Interpreting and Working with Equilibrium Constants

hello and welcome to the chemistry solution this tutorial is on interpreting and working with equilibrium constants so in one of the last tutorials we looked at how to write equilibrium expressions in this tutorial i want to look more at interpreting what these equilibrium constants mean and working with equilibrium constants so what does the magnitude of the equilibrium constant tell us well if you have a value here for k that is very large it means at equilibrium really the concentrations of your products are going to be greater than the concentration of your reactants and so if our equilibrium constant has a value that's much greater than one we know that this reaction is what we would call product favored and that our equilibrium lies to the right because products are on the right side of our chemical equation if we had the opposite scenario where our equilibrium constant is much smaller than one you can think about this in a mathematical sense that means your concentrations of your reactants at equilibrium must be much greater than the concentration of your products and so in this scenario we would say that the equilibrium lies to the left and that we have a reaction that is reactant favored and so looking at this reaction here 2a being converted to b plus c if we have an equilibrium constant that's equal to 0. 014 what conclusion can we make from this information well let's just write out our equilibrium constant expression here which we know is going to be equal to the concentration of our products raised to the power of their respective coefficients divided by the concentration of our reactants raised to the power of their respective coefficients if this value for our equilibrium constant is smaller than one that means that at equilibrium we must have a higher concentration really of a our reactant than we do of b and c so i would say that at equilibrium reactants predominate now let's spend a little bit of time working with equilibrium constants so the equilibrium constant expression for a reaction written in one direction is the reciprocal of the one for the reaction written in the reverse direction so if i have this reaction here n2o4 being converted to 2no2 i know that my equilibrium constant expression would be equal to the concentration of no2 squared concentration of our products raised to the power of their respective coefficient divided by the concentration of my reactant raised to the power of its respective coefficient and i'm telling you here that the value for this equilibrium constant is equal to 0. 212 if i were to flip this chemical reaction around and write it in this direction now i'm defining 2no2 being converted to n2o4 as the forward direction and my product now is n2o4 so i would write this on the top of my equilibrium constant expression and the concentration of my reactants now no2 goes on the bottom of my equilibrium constant expression so you can see how this equilibrium constant expression is flipped from what it was up here and so if you take this fraction and you flip it upside down we're taking the reciprocal of that which means that the value of the equilibrium constant for this reaction would be equal to the reciprocal of the equilibrium constant for our top reaction so 1 divided by 0. 212 but there's more if the stoichiometry of the reaction is changed the equilibrium constant is also changed remember that equilibrium constants are specific to a particular chemical reaction as written and also at a defined temperature and so if we take a chemical reaction like this one here and multiply the entire thing through by two notice how that changes the coefficients in my balanced chemical equation and look at how that plays out in writing our equilibrium constant so up at the top here we have the concentration of no2 squared divided by the concentration of n2o4 and here now that we've multiplied this equation through by two we have the concentration of no2 raised to the fourth power divided by the concentration of n2o4 squared the other way that

we could have written this would have been to take our original equilibrium constant expression here and squared the entire thing notice if we squared this entire equilibrium constant expression up here that gives us this equilibrium constant expression here as written for the same equation when multiplied through by two and so if you multiply through a reaction by some value n then your new equilibrium constant for that reaction becomes the original value of the equilibrium constant raised to the power of n in this case n was 2. we multiplied this entire equation through by 2 and then looked at how that changes the value of our equilibrium constant but you can also consider how you could derive the equilibrium constant for a net reaction made up of two or more individual steps and steps is the product of the equilibrium constants for the individual steps and so let's look at how this would work out here let's first of all write the equilibrium constant expression for our overall reaction i know this equilibrium constant is going to be equal to the concentration of no2 squared divided by the concentration of o2 squared times the concentration of n2 and i want to know what this value is and so notice that it's adding these two steps together here it gives us this overall equation down here and so let's consider now what are the equilibrium constant expressions for step one and step two and i'm going to do that right down here at the bottom so the equilibrium constant expression for step one would be equal to the concentration of no squared divided by the concentration of my reactant raised to the power of their respective coefficients in this case each of those are one and now let's write the equilibrium constant expression for step two that's going to be equal to the concentration of no2 squared divided by the concentration of o2 raised to the first power times the concentration of no squared well look what happens if we multiply these two equilibrium constant expressions together notice that the concentration of no2 squared is going to cancel out and i'm going to be left with the concentration of no2 squared on top divided by the concentration of o2 times o2 so o2 squared times the concentration of n2 and that's exactly what we defined as the equilibrium constant expression for this overall reaction so the value for the equilibrium constant for this overall reaction is going to be equal to the value of the equilibrium constants for each of our individual steps so this would be equal to 4. 3 times 10 to the negative 25th multiplied by 6. 4 ninth and so the value of our equilibrium constant for our overall reaction would be equal to 2. 8 times 10 to the negative 15th and going back to the first part of this tutorial what does that tell us about this reaction well we notice that this equilibrium constant is very small much smaller than one that would indicate to us that this reaction this overall reaction is very reactants favored at equilibrium so at equilibrium you're going to have high concentrations of reactants and low concentrations of products okay so let's just do a little bit of practice here if i give you this equation h2 plus i2 being converted to 2hi and i tell you that the equilibrium constant for this reaction is 56 what is the equilibrium constant for the reverse reaction and so if i

were to flip this reaction around that's going to flip how i'm writing my equilibrium constant i'm going to take the reciprocal in this first reaction here i would have had h i squared on the top and h2 and i2 on the bottom when i flip this equation around now h2 and i2 i would call my products those would be on the top and the concentration of h i would be on the bottom so i've taken the reciprocal of this and so the equilibrium constant for this reverse reaction would be the reciprocal of 56 so 1 divided by 56 and you could put this in your calculator and come up with a decimal if you wanted to okay let's try one more here what if i give you two individual steps that add together to give an overall reaction what would be the value for the equilibrium constant for this reaction here and so if you add two individual steps together to give you an overall reaction the value for the equilibrium constant for our overall reaction is going to be equal to the product of the equilibrium constants for each of the individual steps so in this case about. 1 and again i know that i need to multiply these together because if i wrote out the equilibrium constants for my individual steps i know that it's by multiplying these two expressions together that i would get the equilibrium constant for my overall reaction so you can see here that bromine is going to cancel out and i would be left with the concentration of no squared times the concentration of brcl squared divided by the concentration of no br squared times the concentration of chlorine well i hope this tutorial was helpful be sure to check back for more tutorials on equilibrium constants and calculations that involve equilibrium constants