Introduction to reaction quotient Qc | Chemical equilibrium | Chemistry | Khan Academy

Today, we're going to be talking about the reaction quotient Q. In this video, I'm going to go over how you calculate Q and how you use it.

We're going to start with an example reaction between sulfur dioxide (SO2) gas, which will react with oxygen gas. This is a reversible reaction that makes sulfur trioxide, or SO3. We should make sure this is a balanced reaction: we have two sulfur dioxides reacting with one O2 to give two SO3.

At equilibrium, we can calculate the equilibrium constant KC. So at equilibrium, we know the concentrations should be constant because the rate of the forward and backward reactions are the same. If we plug those concentrations into this expression, we will get KC.

So, KC is the product concentration raised to the second power, so that's from this stoichiometric coefficient, and then our reactant concentrations: SO2 squared and the concentration of O2. We know at some temperature, if you plug in the equilibrium concentrations, KC is equal to 4.3.

But what if we're interested in looking at the reaction and it's not at equilibrium yet, or maybe we just don't know if it's at equilibrium? In that case, when you're not sure it's at equilibrium, or really at any point in your reaction, or any time, we can calculate the reaction quotient Q.

So, QC is equal to the concentration of our product squared, so the concentration of the product raised to the stoichiometric coefficient times the reactant concentrations also raised to their stoichiometric coefficients: SO2 squared and O2.

So you might be wondering at this point, what's the difference? The equation for QC and KC will always look exactly the same. The main difference is when you use them. The equilibrium constant K you calculate only with the equilibrium concentrations, so the C means everything is in terms of the molar concentration.

For the reaction quotient Q, again, everything is in terms of molar concentration, but we can calculate it with any concentrations, and we don't have to be at equilibrium molar concentrations.

So, let's calculate this for a set of example concentrations. At some point in our reaction, we have the following concentrations: we have 0.10 molar SO2, 0.30 molar O2, and 3.5 molar of our product.

If we plug these numbers into our expression for QC, we get 3.5 mol squared in the numerator and 0.10 squared times 0.30 in the denominator. If I plug this into my calculator, I get that QC with this set of concentrations is 4.083.

So now we know how to calculate QC. Next, we're going to talk about what it tells you.

There are three possible scenarios. When Q is equal to K, that tells us we're at equilibrium. If at any point you're not sure if your concentrations are the equilibrium concentrations, you can calculate Q and check if it's equal to K. In this case, it's not.

The other two possibilities are that Q is greater than K, which is the case here, or Q can be less than K. So let's go through both of those possibilities. We can draw all of the possible values of Q on a number line, or a Q line.

Q can have values anywhere from zero to infinity. When you have no product, your numerator is zero and Q is equal to zero. That tells us Q equals zero when you have all reactants and no products.

Then, if you have no reactants left and all products, we have zero in the denominator, and that gives us a Q value of infinity. That means at Q equal to infinity, we have all products. We have a bunch of values in between, and I'm going to just write some intermediate values in here.

But the actual intermediate values here aren't super important; we're mostly going to want to compare the relative values of our Q and K. So Q here is equal to 48.3, which I will place right around here.

So that's QC, and our K in yellow is 4.3, so we'll place that right around here. We can see that our Q is larger than K, and it's closer to having all products. At the concentrations we have up here, we have way more products than we should at equilibrium.

So our reaction is going to try to adjust the concentrations to get to equilibrium. What that means in terms of our number line is that our concentrations are going to shift so that Q can get closer to K. Since our shift is to the right and it's moving towards all reactants, our reaction is going to favor reactants to get to equilibrium.

So when Q is greater than K, like here, we're going to favor reactants. The last scenario is when Q is less than K. In that case, our reaction will favor products.

We can show that also on our number line if we had a different set of concentrations where Q was less than K, which I will show using this color here. If we had, say, a Q value around here, then our shift would be to the right, towards making more products.

Therefore, that would mean our reaction is going to try to reach equilibrium by favoring the forward reaction. So that's how you calculate Q and how you use it to see how the reaction concentrations will shift to get to equilibrium.

In our next video, we'll go over an example problem using Q and trying to figure out how the reactant concentrations will shift for another reaction.