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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.