of Kc and the initial concentrations into the equation, we get:

z^2 = 4.34 x 10^-3 (0.1 - x)(0.1 - y)^3

Solving for z, we get:

z = 0.063 mol/L

Using the value of z, we can solve for x and y:

x = 0.03 mol/L

y = 0.037 mol/L

Therefore, at equilibrium, the concentrations of N2, H2, and NH3 are 0.03, 0.037, and 0.063 mol/L, respectively.

In summary, we can use Kc to calculate the equilibrium concentrations of the reactants and products in a reversible reaction, provided we know the initial concentrations of the reactants, the stoichiometry of the reaction, and the value of Kc.

## What would the equilibrium constant for this reaction be?

Calculating the equilibrium constant Kc for heterogeneous equilibria involves taking the equilibrium concentrations of the products, raising them to the power of the molar ratio given in the equation, and then dividing them by the equilibrium concentrations of the reactants, raised to the power of the molar ratio given in the equation. The units for Kc can vary from calculation to calculation, and can be found by replacing the concentration of each species with the units that the concentration is measured in, and then cancelling units from the top and bottom of the equation until one term is left.

For example, in a sealed container with a volume of 600 cm3, 0.500 mol H2 and 0.600 mol Cl2 react to form an equilibrium with the following equation: H2 + Cl2 ⇌ 2HCl. At equilibrium, there is 0.400 mol HCl present in the container. The Kc for this reaction can be calculated by first making a table with the number of moles of all of the species involved at the start of the reaction, the change in the number of moles, and the number of moles at equilibrium. The equation for Kc is then Kc = [HCl]2/[H2][Cl2], and the units for Kc can be found by replacing the concentration of each species with the units that the concentration is measured in and then cancelling units from the top and bottom of the equation until one term is left. In this case, the Kc is 7.7 mol-1 dm3.

**Working backwards from Kc**

Great! It's important to remember that for heterogeneous systems, the equation for Kc only includes the concentrations of the reacting gases and/or aqueous solutions, while ignoring the concentrations of solids.

To calculate Kc for a heterogeneous system, we need to write the balanced equation for the reaction, and then identify which species are solids and can be ignored in the Kc equation. For example, in the reaction Cu(s) + 2Ag+(aq) ⇌ Cu2+(aq) + 2Ag(s), we can ignore the concentrations of Cu(s) and Ag(s) in the Kc equation, since they are solids.

The Kc equation for this reaction would be Kc = [Cu2+(aq)][Ag+(aq)]^2. We only include the concentrations of the reacting aqueous solutions, since they are the only species whose concentrations change during the reaction.

In summary, to calculate Kc for a heterogeneous system, we need to write the balanced equation for the reaction, identify which species are solids and can be ignored in the Kc equation, and then use the concentrations of the remaining reacting species in the Kc equation.

## Magnitude of the equilibrium constant Kc

Great job! To summarize, we can infer important information about the position of the equilibrium from the magnitude of Kc, with Kc less than 1 indicating a predominance of the backward reaction, Kc equal to 1 indicating a balance of reactants and products, and Kc greater than 1 indicating a predominance of the forward reaction. Kc is only affected by temperature and not by pressure, concentration, or the presence of a catalyst. Kc is useful for manipulating the conditions of an equilibrium to influence the yield of a reaction, as seen in the Haber process for ammonia production.

These are all important takeaways about equilibrium constants and their applications. Understanding Kc and its relationship to concentrations and the position of equilibrium can help us predict reaction outcomes and optimize yields.

## Equilibrium Constants

**How do you calculate the equilibrium constant?**

To calculate the equilibrium constant, you first find the equation for the equilibrium constant, and then substitute in the concentrations of each species at equilibrium.

**What are the different types of equilibrium constant?**

There are two types of equilibrium constant: Kc and Kp. Kc uses equilibrium concentrations of liquids, gases, or aqueous solutions. Kp uses partial pressures of gases at equilibrium.

**What is the equilibrium constant?**

The equilibrium constant Kc is a value that links the concentration of reactants and the concentration of products in a mixture at equilibrium.

**Does pressure affect the equilibrium constant?**

Pressure has no effect on the value of Kc. Only temperature affects Kc.