Definition of pH

- [Voiceover] In the video on the auto-ionization of water we saw that you could have two neutral water molecules, but one of them could swipe a hydrogen ion from the other and then you could be left with a hydronium ion, and the one that had the hydrogen ion swiped from it, remember a hydrogen ion is really just a proton. This one actually gains an electron, it gains an electron from that hydrogen. It takes all the electrons from this covalent bond, right over here, and it forms another lone pair and it gets a negative charge, and that becomes a hydroxide ion. Or we could also describe that auto-ionization like this, that if I have one water molecule, well the oxygen grabs both of the electrons from this lone pair, swipes hydrogen of the one electron it had, and all it's left with is its protons. Well, hydrogen ion, it's really just talking about a proton because the most common isotope of hydrogen only has a proton in it's nucleus, it does not have a neutron. So you take away its electron, you just have that proton left. And the whole point of doing this to show, well look, its not going to be a typical thing, most of the water molecules aren't going to be doing this, but this is going to happen if you have a large enough quantity of water molecules. And we've even seen to what degree that happens, how typical that is by looking at the concentration. If we looked at the concentration, so if we're talking about pure water, we've seen that the concentration, and we can think about it in two ways. If we think about this top way of expressing the auto-ionization, we can say the concentration of hydronium ions, or if we think about this one over here, we could think about the concentration of hydrogen ions. And the reason why these two things are equivalent, is because these hydrogen ions are really just going to associate themselves with the water molecule and become hydronium. But in pure water, at 25 degrees Celsius, we've seen that these are going to be approximately the concentration, whether you think of it as hydronium concentration or hydrogen ion concentration, it's going to be approximately one times ten to the negative seven molar. What does that mean? Well molar, this is just the units for molarity, that's the same thing as one times ten to the negative seven moles, moles per liter. If you have trouble remembering what moles are, first of all I encourage you to watch that video on Kahn Academy on moles. But, we just have to remind ourselves it's a quanity. Just as a dozen means twelve of something, a mole of something means 6.022 times, and roughly 6.022 times 10 to the 23rd of that thing. So it's just a very, very, very large quanity. So that's the concentration, that you could say the hydrogen ion concentration in pure water at 25 degrees Celsius. But, we could ask ourselves that same question for other types of solutions. For example, orange juice. So let's just say right over here, so in orange juice, the hydrogen ion concentration, and once again I could also say this is a hydronium concentration. Depending on your glass of orange juice, it wouldn't be atypical to find a glass that has a hydrogen ion concentration of say one times ten to the negative 3.5 molar. So once again, this is actually a lot more then this, actually let me make it a round number, you actually might be able to find something at one times ten to the negative four molar. I looked it up on the internet, there's actually a range kind of in the mid threes to low fours of hydrogen ion concentration for orange juice. So you could find something like this, and as you can tell, it's good to always just think about the numbers, this is actually a much higher concentration than this over here. The exponent over here is less negative, so this is a higher concentration, so this is a higher concentration. We could look at something that has a lower concentration. Say something like bleach. So bleach, I'll write that right over here, I actually looked it up on the Clorox website. The Clorox bleach, they say that their hydrogen ion concentration is approximately - so their hydrogen ion concentration - is approximately equal to one times ten to the negative twelve molar. So this is a much lower concentration than you would have in just water right over here, in pure water at 25 degrees Celsius. So this is a much lower concentration, this exponent over here is more negative. This is a lower concentration. Well this is all well and good, but it can get a little bulky talking about concentrations in terms of the scientific notation, something times something to the negative whatever molar. So to help simplify that, people have invented the idea of a pH. Let me introduce it in a color that I have not used yet before. You use lowercase p, uppercase h. I've looked into where this notation comes from, the h most people agree is referring to the hydrogen in some way, but the p some people think is referring to potential, some people just think it's a random letter that was associated in with one of these historical artifacts. But, this is defined as the negative log of, and we could say negative log, if we don't write a base, you assume it's base 10. But, the negative log of the hydrogen ion concentration, or it's equivalently the negative log, because the hydrogen ions are really hydronium ions, H3O. It's really the same thing as this as well. So given this definition of pH, let's calculate the pH's for pure water at 25 degrees Celsius, the pH of this glass of orange juice, or the pH of this bleach. Well, the pH of this pure water is going to be, so the pH here, so I have some space right over here, it's going to be the negative log, and I'll write the base 10 there just cause that's assumed, of its hydrogen ion concentration, which is one times ten to the negative seven molar. We want molarity right over here, you want molarity right over here. Well, one times ten to the negative seven is the same thing as ten to the negative 7, and if you look at just the part where the log here, before we think about the negative. This is just saying to what power do we have to raise ten, to get ten to the negative seven power? Well, that's just going to be negative seven. If what I just did is confusing, I encourage you to review logarithms on Khan Academy. So we're going to have the negative of negative seven, which is going to be equal to positive seven. So the pH of pure water at 25 degrees Celsius, and temperature would matter because it might affect auto-ionization. The pH at 25 degrees celsius is seven. What about this orange juice? Well the pH over here is going to be the negative log of - Instead of writing one times ten to the negative four, I can just write ten to the negative four, and of course that's a base 10. Well, what do I have to raise ten to, to get ten to the negative four, well I'll have to raise that to the negative four power. The negative of negative four is positive four. By that same argument, or by applying the same definition, the pH of this bleach is going to be equal to the negative log of ten to the negative twelve. I'm just ignoring this one times right over here, I could write one times ten to the negative twelve, but that's not going to change its value. That of course is going to be equal to the negative of negative twelve, which is positive twelve. So it might be fun to plot all of these. Let me do that. So let me plot these pH's. So we draw a line right over here, and let's say that this is zero, one, two, three, four - which I'm not gonna be able to all the way to twelve, so I'll have to make my scale a little bit smaller. Zero, one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, and I could keep going over here. So let me write this, one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve. So these are our pH's over here, I could plot em. That water at 25 degrees Celsius is gonna be right over here, and that is my water. That's sometimes referred to as a neutral pH. If I look at that orange juice with a pH of four, that orange juice is gonna be right over here, and I've seen ranges for orange juice, that's actually more in this range right over here, so depending on your glass, or whether it's gone bad or not, so that's going to be orange juice, could be found in that range. So I'll write orange juice, orange juice. And then this bleach, and it depends on the concentration and all of that, but this bleach in particular is right over here, this bleach is right over here. I could plot other things, your stomach, the juices in your stomach, are highly, highly - well I'll talk about the acidic a little bit more - but your stomach juices are going to be - let me do this in a new color - are going to be in this range right over here. So stomach acid, and often instead of stomach juices, stomach acid. If you had something like seawater, it's going to be in this range, right over here, seawater. Now let's think about what this is telling us, and remember this is a logarithmic scale, as we go to the right, our concentration is going down, it's important to recognize, and that's all because of this negative right over here, in our definition. But we saw that bleach has a much lower concentration than the water has. So this is lower hydrogen ion concentration. As we go to the left we have a higher hydrogen ion concentration. Higher hydrogen ion concentration. In general, if something has a pH below seven, we tend to refer to it as acidic. We say it is acidic. So typically when you add acids to neutral water, your pH is going to go down, it's going to get more and more acidic. As you go to the right, if you have a pH above seven, sometimes you'll hear people say basic and sometimes you also might hear people say alkaline. It is becoming more alkaline, it's hydrogen concentration is getting lower, and lower, and lower as we move to the right. I really want you to appreciate the logarithmic nature of it because if I handed you some seawater with a pH of eight, you might say okay no big deal pH of eight relative to a pH of seven, but this is a logarithmic scale, if we're moving to the right, we have a ten times lower concentration of hydrogen ions. If we were to move three spaces to the right on this, where it's one-tenth, one-tenth, one-tenth, we have one-thousandth the concentration of hydrogen ions. It's pretty interesting to think about how much lower the hydrogen concentration is in say bleach than in water, and how much lower that is than say stomach acid or orange juice.