Reaction rates
Introduction to pH, pOH, and pKw Autoionization of water into hydronium and hydroxide ions. pH, pOH, and pKa.
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- Sal: --the consistent theme we're discovering in
- chemistry, that everything is about random
- bumps between molecules.
- And when they bump randomly into each other, a lot of
- different things can happen in terms of knocking different
- parts of the molecules off of each other and bonding to
- different things.
- This includes pure water, which for the most part, one
- would think is a pretty stable substance.
- And it really is.
- But it turns out-- let's say if we start
- with 2 water molecules.
- And when I put a 2 here, and any of these is going to turn
- into an equilibrium equation.
- It could represent 2 molecules, it could represent
- 2 moles of molecules.
- What matters is just the ratios in these equations.
- And I think you know that.
- But let me just draw 2 for an example.
- So let's say I have the oxygen end.
- Let's have another oxygen here.
- They both are attached to some hydrogens.
- They're sharing electrons with some hydrogens here.
- And we know that oxygen is a lot more electronegative than
- hydrogen, so it hogs all of the electrons and what that
- creates is a partial positive charge at the hydrogen side of
- the water molecule.
- They're almost naked protons being attached
- to the water molecules.
- This is positive here.
- And then the oxygen sides have a partial negative charge
- because they're hogging all the electrons.
- And this bond between the negative side of the oxygen
- molecules and the positive side of another oxygen
- molecule-- this is called a hydrogen bond-- this is what
- keeps water together and what keeps it definitely in it's
- liquid or solid states.
- And in solid states, these bonds become-- they only stay
- together in some lattice structure.
- And in a liquid state, they can kind of break
- and form new ones.
- But they keep them close to each other, rubbing against
- each other.
- Now it turns out if you just have exactly the right set of
- circumstances-- this isn't the exact some circumstances, but
- I think you can imagine.
- If this moved just exactly close enough, it had enough
- kinetic energy to move right past this one, there's some
- probability-- and I'll draw an equilibrium reaction here,
- because that is what we are dealing with.
- The equilibrium reaction.
- There's some probability that this hydrogen right here gets
- stuck to this guy.
- He gets so close, and maybe this guy bounces in some other
- weird way that we get left with-- let me draw the same 2
- characters, the 2 oxygens.
- Actually let, me draw the second guy.
- Let's say that he just he just somehow passed the other guy.
- So he had some movement.
- Let's say he moved in that direction.
- This is obviously is not scientific, but it gives you a
- narrative around what could happen.
- This guy's hydrogen protons.
- And this was attracted to this oxygen side.
- And if just under the right circumstances-- Remember.
- Everything here is probabalistic.
- There's always a probability of almost anything happening.
- This guy can get attached to the negative side of this
- water molecule, the water side.
- And then this guy is only left with one hydrogen right here.
- And then this molecule as a whole, this is OH, hydroxide.
- And it has a minus charge, right?
- Because water was a neutral molecule.
- You had just as many protons and electrons.
- Now we have 1 less proton than electrons.
- So in this case, just the hydrogen nucleus itself--
- which is just a proton because we learned that hydrogen
- doesn't have any neutrons in it's normal form.
- This is essentially a proton when we draw a hydrogen.
- It gets bumped off or scraped off and ends up on this water
- molecule, so this guy lost a proton, has the
- same number of electrons.
- So he now has a negative charge.
- This guy has the same number of electrons, but now he's got
- an extra proton.
- So he has a positive charge.
- So this is H3O with a positive charge.
- And this little version right here where we gave a water
- molecule and it somehow gains an extra hydrogen proton or
- hydrogen atom.
- This is called hydronium.
- And this process where water can kind of spontaneously--
- and I'm not saying that water-- you know, a whole
- glass of water, this is going to happen.
- It's actually happening to a very
- small number of molecules.
- That if you view this is an equilibrium reaction-- when
- you have 2 waters, the reaction is much more weighted
- in the leftward direction.
- But this can happen, and that's what the whole point of
- this is to think about.
- But this process is called autoionization.
- Because you just have water by itself, and just buy some
- random circumstances of some molecules bumping into each
- other just right, some subset of the water
- will ionize like this.
- Where one part will lose a proton and the other
- part will gain one.
- So this is autoionization.
- And of course this is an equilibrium reaction, so now
- these guys might go bump into 2 other
- things and become water.
- Maybe they'll bump into each other again and
- they'll become water.
- So goes back and forth.
- So there's some equilibrium concentration of this.
- Let me write it as a proper equilibrium reaction.
- So you could have 2, maybe moles of water molecules.
- They are in equilibrium with H3O positive.
- And all these are in an aqueous solution.
- And that's a bit of a redundancy because aqueous
- solution means that you're dissolved in water.
- So of course water is dissolved in water.
- But then H3O dissolved in water.
- So all around here, you have water molecules.
- This isn't isolation.
- You have gazillions of water molecules all around.
- Plus OH minus aqueous.
- Now.
- Sometimes you'll see that exact
- reaction written as this.
- And it's important if you realize it's the same thing.
- H2O in equilibrium with just 1 hydrogen ion popping off.
- Everything's in an aqueous solution.
- Let me write that down.
- Everything is being dissolved and water.
- Plus OH minus in an aqueous solution And this equation
- right here-- and what I wrote at the top.
- And let me cut and paste this so you can see
- them at the same time.
- Copy.
- Go down here.
- And paste this.
- These are essentially equivalent, although the
- second equation right here describes
- what exactly happens.
- So the first equation is creating a picture.
- You have one water molecule and there's some small
- probability that one of its hydrogens just pop off.
- And you're just left with a hydrogen and a hydroxide,
- which is just an oxygen and a hydrogen atom together.
- But the reality is that these hydrogen protons don't exist
- in water on their own.
- Whenever they are in water, in an aqueous solution, they
- essentially get a ride with another water molecule.
- And that's what happens here with the hydronium ion.
- But the whole reason why I'm going into this whole
- discussion about the autoionization of water is
- because people really care about the concentration of--
- depending on how I view it-- hydrogen atoms, hydrogen
- protons in a solution, or you could say hydronium protons in
- a solution.
- The concentration of these 2 things are
- going to be the same.
- Right?
- Because all of these really are riding on another water
- molecule and becoming hydronium.
- How do you measure this-- or a better question is what is the
- equilibrium of this reaction?
- So it turns out that in just regular water, the
- concentration-- and I'll maybe I'll switch to this one.
- The concentration of-- this is in regular water
- at 25 degrees Celsius.
- Let me write that down.
- 25 degrees Celsius, which is roughly room temperature.
- With pure water.
- The concentration of pure water.
- In pure water, the concentration of hydrogen
- ions, and you could also say that that's the concentration
- of hydronium ions, or cations, because they're positive.
- It equals 10 to the minus seventh molar.
- Right?
- So for every 1 liter of water, you have 10 to the minus 7
- moles of hydronium ions.
- Which is still a pretty good number because it's 10 to the
- minus 7 moles, so it's 10 to the minus 7
- times Avogadro's number.
- So let me just do that.
- So it's 10 to the minus 7 moles per liter of water,
- which is the same thing as 10 to the minus 7 times-- a mole
- is just a number.
- 6.022 times 10 to the 23.
- So you do the math here.
- You still end up with what?
- 60 times 10 to the 16th power molecule.
- So you still have a large number of molecules.
- It's just a small fraction of the total number molecules are
- actually these hydrogen or these hydronium ions.
- And it turns out that your concentration of hydroxides is
- also-- so your concentration of hydroxides is also 10 to
- the minus seventh molars.
- So if we know that, we can now actually figure out the
- equilibrium constant for this autoionization of water.
- We can figure out the equilibrium constant.
- So let's do that.
- And we'll do it with the first one.
- So let's say you have-- I'll switch colors.
- H2O in an aqueous solution.
- It's in equilibrium with hydrogen ions
- in an aqueous solution.
- But we know in reality they've gotten rides
- with other water ions.
- With the other water molecules, not ions.
- They turn them into hydronium ions.
- Plus hydroxide molecule.
- The equilibrium for this reaction, the equilibrium
- constant, we'll call it for the K sub w for water.
- It equals the concentration of the products of hydrogen ions
- times a concentration of the hydroxide ions.
- Now, in a normal situation, we would divide it by the
- concentration of the reactants.
- But in this case, and we learned this before, the
- reactants are what the solvent is.
- We are in water.
- So you we won't include this.
- And if you want the intuition behind that, remember this
- whole thing comes out from the probability of-- this is the
- probably of the backwards reaction happening as related
- to the concentrations of these two things
- multiplied by each other.
- And the probably the forward reaction happening is related
- to the probability of finding two of the product-- of the
- reacting molecules in one space.
- And you're always going to find these
- molecules in some place.
- It's just going to be a constant probability that some
- water spontaneously turns into these two products.
- So whenever you have a reaction like this equilibrium
- reaction, and the one side is essentially just a solution,
- you just don't include it.
- So the equilibrium-- or you could just think of
- it as a 1 down here.
- So the equilibrium constant of this autoionization water is
- right there.
- And I just gave you what the numbers were at room
- temperature.
- So the equilibrium constant is equal to-- the concentration
- of hydrogen is 10 to the minus 7 times a concentration of
- hydroxide is also 10 to the minus 7.
- So it equals 10 to the minus 14th power.
- Now.
- And that's a good thing to memorize.
- The equilibrium constant of the autoionization of water.
- And just so you know, this is all going to lead into acids.
- Because essentially people care a whole bunch about what
- this concentration ends up being.
- And we're going to touch on that a
- little bit in this video.
- Now it turns out that people chemistry, for whatever
- reason, they don't like talking in these terms. They
- don't like saying 10 to the minus 14th power.
- So what they do is they take the negative log of things.
- Negative log base 10.
- And if logs are intimidating to you, review the videos on
- logarithms.
- So what they do is they take the minus log of both sides.
- And when someone just writes log without a number, you can
- assume it's base 10.
- But they take the minus log of the equilibrium constant.
- The minus log base 10 of 10 to the minus 14 is equal to--
- well 10 to what powers is 10 to the minus 14?
- Well, it's minus fourteen, right?
- And then you have that minus in front.
- You have this minus, and the log part is just minus 14.
- And so the minus log of the equilibrium constant of water
- is equal to 14.
- And this idea right here is called a pKw.
- pK.
- Let me put the p in a different color just so you
- see where it's-- pKw.
- But all p means, whenever you see it in chemistry, it just
- means minus log base 10.
- Minus log base 10.
- And there's some debate as to what p stands for, I try to
- think of it as power, although it's a minus log, it's a
- exponent-- but whatever.
- It means you're taking the minus log of something.
- And what it does is, it's just a way kind of a way to get out
- of the exponent world-- although I think it's nicer to
- stay in the exponent world because you really know what
- you're talking about-- into some nice
- clean number like 14.
- So when someone says that's the pKw is 14, all they're
- saying is that the equilibrium constant, which is just this
- part right here, is 10 to the minus 14.
- Now, the same convention is used on the hydrogen
- concentration.
- The next few videos are all going to revolve around the
- hydrogen concentration in water, essentially.
- We'll talk a little bit about what happens when you're
- outside of water.
- Now the hydrogen concentration of water at room temperature,
- I've told you, has been determined to be 10 to the
- minus 7 molars.
- People aren't happy just with that, so what they want to do
- is do the same thing.
- They want to take the minus log of both sides.
- So they say that pH-- and you've probably
- heard the word pH.
- It's a lot of cosmetics.
- pH balance.
- Now you know what it means.
- They're really just saying that we have the right number
- of hydrogen ions in our lotion or our perfume or whatever
- we're trying to sell you.
- So the pH is equal to the minus log of the hydrogen ion
- concentration, which is equal to the minus log, remember,
- it's just a base 10 if I don't specify otherwise, of 10 to
- the minus 7, which is equal to-- well, 10 to what power is
- 10 to the minus 7?
- This is equal to minus 7.
- Then we have the minus outside, so then
- this becomes 7.
- Now.
- You can do that same exercise for the pOH.
- pOH.
- The concentration of hydroxide ions.
- What's the negative log of the hydroxide concentration.
- The hydroxide concentration, we saw, was the same
- concentration as the water concentration.
- Oh, I didn't write it there.
- Where did I write it?
- Right there.
- 10 of the minus seventh molars.
- So water has the same number of hydroxides
- and hydrogen ions.
- And that's because this water is just associating into the
- two of them.
- But of course this is equal to minus 7, right?
- Log-based.
- This number right here is 10 to the minus 7.
- So it equals 7.
- So the pH and the pOH of water is both equal to 7.
- Now.
- In the next few videos, we're going to start covering the
- notion of acids and bases.
- And it turns out that an acid is just something that
- increases the hydrogen concentration.
- Well, that's one version of acids.
- We'll talk about other broader definitions.
- But it's called the arrhenius acid.
- Which we'll talk about in the next video.
- But if something is making the hydrogen concentration go up,
- if we put something in water that makes it go up, what's
- that going to do the pH?
- Well, if this number right here goes up, then the log of
- that number is going to go up.
- But then the minus log of that number--
- So let's say for example 10 to the minus 7.
- That's all good.
- But let's say we take it from 10 to the minus 7.
- So 10 to minus 7, that's kind of neutral
- water, doing nothing.
- We have a pH.
- The pH is 7.
- We just figured out this calculation.
- That's where the hydrogen concentration is equal to 10
- to minus 7.
- Now let's say we were to do something to the water where
- the hydrogen concentration were to increase.
- So we add hydrogen.
- We add concentration of hydrogen.
- So let's say 10 to the minus 3.
- This is obviously a much higher concentration of
- hydrogen than that.
- So the hydrogen concentration is now 10 to the minus 3.
- What's our new pH?
- So the new pH is going to be equal to the minus log base 10
- of 10 to the minus 3.
- That's equal to that minus there.
- 10 to the minus 3 power is equal to 10 to the minus 3.
- So it's minus 3.
- So this becomes plus.
- So now our pH is equal to 3.
- So the big take-away from this is we care about the hydrogen
- concentration.
- When something increases the hydrogen concentration, that
- is considered an acid.
- And when you increase the hydrogen concentration, when
- you put an acid into an aqueous solution, you are
- lowering the pH.
- So the lower the pH, the more acidic you have, or the higher
- concentration of hydrogen protons you have. And we'll
- talk in the next video about the opposite of that, which is
- which is basic things.
- And bases increase the concentration of hydroxide.
- Anyway, see you in the next video.
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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