Magnitude of the equilibrium constant | Equilibrium | AP Chemistry | Khan Academy
The magnitude of the equilibrium constant tells us the relative amounts of products and reactants at equilibrium. For example, let's look at a hypothetical reaction where gas A turns into gas B. For the first example, let's say that gas A is represented by a red sphere and gas B is represented by a blue sphere.
Down here we have a particulate diagram showing an equilibrium mixture of our hypothetical reaction. Let's write the equilibrium constant expression for this hypothetical reaction. So we're going to write Kc is equal to, and we think products over reactants. Our product is B, so this can be the concentration of B. Since the coefficient is a one in the balanced equation, it's the concentration of B raised to the first power divided by the concentration of our reactant, which is A. A in the balanced equation also has a coefficient of one, so this is the concentration of A raised to the first power.
If we assume that each particle in our particulate diagram represents 0.1 moles of a substance and the volume is 1 liter, we can calculate the concentration of both A and B. For example, for B, there are five blue spheres, so that would be five times 0.1 moles or 0.5 moles. For the concentration of B, we have 0.5 moles divided by a volume of 1 liter. So, 0.5 divided by 1 is 0.5 molar. Therefore, we can go ahead and plug that in for our concentration of B. It's 0.5 molar.
Next, we can do the same thing for A. There are also five red spheres, so therefore the concentration of A is also 0.5 molar. We can plug that into our equilibrium constant expression. 0.5 divided by 0.5 is equal to 1. Therefore, Kc, the equilibrium constant, is equal to 1 at whatever temperature we have for our hypothetical reaction. Our equilibrium constant Kc is equal to 1, and we saw in our particulate diagram that at equilibrium we have equal amounts of reactants and products.
Therefore, just by knowing the value for the equilibrium constant, we know about the relative amounts of reactants and products at equilibrium. Let's look at another hypothetical reaction which also has gas A turning into gas B. However, this time gas A is green and gas B is red. Let's calculate the equilibrium constant Kc for this reaction. Once again, our particulate diagram shows an equilibrium mixture.
So, Kc is equal to the concentration of B over the concentration of A. It's a lot faster to simply count our particles. For B, which is red, we have one red particle here, so we can go ahead and put in one. Then for gas A, we have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 particles. So 1 divided by 10 is equal to 0.1. Therefore, Kc is equal to 0.1 for this hypothetical reaction at a certain temperature.
The magnitude of the equilibrium constant tells us about the reaction mixture at equilibrium. For this reaction, Kc is equal to 0.1. Since K is less than one, if we think about what that means, K is equal to products over reactants. Therefore, if K is less than one, that means we have a smaller number in the numerator and a larger number in the denominator, which means there are more reactants than products at equilibrium.
Let's look at another hypothetical reaction where gas A turns into gas B. This time gas A is yellow and gas B is blue. If we look at our particulate diagram showing our reaction mixture at equilibrium, there are 10 blue particles and only one yellow particle. So when we plug into our equilibrium constant expression, this time it's going to be 10 over 1. Therefore, the equilibrium constant Kc is equal to 10 for this particular reaction at a certain temperature.
Once again, the magnitude of the equilibrium constant tells us something about the reaction mixture at equilibrium. For this hypothetical reaction, Kc is equal to 10. Since K is greater than one, once again, we have products over reactants. Therefore, the numerator must be larger than the denominator, which means we have a lot more products than reactants at equilibrium.
Let's look at the reaction of carbon monoxide and chlorine gas to form phosgene at 100 degrees Celsius. The equilibrium constant for this reaction is 4.56 times 10 to the ninth. Since the equilibrium constant K is greater than 1, we know there are more products than reactants at equilibrium. With the extremely large value for K, like 10 to the ninth, we could even assume this reaction essentially goes to completion.
For the reaction of hydrogen gas and iodine gas to form hydrogen iodide, the equilibrium constant Kc is equal to 51 at 448 degrees Celsius. Since the equilibrium constant is relatively close to 1, this means at equilibrium we have appreciable amounts of both our reactants and our products.
Let's look at the reaction of nitrogen gas plus oxygen gas plus bromine gas to form NOBR at 298 Kelvin. The equilibrium constant for this reaction is 9.5 times 10 to the negative 31st. Since the equilibrium constant K is less than 1, we know at equilibrium there are more reactants than there are products. With an extremely small K value like 9.5 times 10 to the negative 31st, this reaction barely proceeds at all. Therefore, at equilibrium, you can have almost all nitrogen, oxygen, and bromine, and very little NOBR.