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# Writing equilibrium constant and reaction quotient expressions

AP.Chem:
TRA‑7 (EU)
,
TRA‑7.A (LO)
,
TRA‑7.A.1 (EK)
,
TRA‑7.A.2 (EK)

## Video transcript

- [Instructor] The equilibrium constant is symbolized by the letter K, and equilibrium constant tells us about the relative concentrations of reactants and products at equilibrium. Let's say we have a hypothetical reaction where reactants A and B turn into products C and D. And in the balanced equation, the lowercase letters are the coefficients. So we have a lowercase a, a lowercase b, lowercase c and lowercase d as coefficients in our balanced equation. If we were to write an equilibrium constant expression for this hypothetical reaction, we'd start by writing the equilibrium constant K and then we have a subscript c here because we're dealing with concentrations in our equilibrium constant expression. And the equilibrium constant Kc is equal to, and in the numerator, we have the concentrations of our two products multiplied together. And the concentration of each product is raised to the power of the coefficient. In the denominator, we have the concentrations of the two reactants multiplied by each other and raised to the power, each concentration is raised to the power of the coefficient in the balanced equation. It's important to emphasize that the concentrations that we're plugging into our equilibrium constant expression are equilibrium concentrations. And when we plug in our equilibrium concentrations into our equilibrium constant expression, we get a value for the equilibrium constant K. And K is constant for a particular reaction at a certain temperature. Let's write an equilibrium constant expression for the following reaction, which shows the synthesis of ammonia from nitrogen and hydrogen, and everything is in the gaseous state. We start by writing the equilibrium constant Kc, c because we're dealing with concentrations, and we start with our product, which is ammonia. So we write the concentration of ammonia and we raise the concentration of ammonia to the power of the coefficient in the balanced equation, which is a two. So this is the concentration of ammonia to the second power. Then, in the denominator, we think about our reactants. So we have nitrogen. So we write the concentration of nitrogen. And since the coefficient is a one in the balanced equation, that'd be the concentration of nitrogen to the first power multiplied by the concentration of our other reactants, which is hydrogens. We write in here H2. And because there's a coefficient of three in the balanced equation, we raise the concentration of hydrogen to the third power. For gases, it's often more convenient to measure partial pressures instead of measuring concentrations. So let's say that A, B, C and D are all gases. We could write an equilibrium constant expression using partial pressures instead of concentrations. And if we did that, instead of writing Kc, we would write Kp where p stands for pressure. And Kc and Kp usually have different values from each other. So if we go back to our previous reaction where everything was in the gaseous state, we could write a Kp expression. So we would write Kp is equal to, we think about products over reactants. So this would be the partial pressure of our product, ammonia, raised to the second power divided by the partial pressure of nitrogen raised to the first power times the partial pressure of hydrogen raised to the third power. For the synthesis of ammonia, everything was in the gaseous state. And when all substances, reactants and products are in the same phase, we call this a homogeneous equilibrium. When the substances are in different phases, we call it a heterogeneous equilibrium. For example, in the decomposition of calcium carbonate to turn into calcium oxide and carbon dioxide, calcium carbonate is a solid and calcium oxide is a solid, but carbon dioxide is a gas. So we have substances in different phases. When we write an equilibrium constant expression for a heterogeneous equilibrium, we leave pure solids and pure liquids out of the equilibrium constant expression. So if we write an equilibrium constant expression for the decomposition of calcium carbonate, let's write a Kc expression first here. So we write Kc is equal to, and we think about products over reactants. For products, we have carbon dioxide in the gaseous state. So it's okay to include that in our equilibrium constant expression. So we write the concentration of CO2. And since the coefficient is a one in the balanced equation, this would be the concentration of CO2 raised to the first power. Our other products is a solid. So we're gonna leave that out of our equilibrium constant expression. And for our reactant calcium carbonate, that's also a solid, so that's also left out of our expression. If we were to write a Kp expression here, we would include the partial pressure of our gas, which is carbon dioxide. So this would be the partial pressure of carbon dioxide to the first power. And once again, we would leave the two solids out of our equilibrium constant expression. The reason why we leave pure solids and pure liquids out of equilibrium constant expressions for heterogeneous equilibria is because the concentration of a pure solid or a pure liquid remains constant over time. So it doesn't help us to include it in our equilibrium expression. Finally, let's talk about the reaction quotient, which is symbolized by the letter Q. A Q expression has the same form as an equilibrium constant expression. And Q tells us the relative concentrations of reactants and products at any moment in time. And just like we could write a Kc or a Kp expression, we could write a Qc or a Qp expression. Let's go back to our reaction for the synthesis of ammonia from nitrogen gas and hydrogen gas. Notice how the Qc expression has the same form as the Kc expression. The difference is, for the Kc expression, all of our concentrations are equilibrium concentrations. So I could put an eq here for the concentrations of ammonia, nitrogen, and hydrogen. So for the Kc expression, it's only equilibrium concentrations, but for the Qc expression, it's the concentrations at any moment in time. So that moment in time might be at equilibrium or it might not be at equilibrium. If Qc is equal to KC, the reaction is at equilibrium, but if Qc is greater than Kc, or if Qc is less than Kc, the reaction is not at equilibrium.
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