Equilibrium Constant - Online Tutor, Practice Problems & Exam Prep

The equilibrium constant (K) characterizes biochemical reactions, indicating the ratio of product concentrations to reactant concentrations at equilibrium. At equilibrium, there is no net change in concentrations, and the system's free energy is minimized, ensuring stability. The value of K reveals whether products or reactants predominate: K < 1 indicates reactants are favored, K = 1 shows equal concentrations, and K > 1 favors products. The equilibrium constant is influenced by temperature and can be expressed mathematically as [P]/[R].

Biochemical Reaction Features

In this video, we're going to begin our discussion of the equilibrium constant. The equilibrium constant is a specific number and a feature that characterizes biochemical reactions, and there are actually four features that characterize all biochemical reactions. Let's take a look at our example below to clarify that. Spontaneity is the first feature of a biochemical reaction, and we covered spontaneity in our previous videos when we talked about the second law of thermodynamics. You can see that we have exergonic reactions and endergonic reactions, and all reactions will fall under one of these two categories.

Now the second feature of a biochemical reaction is the equilibrium constant. Again, recall that the equilibrium constant is a specific number, so the equilibrium constant is a specific number that characterizes a biochemical reaction, and notice that it has to do with a balance. The balance has to do with the ratio of products to reactants, and we'll talk more about that as we move forward in our course.

The next feature is the reaction direction, and that's determining whether the reaction is going to proceed in a forward direction or a backwards direction. We'll talk about this when we get to our next lesson. Velocity has to do with how fast a reaction is going to occur, so the rate at which the reactants convert into products. We'll talk about velocity when we talk about enzymes later on in our course.

In our next video, what we're going to do is refresh on what equilibrium actually means. So I'll see you guys in that video.

Equilibrium

So recall that a reaction at equilibrium has all of the following characteristics, and the first is that there's no net change in the concentrations of reactants or products, and that's because the rate of the forward reaction is equal to the rate of the reverse reaction. Also, a reaction at equilibrium has no change in free energy, meaning that ΔG or the change in Gibbs free energy is equal to 0 at equilibrium. At equilibrium, a reaction system's energy is at its minimum or at its lowest. Because the energy is at its lowest, that means that the system is most stable at equilibrium. Finally, at equilibrium, there's a very specific ratio of the concentrations of products over the concentration of reactants, and this ratio is constant for a set condition. Again, because at equilibrium, the reaction system's energy is at its lowest and most stable, all reactions proceed towards restoring equilibrium.

Let's take a look at our example below where we have this graph that your professor is likely not going to ask you guys to analyze, but this graph is used all the time to explain equilibrium. This graph is analyzing a simple reaction where we're converting reactant a into product b. On the y-axis, we have the free energy of the system, and on the x-axis, we have the component concentrations. On the far left of the x-axis, we have pure a concentrations, and on the far right, we have pure b concentrations. Notice that equilibrium is indicated by this blue box here and notice that the energy is at its very lowest at equilibrium. Also notice that at equilibrium, shown by these equilibrium arrows here, that there are 3 units of a for every 2 units of b and so the concentration of a does not equal the concentration of b at equilibrium, and this is totally fine. The concentration of a does not have to equal the concentration of b at equilibrium, but the forward reaction rate has to equal the reverse reaction rate at equilibrium.

The next thing that I want to tell you guys is that when the concentration of A is greater than the concentration of A at equilibrium, so like 4 A is greater than 3 a, then the reaction is going to proceed in a forward direction in order to restore the equilibrium concentrations. Also, when the concentration of b is greater than the concentration of b at equilibrium, like 4 b is greater than 2 b, then the reaction is going to proceed in a reverse direction in order to restore equilibrium. We'll talk more about equilibrium in our next video when we talk about the equilibrium constant. So I'll see you guys in that video.

Equilibrium Constant

So recall that the ratio of product concentrations over reactant concentrations, specifically at equilibrium, is called the equilibrium constant. And the equilibrium constant can actually be abbreviated by this symbol shown here. Now, the equilibrium constant actually changes with different conditions, and it changes with temperature. But the good thing is that in biological systems, if the temperature is not already given to us, then we always assume the temperature is going to be right around 298 Kelvin, or about 25 degrees Celsius. Now, in our example below, we're showing the equilibrium constant equation. And we already know that it's the concentration of products, specifically at equilibrium, over the concentration of reactants, specifically at equilibrium. And again, recall that the brackets here mean the concentration of. And so it turns out that the equilibrium constant is just a number, and by looking at the value of this number, we can actually determine whether the products are predominating, or the reactants are predominating. And by predominating, what I mean is they have a higher concentration when they're predominating. And so if we take a look at this chart over here, we can see that when the equilibrium constant is exactly equal to 1, what that means is that the concentrations are exactly equal at equilibrium. Now, in this scenario, if the equilibrium constant is really small, smaller than 1, what that means is that the concentration of products at equilibrium is going to be smaller than the concentration of reactants at equilibrium, and the reactants are going to be predominating over the products because their concentration is higher at equilibrium. Now, in the last scenario, if the equilibrium constant is large and greater than 1, what that means is that the concentration of products at equilibrium is going to be greater than the concentration of reactants at equilibrium. And so in this scenario, the products are going to be predominating because their concentrations are higher. And so it turns out that most reactions actually have multiple products and reactants. And so in order to adjust our equilibrium constant, what we need to do is we need to multiply their concentrations together to get the equilibrium constant. And so it also turns out that a lot of molecules have multiple coefficients or they have coefficients. And coefficients are simply numbers that are in front of the molecules. And they're included in the equilibrium constant as well, but they're included as exponents. And so if we take a look at our example below, which has multiple products and reactants and coefficients, we can see how this works. And so in our reaction, we have 2 reactants, reactant A and reactant B, in capital letters. And we have 2 products, product C and product D, in capital letters. And then the lowercase letters that are colored are the coefficients. And so, again, recall that our equilibrium constant over here is the concentration of products at equilibrium over the concentration of reactants at equilibrium. And so one of our products is already inputted into our equilibrium constant. That's product D. And so notice that the capital letter D is in the brackets, coefficient is included as an exponent. So we can do the same for our other product. So we'll put C, capital letter, in the brackets, and then the lowercase letter, the coefficient, will go as an exponent. And the same applies for the reactants, which are down below. Reactant A is already input, so we can put in reactant B, which is going to have a capital B in the brackets, and then the coefficient will be included as an exponent. And so, we'll be able to get more practice with this in our practice video, so I'll see you guys there.

What is the equilibrium constant expression for the following reaction?

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

• A. 2[NH₃] / 3[N₂]H₂]
• B. [N₂][H₂]³ / [NH₃]²
• C. 3[N₂][H₂] / 2[NH₃]
• D. [NH₃]² / [N₂][H₂]³

Here’s what students ask on this topic:

What is the equilibrium constant and how is it calculated?

The equilibrium constant (K) is a specific number that characterizes the ratio of product concentrations to reactant concentrations at equilibrium. It is calculated using the formula:

$\frac{\left[P\right]}{\left[R\right]}$

where [P] represents the concentration of products and [R] represents the concentration of reactants at equilibrium. For reactions with multiple products and reactants, the equilibrium constant is expressed as:

$\frac{\left[C{]}^c\right[D{]}^d}{\left[A{]}^a\right[B{]}^b}$

where A, B, C, and D are the reactants and products, and a, b, c, and d are their respective coefficients in the balanced chemical equation.

How does temperature affect the equilibrium constant?

The equilibrium constant (K) is temperature-dependent. Changes in temperature can shift the position of equilibrium, thereby altering the value of K. For endothermic reactions, an increase in temperature typically increases K, favoring the formation of products. Conversely, for exothermic reactions, an increase in temperature usually decreases K, favoring the formation of reactants. In biological systems, if the temperature is not specified, it is generally assumed to be around 298 K (25°C).

What does it mean if the equilibrium constant is greater than 1?

If the equilibrium constant (K) is greater than 1, it indicates that the concentration of products at equilibrium is greater than the concentration of reactants. This means that the reaction favors the formation of products, and they predominate in the equilibrium mixture. Mathematically, this is expressed as:

$\frac{\left[P\right]}{\left[R\right]}>\; 1$

What are the characteristics of a reaction at equilibrium?

A reaction at equilibrium has several key characteristics:

• No net change in the concentrations of reactants and products, as the rate of the forward reaction equals the rate of the reverse reaction.
• The change in Gibbs free energy (ΔG) is zero, indicating no change in free energy.
• The system's energy is at its minimum, making it most stable.
• A specific ratio of product concentrations to reactant concentrations, which is constant for a given set of conditions.

How can the equilibrium constant indicate whether products or reactants predominate?

The value of the equilibrium constant (K) reveals whether products or reactants predominate at equilibrium:

• If K > 1, products predominate, meaning their concentrations are higher than those of the reactants.
• If K < 1, reactants predominate, meaning their concentrations are higher than those of the products.
• If K = 1, the concentrations of products and reactants are equal, indicating neither predominates.