Transcript for:
The pH Scale and pH Calculation

the ph scale and ph calculation is going to be what we're covering in 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 links in the description for you can find those courses now this lesson is part of my new general chemistry playlist i'm releasing several a week throughout the school year so if you want to be notified every time i post one subscribe to the channel click the bell notification all right before we can talk about the ph scale and ph calculations here we just got to talk about what's going on inside of an aqueous solution so it turns out water auto ionizes or auto dissociates so look at a water molecule it can split apart into a pair of ions here so a hydrogen ion and a hydroxide ion now sometimes we write this a little bit differently here so it turns out that free h plus is really unstable and it probably doesn't exist freely in an aqueous solution it is probably going to combine with another water molecule or water molecules as we'll see and so sometimes we write this reaction a little bit different and we write it like so and so instead of one water molecule splitting to give you a hydrogen if you have two of them one acting as a bronsted acid one acting as the bronsted base and you transfer an h plus from one to the other you get h3o plus and hydroxide and so in this case h3o plus is hydronium and it looks like you've just simply added an h plus to water well the truth is one of these free h plus ions again that doesn't exist is probably not just actually associated with one water molecule it might be associated with you know two or three or four water molecules all at the same time and so even this is a little more accurate you know instead of saying we have naked protons there's a way to look at that in your solution it's a little more accurate but even this is not you know completely uh an accurate representation of what's really going on in the solution so but whether we just look at it this way as a hydrogen ion constant you know hydrogen or hydronium ion both mean the same thing and we're going to treat them as equivalent in this chapter as we'll find out so we talk about like the the formula for ph ph equals the negative log of the hydrogen ion concentration you could just have simply as written this is you know also as negative log of the hydronium h3o plus concentration exactly means the same thing exactly equivalent just keep that in mind now if we take a look at this reaction here you can see that for every h plus you get an o h minus and their concentrations would be equal in a solution that is pure water if all you got is water then these are going to be equal so when that's the case it's going to turn out that's going to correspond to a ph of 7 as we'll get there a little bit and i'm just bringing that up because i figure you're probably good chance you're already somewhat familiar with the ph scale so but it turns out the equilibrium constant for this reaction is just simply equal to the concentration of h plus times the concentration of o h minus notice they're both aqueous and we leave the liquid out here and it turns out we call this equilibrium constant a special title it's kw just the equilibrium constant for the autoionization of water and again you could also write it as h3o plus times oh minus as well same diff and it turns out that at 25 degrees celsius this has a value of 1 times 10 to the negative 14. and so when we're doing ph calculations we're going to assume that we're at 25 degrees celsius unless we're told otherwise all right so if we've got pure water once again we said that these are equal and so these two concentrations are equal but they also multiply out to give you 1 times 10 to the negative 14. and so what you can do is you can take that 1 times 10 to the negative 14 and set it equal to x squared since these are equal take the square root and you'll find out that x equals 1 times 10 to the negative 7 molar and so in pure water both the h plus and oh minus concentrations are equal to 1 times 10 to the negative 7 molar what happens when you add an acid well when you add an acid it shifts this equilibrium back to the left and you just put a bunch of h plus in there and so it's going to cause it to go back down a little bit what's really going to happen is you're going to lose the hydroxide when it shifts back to the left in the equilibrium and so as a result when you add an acid you end up getting more h plus and the oh goes down and so characteristic of an acidic solution is a solution that has more h plus than o h minus if you add a base it does the exact opposite you're putting more hydroxide into the solution just going to shift the equilibrium back consuming up some of the h plus and so you're going to end up with more hydroxide than h plus instead so that's kind of the hallmark you know do you have more h plus in your solution you're an acidic solution do you have more oh h minus in your solution well then you have uh a basic solution and it turns out we uh there's such wide range of concentrations that are possible here that it's much easier to use a logarithmic scale and so this logarithmic scale is the ph scale so ph is negative log of the h plus concentration we also have something called the poh which is the negative log of the o h concentration and so if you know the h plus concentration you can plug it in right there take the negative log and you get the ph so like if you've got pure water well in pure water both the h plus and oh minus concentrations are both equal to 1 times 10 to the negative 7 molar and so you're just gonna take the negative of the log of one times ten to the negative seven molar and you'd let your calculator do the math for you and find out that equals to exactly seven and so pure water it turns out at 25 degrees celsius has a ph of seven it also has a poh of seven if the oh is also one times ten to negative seven molar take the negative log of that you're also gonna get seven and so the ph and the poh are both seven it turns out and it turns out your ph and your ph are always going to add up to 14 at 25 degrees celsius as well and that actually comes from that kw expression we see right here if you take the negative log of both sides of this equation and rearrange it a little bit you get this expression right here that you might remember from high school ph plus poh adds up to 14. all right so the other side what if you're given the ph or the poh and you want to turn that into the h plus or oh minus concentration so again let's take a look at that ph definition ph equals negative log of the h plus concentration you should know that a ph so p here just means negative log if i say ph negative log of the h concentration poh negative log of the oh concentration p your mom negative log of your mom p just means negative log we'll use it in one other context actually not p or mom but p k a which would be the negative log of the k a value which will be another equilibrium constant we get to in a little bit here so p means negative log ph negative log of h plus now what if you want to rearrange this to solve for that h plus concentration well you either multiply or divide both sides by the negative 1 there so we get negative ph equals log of h plus and then to get rid of that log you have to take the anti-log and the anti-log is simply 10 to the power of and so you'll do 10 to the power of both sides and on this side it cancels 10 to the log they're inverse functions they cancel and so you'd be left with h plus equaling 10 to the negative ph and so that's our other equation here h plus equals 10 to the negative ph in similar fashion if you solve this equation for the hydroxide concentration you'll get that the hydroxide concentration equals 10 to the negative poh cool and then again we've got the kw expression and then the negative log of that to get ph plus poh always add up to 14. these are the equations we're going to be working with and this is important there's actually four quantities going on here we've got the h plus concentration the ph the oh minus concentration and the poh and it turns out they're all mathematically interdependent on each other if i give you any one of these four you should be able to solve for the other three using these equations right here and that's exactly what we're going to do so we're going to set up a table and in fact if you've got the study guide in front of you we're going to fill in the missing blanks on that table let's have some fun all right so before we dive into the calculations themselves we just want to investigate this ph scale just a little bit more and so again if you've got pure water you've got a neutral solution we say and your ph is exactly seven so but if you add an acid you're going to end up with more h plus than o h minus and that's going to cause your ph to go down and so any ph that's lower than seven is going to be acidic now it turns out your ph is not bounded on a logarithmic scale it's actually not bounded by zero if you have a really concentrated strong acid you can actually have phs that go negative a little bit so just keep that in mind other end of the scale your bases if you have more if you've got a base your solution you're gonna end up with more hydroxide than h plus and your ph is gonna end up being higher than 7. also it's not bounded by 14 a lot of people think oh 14 is the limit it turns out it's not again on the logarithmic scale there's technically no limits here and if you have a really concentrated solution of a strong base you can get phs that are higher than 14. now most you guys are going to be familiar with a ph scale like this and you can tell if a solution is acidic or basic based on if the ph is lower or higher than seven but being able to figure out if a solution is acidic or basic based on the poh or based on the h plus concentration or based on the oh minus concentration can seem a little bit tricky and confusing so if you're asked to figure out if a solution is acidic or basic i highly recommend whatever you've got you turn it into a ph and go from there one other thing you should know about this ph scale is that is a logarithmic scale every unit you go up or down in ph is a power of 10. so like if you compare say ph seven to ph six which one's more acidic well ph six is the question is how many times more h plus does it have well one ph unit is ten times more h plus so at a ph six compared to ph seven you have 10 times more h plus what if i compared ph 5 to ph 6 well ph 5 would have 10 times more h plus than a solution that's ph 6. so if ph 6 has 10 times more than ph 7 and ph five has ten times more h plus than ph six then ph five how many times more h plus does ph five have than ph seven well ten times more than six and six is ten times more than seven so ten times ten would be a hundred times more and so a ph 5 does indeed have a hundred times more h plus than a ph seven and you can kind of look at it as being kind of ten to the change or difference not really change but difference in ph so between five and seven there's a difference of two ph units and ten to the two is a hundred times more h plus at ph five than at ph seven cool works the same way the other way if you want to look at hydroxide instead so if i said who's got more hydroxide ph 7 or ph 8 well ph 8 has more hydroxide how many times more 10 times more because it's one ph unit away what if i said ph 9 compared to ph 7 100 times more hydroxide ph 10 compared to ph 7 a thousand times 10 to the third times more hydroxide and so you can do it on the basic side with hydroxide or you know on the acidic side with h plus but it turns out you could look at the entire scale in terms of h plus or the entire scale in terms of o h minus if you wanted to so if i want you to compare you know a ph of say one with a ph of at the other side of the spectrum say of 10 and i want to say which one has a greater concentration of h plus well the more acidic solution does which one has a greater concentration of oh minus well the more basic solution does but if my question was how many times more h plus do i have a ph 1 then ph 10 10 to the ninth which is a billion times more so so 9 ph units lower 10 times more h plus what if i said how many times more o h minus does the ph 10 solution have in the ph 1 solution and again it's going to be 10 to the ninth times more oh minus when you're at ph 10 that at ph 1. cool so just want to make sure you realize this logarithmic scale so we use these in a variety of places uh you know in everyday life and and we don't even realize it we don't realize how big of a difference it is you know you might just like oh ph 7 ph8 who cares what's the difference no no ph8 is got 10 times more hydroxide than ph 7 things of this sort so you might see you know also see this say for earthquakes the richter scale it turns out is at a logarithmic scale now it's not log base 10 so it's not like you know as you go from a an earthquake of 5.0 to an earthquake of 6.0 it's not 10 times worse or 10 times stronger earthquake it turns out it's 31 times stronger so you might be like oh 5.0 six point on the richter scale big deal no difference no no it's 30 times 31 times more powerful earthquake what if i go from like a 5.0 to a 7.0 well now it'd be 31 times 31 over 900 times more powerful earthquake at 7.0 on the richter scale compared to 5.0 on the richter scale so makes a huge difference when you realize that oh that's a logarithmic scale one degree to the next is a huge difference same thing on this ph scale every ph unit away is 10 times more of either h plus or oh minus depending on which way you're going all right so now we're going to take a look at some calculations here and in every space on this uh this lovely table here i've given you one of the four and we're just going to calculate the other three and on your study guide is also this lovely uh diagram here which shows you how you can convert one of these to any of the others so in this case the first one we're given the h plus concentration from the h plus concentration i could just directly calculate the oh minus concentration using the kw expression or i could just calculate the ph directly using the definition of ph being negative log of the h concentration but if i wanted to calculate the poh i don't have a direct calculation i'm going to have to do it in two steps in one of two different ways all right so also if you're dealing with nice round powers of 10 where you've got like 1 times 10 to the something so life is good a lot of those you'll learn to do in your head a little bit so i still highly recommend pulling out your calculator uh especially if you're not good with logs and stuff like this so however it turns out when you've got 1 times 10 to the something well anything times 1 is itself and so 1 times 10 to the negative 7 is no different than just simply saying 10 to the negative 7. now if you've got 3.2 times 10 to the negative 8 that's not the same as just saying plain old 10 to the negative 8 because multiplying by 3.2 doesn't leave you know doesn't leave something unchanged so but if you've got just 1 times 10 to the negative 7 just treat that as 10 to the negative 7. and what's nice is 10 to the power of that's the anti-log and when you take the log of the anti-log they cancel and so taking the log of 10 to the negative 7 just gives you negative 7 but taking the negative log of it changes the sign and gets you positive 7. and so if i take the negative log of this i'm going to get a ph of 7. and so we can do that pretty quickly and so here in this case if i got from the h plus to the ph well for me i like going this direction and going to the poh i find it much easier to add two things up to 14 and figure out which one i don't know then multiplying to give 1 times 10 to the negative 14 instead and so from here i'm going to jump straight ph is 7. well 7 plus what equals 14 well plus another 7. and then the o h concentration is just 10 to the negative of whatever your poh is and so this is going to be 10 to the negative 7 molar which is the same as 1 times 10 to the negative 7 whether you want to put the 1 or not it's the same thing either way cool and we only started with the h plus and we filled in the other three let's do another example so here we've got a ph of three and my first question for you is that an acidic solution or basic solution and hopefully said oh that's a ph lower than seven that's an acidic solution and so where do you wanna go from here from the ph we could either get the h plus or the poh pretty quickly so let's get that poh then and in this case what do i have to add to 3 to get 14 well we're going to add 11 to that so the poh is 11. and then to get the h plus and the oh minus well h plus just equals 10 to the negative of whatever your ph is so this is going to be 10 to the negative 3 molar which is the same as just 1 times 10 to the negative 3 molar same diff and over here for the oh it's just 10 to the negative of whatever the poh is and so 10 to the negative 11 in this case molar which again is the same as 1 times 10 to the negative low molar and we just filled in that whole column let's move on so now i've given you the hydroxide oh actually not leave that alone so now i'm giving you the hydroxide and so where do you want to go from here well with the hydroxide concentration we can get the poh pretty quickly so and you can get the h plus but again i hate this route right here i hate having to multiply to give 10 to negative 14. so because i struggled to defend my head much of the time but you can go go that route but for me if i've given the hydroxide i'm just going to turn that into a poh and once i turn that into a poh i'll then turn that into a ph since ph and ph add up to 14 and then once i've got the ph i can go back to the h plus i just hate this part of the path if you like it great all right so with a hydroxyl being 1 times 10 to the negative 10 then i could take the negative log of that to get the poh and the log of 10 to the negative 11 is negative 11. the negative log of 10 to the negative 11. oh where am i at sorry let's try that again the log of 10 to the negative 10 is just negative 10 but the negative of the log of 10 to the negative 10 is going to be positive 10. cool and if the poh is 10 well then the ph is going to have to be 4 so that they add up to 14. and if the ph is 4 well the h plus is going to be 10 to the negative 4. molar which again is the same as 1 times 10 to the negative 4 molar now my question for you is is a solution acidic or basic well if i often ask students that before we've actually calculated the ph and a lot of students will look at this and very quickly they're like oh 10 that's basic oh that's poh and it's backwards from the normal ph scale and that's why i said just turn it into a ph look at that ph to figure out if it's going to be acidic or basic and in this case any one of these numbers can ultimately tell you this if your ph is less than seven now that's the one we're most used to seeing that's going to be an acidic solution if your poh is greater than seven that's an acidic solution if your h plus concentration is greater than one times ten negative seven that's an acidic solution and if your oh concentration is less than one times seven negative 7 that is an acidic solution so lots of things can tell me the synthetic solution but the one that is most reliable to get right is just looking at that ph and seeing if it's less than seven all right next one we've got a poh of two so in this case with a poh of two uh a couple places we can go with the poh we can get the ph pretty easily we can get the hydroxide fairly easily as well so i'm gonna get that ph first and the ph here is gonna be 12 since that's what i have to add to 2 to get 14. and then the oh is just going to be 10 to the negative 2 molar and the p the h concentration would be just 10 to the negative 12 molar which the same again is 1 times 10 negative 12 molar life is good this is not so bad when you've got nice whole numbers for phs and pohs you're going to probably get to a point where you can do this pretty reliably in your head i think using your calculator to check your answer is always a good thing but what if it's not 1 times 10 to the something well then that's time to pull out your calculator here now it turns out if it's 3.2 you can probably do it in your head as well because that's exactly the halfway point it turns out that 3.2 is the square root of 10 so which becomes relevant if we kind of split this up into some powers here but in this case i'm just going to recommend you use your calculator now one thing you should know here when you take the negative log of a number so as that h plus goes up that ph is going to go down so let's just say for a minute that this was a 1 times 10 to the negative 8 then the ph would be 8. but since this number is now bigger than that bigger than one times negative eight then your ph is going to end up smaller than eight it's going to be seven point something so at the very least i can approximate i know it's gonna be seven point something so if i had a multiple choice test and there's only one answer of the choice that said seven point something i'd pick it so however let your calculator do the work for you and so in this case if we take the negative log of 3.2 times 10 to the negative eight we're gonna get 7.5 so and if you go to take the mcat or the d80 or the oet someday they're not going to give you a calculator on your chemistry section and i will teach you how to do these calculations or at least approximate them in your head but for now in your gen chem class by all means do this with a calculator all right now if the ph so we started off with the h plus we got the ph and i'm going to move on to the poh and again what do i add to 14 or i'm sorry what am i going to add to 7.5 to get 14 and i highly recommend you probably do this with your calculator when it's nice whole numbers life's not so bad when they're not whole numbers for some reason adding to 14 is such a pain in the butt and so here if we do 14 minus 7.5 you're going to get 6.5 and like i said something about it that just makes that math challenging for subtracting from 14 there now now we can go to our hydroxide and hydroxides just 10 to the negative poh and so we're going to put in 10 to the negative 6.5 molar and we got a problem now if i'm just doing some work along the way no i don't care but if i'm looking for the answer on the you know a multiple choice test and i'm looking for that answer to be my hydroxide concentration it's not going to be there and so you've got to take your calculator here and put in 10 raised to the power of negative 6.5 and let your calculator tell you what this is equal to and it's going to be 3.2 times 10 to the negative 7 molar so this is not proper scientific notation here 3.2 times 10 to the negative 7 molar and again that's what i plugged into the calculator though that improper 10 to the negative 6.5 that's exactly what i put in my calculator i just let my calculator express it in proper scientific notation cool and now we've filled in this entire box so big takeaways here so you should understand some things about your ph scale logarithmic scale and things of this sort you should know how to do all these lovely calculations at 25 degrees celsius and again we're always going to assume 25 degrees celsius unless we're told otherwise and in this case given any one of these four you should be able to calculate the other three now one last thing on this what if you get a question where you're not at 25 degrees celsius what if they told you that say kw was 1.0 times 10 to the negative 13. um and let's just say this was at like 37 degrees celsius so like body temperature right so and they said oh it's not you know it's not 1 times 10 negative 14 anymore it's 1 times 7 minus 13. and what are the implications of this well keep in mind that your kw again is still equal to the h plus times the oh minus which is now going to equal 1.0 times 10 to the negative 13 at this new temperature so again if they don't tell me anything about temperature anything i'm just going to assume that these multiply out to give me 1 times 10 to the minus 14 and that we're at 25 degrees celsius but if in the question they give us something like this well it means they're on their way to asking you something specific so it turns out that when this multiplied out to give 1 times 10 to the negative 14 so that's where the idea that ph and poh adding up to 14 comes from well now it's not going to add up to 14. it turns out in this case i picked a nice round number it's going to add up to 13. it's also from where we get the idea that you know neutral ph is ph 7 well not at this temperature anymore and so what we do is again in pure water these are still going to be equal and so x times x essentially is going to equal 1.0 times 10 to the negative 13 and x going to equal the square root of that so we'll take the square root of 1 times 10 to the negative 13 and get 3.2 times 10 to the negative 7. and if we take the negative log of that then we can find the ph as well as the poh since this is equal to either one of these it's equal to the h plus and it's equal to the oh minus concentrations and so in this case we'd find out that it's actually equal to 6.5 both the ph and the poh and notice 6.5 plus 6.5 adds up to 13. and so at this new temperature the ph and poh don't add up to 14 they add up to 13. and neutral ph is no longer 7 it would be 6.5 these are equal again in pure water but they're not equal to 1 times 10 to the negative 7 molar and the ph and poh are not equal to 7 anymore in pure water they're now equal to ph and poh of 6.5 instead a ph of 7 would actually be basic at this new temperature now i'm just making numbers up here i have no idea what the kw value is at 37 degrees celsius off the top of my head or anything i just want to see a context for which you might be asked a little bit more and this is the one context where you're likely to see them give you the kw at some other temperature and then ask you you know is ph 7 still neutral or is it acidic or basic or they might say what is the new neutral ph 6.5 things of this sort but the key is you're just setting x squared equal to kw to find out the new concentrations of oh minus and h plus that are equal to each other in pure water at this new temperature now if you found this lesson helpful hit that thumbs up button best thing you can do to support the channel lets youtube know to share this lesson with other students as well and if you are looking for practice problems for ph calculations or for anything else in general chemistry as well my general chemistry master course includes over 1200 practice questions final exam rap interviews practice final exams i'll leave a link in the description a free trial is available happy studying