the equilibrium constant is symbolized by the letter k and the 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 lower case 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 in the 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 see 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 and 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 reactant which is hydrogen so 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 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 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 product is a solid so we're going to leave that out of out of our equilibrium constant expression and for our reactant calcium 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 casey 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