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pH, pOH of strong acids and bases

Deriving the relationship between pKw, pH, and pOH. Calculating the pH or pOH of strong acids and bases. Created by Sal Khan.
Video transcript
Sal: We know that if we leave water to its own devices-- so you have some H2O-- that it's an equilibrium with the autoionized version of itself. So a little bit of it will turn into some hydrogen ions, and we know that this really takes the form hydronium. That these attach themselves to other water molecules. And it could be H3O, but we'll just write it as a hydrogen ion. Which is really just a free-floating proton. Plus hydroxide ion. And we also know that in kind of an equilibrium state at 25 degrees Celsius. And remember, equilibrium constants and equilibrium reactions are only dependent on the temperature. Nothing else. For a given molecule, of course. So 25 degrees Celsius. And we also know, we did this two videos ago, that the equilibrium constant-- as a review, that's the concentration of the products divided by the concentration of the reactants. But the reactant in this case is just water. It's the actual solvent. And if the reactant is what you're-- it's everywhere. So if you just go back to that intuition example, the probability of finding it is 1. So it's just always there, so you don't included it. So you can just say divided by 1 or whatever, and this is equal to the equilibrium constant of water. We learned that that's 10 to the minus 14. Because water by itself will have a hydrogen concentration of 10 to the minus 7 and a hydroxide concentration of 10 to the minus 7. And if you take a log of everything-- so if you take the pKw-- What was that? If you put a p in front of something, that means you're taking the negative log of it. So the negative log of 10 to the minus 14-- the log base 10 up to the minus 14 is minus 14. So the negative log is just 14. So pKw is 14 and that is equal to-- if I take the negative log of this side right here-- let me do that. This is just a logarithm property. This is more math than chemistry. So the log of H plus times OH times our hydroxide ion. That's the same thing, just the logarithm properties. It's the same thing as minus log of H plus minus, or you could say plus the minus log of OH minus. And what is this? well this is just the pH, which is equal to the minus log. This is 10 to the minus 7, right? 10 to the minus 7. The log of that is minus 7. You have the minus in front. So its pH is equal to 7. And what is this? This over here. This is our pOH. The minus log of the hydroxide concentration. And of course, that was also 10 to the minus 7. And so our pOH is equal to log of that is minus 7. You have a minus in front. It's equal to 7. So you get right there that little formula that the pKw, or the negative log of the equilibrium constant of water, pKw is equal to the pH of water plus the pOH of water. And this, at 25 degrees Celsius, this is the thing that's going to stay constant because we're going to start messing with these things by throwing acid and base into the water. This thing is always going to be 14 at 25 degrees Celsius. Remember, as long as you keep temperature constant and you're not messing too much with the molecule itself, your equilibrium constant stays constant. That's why it's called a constant. So with all of that out of the way, let's think about what happens if I throw some acid into a-- let's say I have some hydrochloric acid. I'll use colors more creatively. So I have some hydrochloric acid. It's in an aqueous solution. We know that it disassociates completely, which means that we're just left with the hydrogen ion, on which of course really attaches itself to another water molecule and becomes hydronium. Plus the chlorine anion, or negative ion. Right there. And let's say that I do this with 1 molar-- or, you know, this is also sometimes written as 1 capital M-- of hydrochloric acid. So essentially what am I doing? I am taking 1 molar of hydrochloric acid, literally means that I am taking 1 mole of HCl per liter of our whole solution. Which is mainly water. It's an aqueous solution. Per liter of water, right? So what's my concentration going to be of these things right here? Or in particular, what's the concentration of the H going to be? Well, if this disassociated completely, right? So all of this stuff-- this is not an equilibrium reaction. Remember. I only drew a one way arrow to the right. There's no even small leftwards arrow. This is a strong hydrochloric acid. So if you really put one molar of this in an aqueous solution, you're not going to see any of this. You're going to just see this. So you're going to have the hydrogen concentration here in the aqueous solution is going to be equal to 1 molar. And there's also going to be 1 molar of chlorine anions, but we don't care about that. If I haven't said already, it would be nice to figure out what the pH of this solution is. Now that I've thrown hydrochloric acid in it. Well the pH is just the hydrogen concentration. We already have the hydrogen concentration. That's 1 molar, or 1 mole per liter of solution. So the pH is going to be equal to the minus log base 10 of our hydrogen concentration. Of 1. 10 to the what power is equal to 1? Well, anything to the 0 of power is equal to 1, including 10. So this is equal to 0 minus 0 is just 0. So your pH is 0. So if you have 1 molar of hydrochloric acid, and you throw it into an aqueous solution. And, well, I guess I'm saying you're putting it into a solution when I tell you it's 1 molar. So if you have a concentration of 1 mole per liter of solution, where the solvent is water, you will end up with a pH of 0. The pH of 0. So pH of water without any acid in it, that was equal to 7. And this is considered a neutral pH. Now we know that if you were to have an aqueous solution with 1 molar of hydrochloric acid, we can say-- I'll do it in red because-- pH of HCl in water is equal to 0. So obviously a low pH is more acidic. And we went over that in previous videos. And let's figure out what the pOH of hydrochloric acid is. pOH of hydrochloric acid in an aqueous solution. Well, this all goes back to Le Chatelier's Principle, right? If you go back to what we said before. This is just pure water right here. If we may have put 1 molar of hydrochloric acid in here, we're essentially just throwing a ton of hydrogen protons in there. We're substantially increasing the concentration of this. And Le Chatelier's Principle says oh, well that means that a lot of this is going to be consumed and the reaction will go and this direction. The equilibrium reaction will go in that direction. But remember. Water by itself only had a 10 to the minus 7 concentration. We're throwing in a million-- I mean it was one ten millionth of a mole per liter. Now we're throwing in-- what is that? 10 to the 7th. We're throwing in 10 million times as much hydrogen ions into that water. So all of this stuff just gets consumed. Maybe it goes there. And so the concentration of this gets thrown down really far because we're dumping so much. And the concentration of this goes up because it can only consume so much of these guys. There's not that much of this. There's only 10 to the minus 7th molar of this. So this ends up being 1 molar. And if this ends up being 1 molar-- because 10 to the minus 7th molar, essentially, you can kind of view it as it all gets consumed with the stuff over here. What ends up being the concentration of the OH? Well, we already know that the pKw is 14 of water at 25 degrees, and the pKw of water is equal to the pH of your solution plus your pOH. So if your pH for hydrochloric acid is 0, right? We have 1 molar of hydrochloric acid. Then your pOH of 1 molar of hydrochloric acid is 14. So right here, our pOH is equal to 14. Now let's do the same thing with a base and figure out what its pH is. A strong base. And I think you'll see that it's the opposite. So let's say I had potassium hydroxide. It's a strong base. So it completely disassociates in water to potassium cations. Positively charged ions. Plus hydroxide anions. It completed disassociates. So if I put anything in an aqueous solution-- I should write that down. Aqueous solution just means we are in water, of course. And if we essentially put 1 molar-- remember the concentration matters. You can't just say, oh, hydrochloric acid has a pH of 0. No. You have to say 1 molar of hydrochloric acid has a pH of 0. And actually I didn't write that. Let me write that. 1 molar. And I'll leave you to figure out what the pH or the pOH of 2 molars of hydrochloric acid is. Or a 10 molar of hydrochloric acid. And figure out what those pH's are. But if we have 1 molar, of potassium hydroxide. We have 1 molar of this. And it completely disassociates when it's in water. So you have none of this left over. What's your concentration of OH? When your OH concentration is going to be 1 molar. Right? If you had 1 mole per liter of this, you're going to 1 mole per liter of this. Because all of this just disappears in the water. So what is your pOH? POH is just the negative log of this. The log of 1 is 0. The negative of 0 is 0. And then your pH in this circumstance-- well, you could say, oh, it was the hydrogen concentration. You don't know what the hydrogen concentration is, but you know that when you throw a bunch of this stuff, it's going to sop up a bunch of hydrogen and the hydrogen is going to go down a lot. But you're like, well, how do I measure it? Well, you remember it. 25 degrees Celsius. The equilibrium constant of water is equal to the pH plus the pOH. We showed that at the beginning of the video. So 14 is equal to your pH plus 0. That's our pOH in this case. So our pH is 14. So if you have 1 molar-- I used potassium hydroxide in this case-- but if you have 1 molar of a strong base-- let me write that down. 1 molar of strong base. Remember, strong is kind of an official term in chemistry. It means complete disassociation. You have a pH of 14 and you have a pOH of 0. If you have 1 molar of strong acid. If someone says that they have something with a pH of 0 that they would like to maybe throw at you, you should decline. Because it'll probably hurt your chances of-- well, anyway. So let's say you have 1 molar of strong acid. It's a pH of 0 and a pOH of 14. Anyway, maybe in the next video I'll actually show you-- This might give you the impression that this is an absolute scale. That 0 is as acidic as you can get, and 14 is as basic as you can get when you get the pH, but that's not that's not the case. You can actually get above this or you can get below this. This was this when you had one 1 molar of a strong acid. If you had 2 molars of a strong acid-- actually if you had 10 molars. Right? Let's say you get your hydrogen concentration to 10 molar. So if you had 10 molar of a strong acid, you apply that in an aqueous solution. It is, when I say it's a molar by definition. What's your pH going to be? Your pH is going to be the minus log base 10 of 10. The log, base 10 of 10, is 1. 10 to the first power is one. So this is equal to minus 1. So minus 1 pH would-- if you had 10 molar of say hydrochloric acid or nitric acid or anything like that. Anyway, that's all for this video. I'll see you in the next one.