Calculations with pH, pOH, Kw, [H+], [OH-]

hello and welcome to the chemistry solution this tutorial is going to go over some calculations involving pH P our H+ concentration our hydroxide iion concentration and KW so as a reminder pH is a way of expressing our hydrogen ion concentration in a solution and if you watched the tutorial that gave a general overview of acids and bases we will use H+ interchangeably with h3o+ understanding that free protons don't exist in solution they are going to join with a water molecule to give the hydronium ion but for our purposes in this video and for the sake of clarity we will use simplification H+ now we tend to use pH to describe the hydrogen ion concentration of a solution instead of just reporting the hydrogen iion concentration of a solution directly because generally these concentrations are very small and pH gives us an easier way to express this value remember that the pH scale is a log scale and that means that for every change by one in PH the hydrogen ion concentration changes by a factor of 10 remember also that pH is equal to the opposite of the log of our hydrogen ion concentration and so that as our hydrogen ion concentration decreases the pH of our solution increases so you can probably see the relationship here where if we have a solution with our hydrogen iion concentration equal to 102 molar that gives us a p of two if we had a hydrogen ion concentration that's 107th mol that would give us a ph of 7 but what you'll notice is that as that hydrogen ion concentration decreases our pH increases es the other important thing to note again is that as your pH changes by a factor of one let's say we were going from a ph of 7 to a pH of 6 in this scenario our hydrogen ion concentration would increase by a factor of 10 and if we were to go from a pH of 6 to a pH of 5 our hydrogen iion concentration would increase by another factor of 10 meaning that if we were to go from a pH of s to a pH of five our hydrogen ion concentration would increase by a factor of 100 and if we were to go from a ph of 7 to a pH of four that would mean our hydrogen iion concentration would increase by a factor of 1,000 so if we know the pH of a solution we can calculate the hydrogen ion concentration or vice versa if we know the hydrogen ion concentration we can calculate the ph and so if we rearrange this equation equ here to solve for the hydrogen ion concentration what we get is that our hydrogen ion concentration is equal to 10 raised to the negative value of the pH we also know that our hydrogen ion concentration times our hydroxide ion concentration is going to be equal to 1 * 10 -14 this is our value here of the ion product constant of water this is a constant at 25° C and so if we know our hydrogen ion concentration we can calculate the hydroxide ion concentration or vice versa we can also use a similar equation to calculate what we would call the P of a solution and the PO of a solution is giving us an indication of the hydroxide ion concentration of our solution so just like where the pH is equal to the opposite of the log of our hydrogen iion concentration the p is equal to the opposite of the log of our hydroxide iion concentration and if you were to do a little bit of manipulation to these equations here what you can rearrange these toin is that your pH plus your PO is equal to 14 the other important thing to remember is that when using these equations when we represent concentrations in Brackets that indicates that these concentrations must have units of marity or moles per liter okay so let's practice one here let's find the pH of a solution if our hydrogen ion concentration is equal to 3. 8 * 10 the8 mol so we're looking for the ph and we can find the pH by taking the opposite of the log of our hydrogen ion concentration so if we take the opposite of the log of 3. 8 * 108 mol what we'll get is that taking the log of 3. 8 8 * 108 will give you a value of -7. 4 and then pH is the opposite of the log which

will give you a value of 7. 4 so try this on your own and if you're not getting the same answer that I do make sure that you're inputting numbers in scientific notation correctly into your calculator so you want to make sure that your calculator is taking the log of this entire value here and generally speaking when you're putting numbers in scientific notation into your calculator you need to either make sure that you're using an exponent key something like e or sometimes it looks like exp or that you're putting this entire value in parentheses and then taking the log of this value often times if you're not getting the right answer but you're setting up the problem correctly it's because you're not putting this number correctly into your calculator in scientific notation and your calculator is potentially taking the log of something like 3. 8 and then multiplying that by 108 so we want to avoid that you want to take the log of this entire value 3. 8 * 108 okay I mentioned a few slides ago that P is a way of expressing the hydroxide ion concentration in a solution and so if we know the hydrogen ion concentration in a solution we can use that to calculate the hydroxide ion concentration and if you know the hydroxide iion concentration you can use that to calculate the PO of a solution remember that if our solution is neutral because of the auto ionization of water and again I'm writing this here in a simplified form in a neutral solution the hydrogen ion concentration will be equal to the hydroxide ion concentration and so in a neutral solution these would both be equal to 10 the7th Mol the other useful relationship that we can use with respect to pH and P is that your pH value and your P value sum together to give you 14 and so what we'll see is that just like with this expression here for KW which indicates that if our hydrogen ion concentration goes up our hydroxide ion concentration must go down or vice versa if your hydrogen ion concentration goes down your hydroxide ion concentration must go up is that pH and P also have an inverse relationship pH is lower when our hydrogen ion concentration is higher and as our pH increases our hydrogen iion concentration gets smaller we're going to see the same relationship with p and our hydroxide iion concentration if your p is very high that indicates a very low hydroxide ion concentration and as your P decreases your hydroxide ion concentration increases so it's another way to indicate this relationship of your hydrogen ion and your hydroxide ion concentrations in solution and you can see that we see the same relationship here with ph and po whereas one value increases the other decreases and vice versa note that if our hydroxide ion concentration and our hydrogen ion concentration are equal to each other at 25° C these would both be 107th molar and both our pH and our P would be equal to 7 and our solution is neutral and so just to recap if your pH is lower than seven we say that solution is acidic and that's going to correlate with P values that are greater than S if your pH is greater than 7 we say that solution is basic and that's going to correspond with values that are less than seven okay so let's practice let's find the hydroxide ion concentration of a solution if the p is 9. 28 so here we're looking for the hydroxide ion concentration we know that the hydroxide iion concentration is going to be equal to 10 to the negative value of our Po and so if we take 10 raised to the power of 9. 28 we'll get a hydroxide ion con concentration that's equal to about 5. 25 * 10 -10 M okay what I've included in here is a few that you can try on your own so now would be a great time to pause this video try a few of these and then we'll come back and check your answers okay so to find the hydrogen ion concentration of a solution with a pH of 3. 49 we're going to use the equation that says that our hydrogen ion concentration is equal to 10 to the pH value so 10^ - 3. 49 and

if you put that in your calculator you should get a hydrogen ion concentration that's equal to 3. 23 * 104 to find the pH of a solution if your hydrogen ion concentration is 4. 1 * 10 -6 we know that our pH is equal to the opposite of the log of our hydrogen ion concentration so we would take the opposite of the log of 4. 1 * 10 -6 and you should get a value of your pH that's equal to 5. 4 and so just thinking about what we understand about the acidity of solutions note that this hydrogen ion concentration is bigger than 10 -7th molar so we would predict that the solution is acidic and our pH value represents that as well now this third one here is a little bit tricky remember that we said that these equations that I've written down below assume concentrations of marity so if our hydroxide ion concentration is given to us in Millar we would need to convert that to marity first and so if our hydroxide concentration is 1. 5 * 10-2 milles per liter we can convert that to units of marity or 10 3 milles in every 1 mole so we would have a hydroxide ion concentration that's equal to 1. 5 * 10 -5 molar or moles per liter and then if we want to find the PO is equal to the opposite of the log of our hydroxide ion concentration which in this case is 1. 5 * 105 molar and we would get a PO of 4. 8 and then the last problem here find the hydroxide iion concentration of a solution with a p of 11. 3 our hydroxide ion concentration is going to be equal to 10 to the P value so 10 to the 11. 3 which would give us a hydroxide concentration of about 5 * 10 -12 Mol okay but we can also use these equations in conjunction with each other so what if we know the PO of a solution and we're asked to find the hydrogen ion concentration of a solution well what you'll probably notice is that there are a few different ways to do this so we could use our equation here to find the hydroxide ion concentration by taking 10 to the ne P value and then using our hydroxide ion concentration to solve for our hydrogen iion concentration we also know that pH plus P equal 14 and so we could use this relationship here to solve for our pH and then use our pH to solve for our hydrogen ion concentration this tends to be the way that a lot of people like to prefer to do these problems but you can certainly do it the way I just described on the previous slide as well so if we know that the pH plus the p is equal to 14 and our p is 5. 18 that means that our pH value must be equal to 8. 82 and now that we know the pH value we can solve for our hydrogen ion concentration which is going to be equal to 10 to the pH value so 10^ 8. 82 is going to be equal to 1. 51 * 1099th mol okay what if we were asked to find the pH of a solution if the hydroxide ion concentration is 9. 9 * 101 mol again there's a few different ways you could approach this problem so you could use your hydroxide iion concentration to solve for the p and then we know that pH plus P equal 14 we could also solve for our hydrogen ion concentration knowing that the hydrogen ion concentration times the hydroxide ion concentration is 1 * 10 -4 and then use our hydrogen concentration to solve for the pH so I'll do this problem this way in this example if we know that H+ * ohus is equal to 10 -14 and we know our hydroxide ion concentration we can solve for our hydrogen ion concentration which in this case will be equal to 1. 01 * 104 mol and then we know that our pH is equal to the opposite of the log of our hydrogen ion concentration and so

in this case here our pH is going to be equal 2 4 okay I hope some of those examples were helpful