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# Writing equilibrium constant and reaction quotient expressions

The equilibrium constant, K, describes the relative amounts of reaction species at equilibrium. The expression for K is equal to the concentrations (or partial pressures) of the products raised to their stoichiometric coefficients divided by the concentrations (or partial pressures) of the reactants raised to their stoichiometric coefficients. The reaction quotient, Q, has the same form as K but describes the relative amounts of reaction species at any point in time. Created by Jay.

## Want to join the conversation?

• What is meant by "the concentration of a pure solid or a pure liquid remains constant over time?" I think I understand, but another explanation and a few examples would go a long way
• The concentration of pure solids and liquids do not change because there density remains the same. So, it is not included while calculating heterogenous equilibrium constants.
• If we were writing a heterogenous equilibrium constant expression would we leave in aqueous reactants/products?
• Well yes you always include aqueous chemical species in the expression. So when you say a heterogeneous equilibrium expression, that just means the chemical species aren't all the same phase. Which could mean a great many of combinations of phases. Which phases are you involving in your reaction?
• Can you explain me the topic of equilibrium constant and it’s units pleaseee you actually explain very good
(1 vote)
• Equilibrium in general is when a reaction’s forward and reverse reaction rates are equal. Essentially reactants are becoming products as quickly as products are becoming reactants. Technically this type of equilibrium is referred to as dynamic equilibrium since there are still chemical reactions occurring once equilibrium has been reached. We observe equilibrium when the concentrations of the reactants and products no longer change dramatically and remain practically constant. This does not mean that the reactant and product concentrations are equal to each other (most times they are significantly different from each other), simply that they remain constant.

The equilibrium expression and constant are ways of quantifying equilibrium. The equilibrium expression for reactions is a ratio of the concentrations of products to reactants. Each term is raised to the power according to their stoichiometric coefficients in the chemical equation. Pure solids and liquids are omitted from the expression since their concentrations are their density, and density does not change for a specific chemical.

The equilibrium constant is the single number which results after inputting the constant equilibrium concentrations of a reaction in its equilibrium expression. Since the equilibrium expression is a ratio of products over reactants, the magnitude of the equilibrium constant gives us some insight into whether the reaction mixture contains more reactants or more products. A large equilibrium constant means more products are present, while a smaller constant means more reactants are present. Often a temperature will be specified for the equilibrium constant. A reaction will have different equilibrium constants which change with temperature. This is because changing the temperature changes the rates of the reactions, which equilibrium depends on.

Hope that helps.
• At , how in the world did Jay figure out that the solids were pure solids? How am I supposed to figure this out? Am I forgetting something or......?
Thanks!
(1 vote)
• So the rule where we omit solids and liquids from equilibrium equations gets more involved when you looking to the particulars of the definitions for equilibrium. However at this level we just omit chemical species from equilibrium equations if they have the (s) or (l) phase state in the chemical equation. The pure part isn't crucial here.

Hope that helps.
• why the stoichiomery becomes the exponents of the molarities?
At aA + bB -> cC + dD , why it becomes (A)^a ,(B)^b , (C)^c and (D)^d respectively?
• How do you calculate the K of an equilibrium expression?
(1 vote)
• I mean we just need the equilibrium concentrations and substitute them into the appropriate equilibrium expression for a reaction.
• so to use the coefficients as powers in the equilibrium expression. it is not necessary for the reaction to be elementary?
(1 vote)
• No it doesn’t need to be elementary since equilibrium only considers the ratio of starting reactants and final products.
(1 vote)
• Do concentration and active mass mean the same?
(1 vote)
• I can recall that the equilibrium constant (K) is the ratio between the rate constants of both ways of the reaction. But then I guess there is a conflict in the way we write the formulas since the superscripts in the rate law are not always the same as the coefficients. Is this a wrong assumption?
(1 vote)
• So how do you know when to use Kc or Kp bc I thought that all the products+reactants had to be gases to use Kp but in the video you used Kp even when there were solids in the equation
(1 vote)
• Kc means you’re expressing the concentrations of your chemical species as molarities, and Kp means you’re expressing the concentrations as partial pressures. Aqueous solutions use Kc, but gasses can use either Kc or Kp like Jay did at . Solids never appear in equilibrium expressions so reactions with solids can still use Kc or Kp since the solid won’t even show up as a term in the equation.

Hope that helps.
(1 vote)

## 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.