titrations and titration curve is going to be the topic of this lesson my name is chad and welcome to chad's prep where my goal is to take the stress out of learning science now in addition to high school and college science prep we also do mcat dat and oat prep as well i'll leave a link in the description for where you can find those courses now this lesson is part of my new general chemistry playlist and if you want to be notified every time i post one subscribe to the channel click the bell notification so in this lesson we're going to take really more of a conceptual look at titrations and titration curves if you're looking for all the ph calculations for titrations those are going to be in the next couple of lessons so just going to warn you in advance here so but a qualitative look at the three different types of titration curves we're going to look at strong acid strong base titrations weak acid strong base titrations and then weak base strong acid titrations you'll find out that all of the titrations we're going to look at here either the acid or the base or both is going to be strong we're not going to take any look at weak acid weak base titrations at all not something commonly you're going to ever come across in your general chemistry course so all right so we're going to start with strong acid strong base and the strong acid we're going to use is hcl and the strong base we're going to use is naoh and first thing you need to realize about a titration is that really commonly like an industry and stuff the whole point of doing a titration is to determine the concentration of some you know acidic or basic species in our case we're going to make that species the hcl we're going to try and determine the concentration of hcl in here and so what we would typically do is we take something like an erlenmeyer flask so and we put inside that erlenmeyer flask our acid solution and whatever you're trying to determine the concentration of we would refer to that as your analyte so and then you're going to set up a buret and inside that buret in this case if the analyte is an acid then your breath is going to be a base and we're going to refer to this guy as your titrant and it could be the other way around if you're you're trying to figure out the unknown you know some unknown concentration of a base well then the base would be the analyte and you'd use an acid as your titrant so these are two common words you should definitely be familiar with and the key is the titrant is going to be standardized and by standardizing it we're going to know its exact concentration that's going to be important because by knowing its exact concentration we'll be able to determine the exact concentration of the analyte again which is usually the whole point of doing a titration so in this case our analyte is an acid it's hcl in this example and so the ph starts out low and as we start shooting naoh into there the ph is gradually going to start to increase but at some point rather than being a gradual increase you're going to get this very rapid increase so from like this point here to this point here might be a difference of only adding a drop or two of naoh and the whole point is to get to this midpoint right here and i'll call it a midpoint really we should properly call it an inflection point so an inflection point is where the slope is either changing from either increasing to decreasing or decreasing to increasing and so you can see here all the way up until that point the slope has been gradually increasing getting more and more steep but now it's going to change to decreasing getting less and less steep and if you're into calculus that means the sign of the second derivative goes from being positive to negative definitely not something you need to know here so but that's an inflection point on this graph so when you hear somebody refer to this equivalence point as an inflection point that's what they mean uh let's put that out here so this is the equivalence point sometimes we shorten that to eq point so and a lot of students forget that it's the equivalence point it is not the equilibrium point so uh and what we mean by the equivalence point is it is the point at which you've added a chemically equivalent amount of acid or base well in our example hcl and naoh react in a one to one ratio and so a chemical equivalent amount just means an equal number of moles an equimolar amount of naoh to our hcl so that's going to be true at the equivalence point so what that means then is that at that equivalence point the moles of hcl are going to be equal to the moles of naoh that's going to be true right at that equivalence point and only at that equivalence point cool and that's going to be really convenient because again we're going to know the molarity of our naoh exactly of our titrant and we'll be able to figure out well what volume of that did we add to get to that equivalence point and once we know the molarity and volume we can use that to find the moles of naoh in fact another way to write this would be to write the molarity of naoh times the volume of naoh because molarity times liters is moles and on the other side of this equation you could write the molarity of the hcl times the volume of the hcl and now we've kind of made a really convenient equation for what's true at this equivalence point so because the truth is you get to you get to you know determine how much hcl you start with you put it in that erlenmeyer flask if you want to start with 10 milliliters great then you start with 10 mil do you want to start with 50 milliliters great start with 50 milliliters it is your choice whoever's you know running the titration gets to choose what that volume of hcl is going to be now the molarity of the naoh is known and we'll just measure with that buret how much naoh it took to get to this equivalence point so we'll know that volume as well and if we know the volume of hcl we start with and then the molarity and volume of the naoh then we can solve for that molarity of the hcl and again that's often the point of a titration again this is only true at that equivalence point oftentimes the entire point of running a titration is to get that equivalence point so we can get the molarity of the analyte so how do you know if you reach that equivalence point well if you're mapping it out the entire time you know and you're adding a little bit of a naoh and then taking a ph reading and you know mapping out this curve well then you could figure that out but that's not usually what we do normally what we do is we use what's called an indicator to kind of figure this out so an indicator is something that is going to change colors over a certain ph range and so it turns out this equivalence point is going to occur right at ph 7 in a strong acid strong base titration so we'll find out here that you know let's say we start off with 10 moles of hcl well how many moles of naoh would it take to reach the equivalence point well again the equivalence point is when we've added a chemically equivalent amount and since again they react in a one-to-one ratio then it would be an equal number of moles so if you start out with 10 moles of hcl then you're going to add 10 moles of naoh now because these are both strong this reaction goes to completion and for reaction that goes to completion you really want to look at this from like a limiting reagent perspective and so 10 moles of our acid and 10 moles of our base they're going to react completely and you're not going to have any hcl or naoh left over whatsoever but what you will form in the end is 10 moles of nacl now you also form 10 moles of water but the whole thing is in aqueous solution so we don't really care about that but you're forming 10 moles of nacl here and the important thing to realize is that nacl is a neutral salt so in the last lesson in chapter 16 we looked at acidic salts and basic salts and neutral salts and we learned that group 1 metal ions and group 2 metal ions and sodium group 1 were negligible as lewis acids whereas most other cations are going to be acidic and then we learned that the conjugate base anions of the strong acids so are the negligible anions and h cells are strong acids so cl minus was a negligible anion so an nacl here having both a negligible cation and a negligible anion was a neutral salt and that is ultimately the reason why the ph is going to be seven at the equivalence point in a strong acid strong based titration so in this case it's because the salts you produce in the titration ends up being a neutral salt that's kind of the idea when we look at the weak acid strong base or weak based strong acid titrations the ph will not be seven at the equivalence point and that's not intuitive you might think well if you've added equal amounts of acid and base shouldn't the ph be seven in neutral no it turns out now if the acid base are both strong yes but not if one's weak and one is strong and it turns out my personal way of remembering this is i just look at whoever's strong and they win at the equivalence point so we'll find out with a weak acid strong base the ph is going to be a little bit basic at the columns point a little bit higher than seven like seven to ten and in a weak base strong acid titration it's the acid that is strong and so the ph will be a little bit acidic at the covenant point probably somewhere between four and seven now that's how i remember it but as we'll see that's not really the reason why but we'll come back to that in a bit okay so one more thing about our indicator here so you want your indicator to change colors right around that equivalence point well it turns out indicators don't just change color over a small ph window it's actually over a pretty significant jump usually a couple ph units jump but what's nice is that you know your ph jumps very quickly right across that equivalence point so again from down here to somewhere up here it's usually only a difference of a drop or two and so you want to choose an indicator that's going to change color right across that window in the six to eight range maybe in this particular titration so and it turns out phenolphthalein is a really common example of a good indicator to use in a strong acid strong-based titration because it will change colors right across that window and it turns out that phenolphthalein itself is i'll also abbreviate it as an indicator here it itself is an acid a weak acid so and it has a weak acid form and it has a conjugate base form which i'll just represent this way it's actually a rather large molecule that i'm not going to draw it or anything like that so but i'll represent it in these two forms here and it turns out so that as you add naoh it itself also gets titrated and so it turns out in its acid form it's colorless in its conjugate base form though it has a pinkish purplish color and so as you blow through this equivalence point again over the course of just like an extra drop or two of naoh the solution goes from being colorless to being pinkish purplish and once that happens you know you've reached the end of your titration so and you've reached what's called the end point and your endpoint is your best approximation of that equivalence point so these color change indicators are by far the most common example of an indicator you're likely to see okay so it turns out then if you know we learned this with buffers in the last lesson so when you've got a weak acid conjugate base well it turns out if the ph equals the pka of your acid then these will be present in equal concentrations but if you go one ph unit lower than that you'll have 10 times more acid one ph unit higher than that you'll have 10 times more conjugate base and so in this case if we want the ph in our titration to turn colors change colors right around ph 7 well then the indicator should have a pka right around seven so cool so you want your indicator to have a pka right around whatever ph you have at the equivalence point cool and it turns out we've got a whole slew of different indicators and the thing is that they're at least brightly colored in one of the two different versions uh so that we can use them like as in the case with phenolphthalein where it's brightly colored in the base form but colorless in the acid form some change from like red to green and things of a sort so but we have a whole host of them and we have that we discovered over time and they change colors at different ph ranges and so we can kind of look up in a table of what their pkas are and choose the appropriate indicator for whatever titration we're doing okay so let's take a look at our weak acid strong base titration and in this case the weak acid we're going to look at is hf and we're still going to use naoh and again because naoh is a strong base as long as the acid or the base is strong or both this reaction will go 100 percent to completion and so we're going to look at it as kind of a limiting reagent problem again and we'll incorporate that into our ph calculations in the next couple of lessons now big difference here is what you're going to find out is with a strong acid strong base titration so you'll find out when you first start the titration you're adding noh you get this nice long linear region so but right at the beginning in a weak strong titration you're going to get a big change in ph right at the beginning and before it kind of flattens out a little bit notice we see the same thing over here with weak base strong acid in this case we're starting out with the base and adding the acids the ph is going to go down so you get a real sudden ph drop right at the initial point before it kind of flattens out a little bit and goes linear and so that's characteristic if you've got a weak strong titration versus a strong strong titration one of the key differences you can tell but it's kind of a minor point as we'll point out here in a second because there'll be an easier way to tell now you're still going to have an equivalence point here that's the inflection point in both of these here it turns out and that equivalence point is still when you've added a chemically equivalent amount of titrant to your analyte and in this case our analyte is the hf we're starting off with an acidic solution and the titrant is the naoh and so at that equivalence point you're going to have the moles of hf equal to let's put that in black the moles of naoh in this case and what that means again we could write that in a more convenient form we could say that the molarity of the hf times the volume of the hf is equal to same thing for the naoh cool and once again you're going to know the molarity of randoh you could figure out what volume it took to get to the equivalence point you're gonna you get to choose what volume of hf you start with and so you can use this to solve for the molarity of your analyte the hf in this particular example cool now what you will find out though if we kind of drag this across though is that again your ph is not going to be 7 at the equivalence point you're going to find out that it's going to be higher than 7. so and again usually not super higher than 7 but somewhere probably in the seven to ten range depending on you know what exact weak acid you've chosen and things of sort and what concentration it has so both playing a factor but the key is the ph is going to be a little bit basic now again my way of remembering this is i look at weak acid strong base the base is strong and it wins at the equivalence point but again that's not really the reason the reason so notice if you start off with 10 moles of hf and you add 10 moles of naoh so they're going to react completely and you know going to neutralize each other completely so that you have no hf and no naoh left whatsoever but in this case you're going to form 10 moles of sodium fluoride and whereas again sodium being group 1 is still negligible the fluoride is not so the fluoride is not the conjugate acid i'm sorry not the conjugate base of a strong acid but the conjugate base of a weak acid and is therefore really a base and so this is a basic salt and that is ultimately the reason why the ph is going to be basic it's because the salt that you produce is a basic salt now if they just you know if if i ask you why is the ph greater than seven in a weak acid strong based titration at the equivalence point so if you said because the salt that is produced is basic salt that is 100 true so but if you had to choose kind of like which of the following is true on a multiple choice test they might phrase it that way but they might phrase it a little bit difference so instead of saying that sodium fluoride is a basic salt they might say that it undergoes hydrolysis let me put that word up on the board here somewhere if you look at that word hydrolysis hydro refers to water lysis means the splitting or destruction of so this is the destruction or splitting of water well it turns out that any chemical reaction that has water is a reactant where water gets used up kind of water's getting destroyed if you will it's getting used up it's getting consumed and they call it a hydrolysis reaction well an acid-base reaction that reacts with water where either an acid reacts with water to produce hydronium or a base reacts with water to produce hydroxide those are examples of hydrolysis reactions sometimes we call them acid hydrolysis or base hydrolysis well with this being a basic salt this is going to undergo base hydrolysis and so in this case your f minus that you produced right here is then going to react with water to produce some o h minus and some hf and so this is the hydrolysis reaction this is why the solution is basic at the equivalence point because the fluoride we produced part of the sodium fluoride salt that's basic reacts with water to produce some fluoride notice it also implies that you actually don't end up with zero hf because the fluoride when it undergoes hydrolysis produces a tiny amount in this equilibrium the solution technically is not going to have zero hf it initially looked like it was going to but you will have a super tiny amount in this case an amount that's equal to the amount of hydroxide you produce cool now we've got something else to address here and it turns out we didn't have to worry about this on the strong acid strong base uh titration but with the weak strong titrations there are not just one important point the equivalence point on the titration they're actually going to be two important points and the other one is going to be halfway to your equivalence point so let's say for example at that point right there happened at like 20 milliliters what we'd do is we'd go back to 10 milliliters so and that point right here would be halfway to the equivalence point we might call it the half equivalence point or the half neutralization point and it is a special point so we didn't have to worry about that here as it turns out but we're going to use this point to find the pka of our acid well for strong acids we just say they associate completely so and that implies that their kas are infinity well they're not infinity they're just really huge numbers so but we never talk about their kas or the pkas but for weak acids we do and that's why this now becomes relevant well right at this half equivalence point let's see what's true here for a second now so if it took 10 moles of naoh to get to the full equivalence point one to one ratio chemically equal amounts well then get halfway there would only be half as much and in this case again this reaction is going to go to completion since naoh is a strong base and naoh would be the limiting reagent and 5 moles of the naoh would neutralize 5 moles of the hf to produce 5 moles of the naf and what you're going to find out is that you're going to have 5 moles of hf left in your solution but you're also going to have 5 moles now of the conjugate base the f minus and notice that's interesting because you have 5 moles of a weak acid and 5 moles of its conjugate base and you guys learned in the last lesson that when you have uh close to one to one ratio of a weak acid and its conjugate base you have a buffer and notice how flat the ph is right around that region that is a buffer solution right in there the ph is not changing a ton so and the truth is you got you know pka it turns out this is right where the point is ph equals pka as well when your weak acid equals your conjugate base we learn that's when ph equals pka in fact if we take a look at the henderson hasselbach one more time real quick when your weak acid and conjugate base are equal the ratio here is one log of one is zero and ph just equals your pka plus zero ie your ph is equals your pka and so again right at that half equivalence point that is where the concentration of hf is equal to your concentration of f minus and as a result that is where your ph equals your pka so and we saw the pka for hf in the last lesson and ended up being 3.2 right around 3.2 and so if this had a you know nice scale on the ph scale on the left here on the y-axis then we could look at this be like oh yeah pk is right around you know just over three or maybe would get closer depending on how good this scale was but it's 3.2 and so you can look at the titration curve of a weak acid strong-based titration and use it not only to you know approximate what's the molarity of the hf that was in there so but you could figure out the pka of the acid so in this case you know i said we started knowing that we're titrating hf the analyte with naoh the titrant but oftentimes when you do a titration you don't even know what your acid is and oftentimes you can do this and then figure out the pka of your acid and sometimes that actually can be indicative enough to help you identify what acid it might be all right now it turns out i said ph equals pka and a pka is always for an acid so at that half glen's point the ph equals the pka of the conjugate acid but it's also true that the poh let's make that look a little better the poh equals the pkb of the conjugate base as well that is also true at that half golden's point as well we don't usually worry about it as much issue we're usually more concerned with the pka of the acid than the pkb of the conjugate base but both are true so but in this case in titrating a weak acid we probably were more concerned with getting the pka of the acid whereas in the next one when we start titrating weak base it might be the other way around so but two important points on this curve and i really want you to know the distinction between those two points we got the equivalence point we got the half equivalence point and a lot of students memorize them what they are and what they mean and they give the same definition and they say well at the equivalence point the moles of acid equals the moles of base and that's a true statement and then they say at the half cohn's point the moles of acid equals the moles of base well that's also a true statement but we're talking about two different bases here so at the equivalence point the moles of the acid you're titrating the analyte acid equal the moles of the titrant base naoh in this case whereas at the half equivalence point it's the moles of conjugate acid and conjugate base that are equal instead so be careful you don't just say acid and base and not realize which base you're referring to because it's two different bases we're saying are equal to the acid in both cases here so hopefully you see that distinction finally let's take a look at our weak base strong acid titration so in our weak base strong acid titration uh your equivalence point now again is not going to be seven but it is the acid that is strong and so you're going to find out that your equivalence point is going to be a little bit acidic it's going to be below 7 now and again usually somewhere in the four to seven range and again the reason though it's not because the acid was strong and it wins i guess my just my way of remembering it the key is that the salt you are producing i was going to write salt i want to write acidic say one thing can't write the same all right i can't write another anyway so there's acidic that's the key the salt we're gonna produce an acidic salt now again the chloride is the conjugate base of a strong acid so it's a negligible anion but the ammonium is not a group one or group two metal ion or one of those rarer uh transition metal ions with a plus one charge it's a polyatomic ion it's not even a metal ion at that it is acidic it's a lewis acid it's a bronzer acid it's acidic and what do acids do well acids react with water they undergo hydrolysis to produce a little bit of hydronium and so if i asked you what is the reason that the ph is less than seven at the equivalence point in a weak base strong acid titration couple correct answers you could say that the salt that is produced is an acidic salt true statement or you can get a little more technical with your jargon and you could say that the salt that is produced undergoes hydrolysis to produce hydronium that's why the ph is going to be less than seven at the equivalence point now once again if you know it took 20 milliliters or 30 milliliters or something like this let's just pick 30 this time 30 milliliters of our hcl to get that equivalence point well then at the 15 milliliter mark halfway there you're at the half equivalence point and the same things are all true here that were true before so once again if i start off with 10 moles of my weak base i would have to add 10 moles of hcl to get to that equivalence point one to one ratio so how much hcl would i have to add to get halfway to that equivalence point only five moles and that makes hcl the limiting reagent and we lose it all and we'll lose exactly the same number of moles of nh3 but also gain the same number of moles of nh4 plus the ammonium ion and so we're still going to have five moles of ammonia left but we'll now have formed five moles of the conjugate acid nh4 plus and that's why the moles of the conjugate base and the moles of the conjugate acid are going to be equal and so in this case the molarity of nh3 is going to equal the molarity of the ammonium ion as well so and as a result once again if your conjugate acid and conjugate base concentrations are equal well again that happens when ph equals pka and again always true as well is that poh equals pkb so if your goal was to get the pka of ammonium great you're good to go if your goal was to get the pkb of ammonia well then rather than looking at the ph you'd want to convert into a poh instead cool so one thing to note on this one this is uh you're much less likely to see a bass getting titrated it's just usually kind of you know secondary talking about acids getting titrated first so and when students do see it though they're like so is the half glen's point here is it over here and the key is remembering that it's halfway to the equivalence point in terms of the volume of titrant added so you definitely don't want to have it past that equivalence point it's definitely before cool uh once again since your weak acid and conjugate base concentrations are equal right there that again is right where ph equals pka and you have a buffer once again and again you can go one ph unit higher or one ph unit lower and the ph doesn't change a whole lot but get outside that region and the ph jumps get right outside that region and the ph will jump in one way shape or form and it's no longer a buffer and so once again on this titration curve there's a couple of interesting points the equivalence point the half equivalence point and once again if you wanted to know the pka of ammonium or the pkb of ammonia you could use that half equivalence point to figure it out cool that kind of wraps up this lesson so in the next couple lessons again we're going to be doing all the ph calculations for titrations in the next one we'll do strong acid strong base titrations and we'll look at ph calculations at a variety of points along the way in that titration and then we'll move on to weak acid strong base titrations and look at calculating the ph at different points along the way and the titration for those as well and we'll see that the weak based strong acid are pretty analogous to the weak acid strong base so we might do one or two but we probably won't do the whole gamut like we will for those now if you found this lesson helpful and you want to support the channel thumbs up button is pretty much the best thing you can do if you're looking for general chemistry practice check out my general chemistry master course i'll leave a link in the description free trials available happy studying