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In this episode, Hank goes over Reversible Reactions, the water dissociation constant, what pH and pOH actually mean, Acids, Bases, and Neutral Substances as well as the not-so-terrifying Logarithms, strong acids, weak acids, and how to calculate pH and pOH. Oh, and litmus paper!
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Transcript Provided by YouTube:
00:00
This may come as a bit of a shock to you, but I’m not super into personal grooming.
00:04
Like I understand soap and shampoo.
00:07
But there’s all this other stuff now, and I keep seeing references to pH balance everywhere.
00:12
pH balanced soaps, and shampoos, and deodorant, and makeup abound in supermarkets and drugstores.
00:18
And I’ve even seen pH balanced water?!
00:21
We’ve talked a lot about balance over the last couple of weeks,
00:24
and pH balance is related to the equilibrium state of a reversible reaction.
00:29
You’re probably also familiar with the pH scale, and you know that it has to do with acids and bases.
00:33
But what is pH exactly?
00:36
And why is it weirdly written with a lowercase ‘p’ and a capital ‘H’?
00:40
And also, what about pH’s alter ego pOH?
00:43
The capitalization thing is probably the easiest to answer, ’cause there is no answer.
00:47
No one really knows what the ‘p’ means.
00:49
The Danish chemist who came up with the term,
00:51
a guy with the absolutely amazing name, Søren Sørensen, never explained his reasoning.
00:56
Some people think that it comes from some form of the word power,
00:59
whether it’s puissance in French, or maybe Latin, pondus.
01:02
But it probably just came from a common habit chemist have of differentiating a test solution,
01:07
labeled ‘p’, from a reference solution, called ‘q’.
01:10
But thinking of the ‘p’ as standing for power, does help us remember the meaning more easily.
01:15
The ‘H’ part is even easier, it stands for hydrogen.
01:18
Because hydrogen ions, or protons, are pivotal to the behavior of acids and bases, which is what pH describes.
01:23
So you can think of pH as basically the power of hydrogen in a solution.
01:27
The strength of the acid or base character of a substance.
01:31
And it all revolves around one very important point of focus, our old friend water.
01:36
[Theme Music]
01:46
If you’ve been watching Crash Course Chemistry from the beginning you’ve gotten the message
01:49
that water is special in more ways than I can list, and pH is just one more of those ways.
01:54
We normally think of water as a perfectly neutral substance, neither acidic nor basic, and that’s true.
02:00
But, as I’ve mentioned before, water can also function as an acid —
02:04
releasing hydrogen ions, also known as protons, and as a base — consuming them.
02:09
How on Earth is that possible?
02:11
In order to explain, we first have to understand what the pH of a substance really tells us.
02:15
While chemically we say that pH represents the power of hydrogen in a solution, it’s mathematically defined as:
02:21
“the negative of the base 10 logarithm of the concentration of hydrogen ions in solution.”
02:26
OK, so now that you’re terrified, I’m here to help.
02:29
So, yeah, logarithms can seem a little bit scary at first, but the ones that we’re using here are super easy.
02:34
And bonus, once you get familiar with them here, it’ll be that much easier to understand them in math class.
02:39
So now that we got the scary mathematical definition, let’s do the simplest mathematical definition.
02:43
At any given moment, there will be a certain number of hydrogen ions in solution — a very small number —
02:48
the concentration will be a number like one times 10 to the negative fifty moles per liter.
02:53
That negative 5, is your base 10 logarithm.
02:56
Take the negative of that, and you get the pH. 5.
02:59
Now let’s get a bit more in to the weeds.
03:01
The logarithm, or log, of a number is the exponent to which another number, called the base,
03:07
must be raised to produce the target number.
03:10
So for base 10 logs, the base is 10.
03:12
They’re what we use most in chemistry, and they’re really easy to understand,
03:16
and also what we base scientific notation on.
03:18
So as an example, the base 10 logarithm of one hundred is 2.
03:22
Because 10 raised to the power of 2, or 10 squared, equals one hundred.
03:26
Base 10 logs are so common that we often leave the subscript 10 off when we write it.
03:31
Like if your calculator has a ‘log’ button, that’s just for base 10 logs.
03:35
So what in the name of Søren Sørensen does this have to do with face melting acids?
03:38
Well I’m getting to that, and it all starts with waters crazy potential to act as both an acid and a base.
03:44
Random changes in the tiny electrical fields around the atoms in water
03:48
occasionally cause the molecules to break apart.
03:51
Specifically a hydrogen ion, or proton, will break off from one molecule and attach itself to another one,
03:57
forming a hydronium ion, H3O+, and a hydroxide ion, OH-.
04:02
This is why water can act as both an acid and a base.
04:05
It’s molecules can both release and accept protons.
04:08
In this case, it’s only interacting with itself.
04:11
But water can interact in the same way with other acids and bases.
04:15
Some times you’ll see the hydronium ion written as a simple hydrogen ion, H+,
04:19
allowing the reaction to be written with only one water molecule.
04:22
It’s not technically accurate, but it’s close enough to reality that it can be used to simplify things.
04:27
So when we say that the pH is the negative log of the hydrogen ion concentration…
04:31
yeah, we actually mean hydronium ion concentration.
04:35
Just another thing that early scientists got a little wrong and now we have to live with.
04:39
Anyway, this dissociation of water is a reversible reaction.
04:43
And in fact, the ions always reform in to water within a tiny fraction of a second.
04:48
But it’s happening all the time constantly.
04:50
In your bottled water, in the water inside your cells, and in the ocean. Always.
04:55
However, at any given instant only a tiny number of molecules are dissociated ions.
05:00
In fact, the exact number of these molecules is well known to chemists.
05:04
It’s the equilibrium constant for this reaction.
05:06
And because it’s such a special reaction, it has it’s own name — the water dissociation constant, or Kw.
05:12
Kw is equal to one point zero times 10 to the negative fourteenth.
05:17
The formula for Kw is set up like any equilibrium constant,
05:21
concentrations of products over concentrations of reactants,
05:24
all raised to the exponents based on the coefficients of the balance reaction.
05:28
There is however one difference.
05:30
Because the ions represent such a tiny proportion of the total mass, the water itself is essentially pure.
05:36
And pure substances, because they don’t have concentrations, aren’t included in equilibrium calculations.
05:42
So the formula for Kw becomes simply the hydronium ion concentration times the hydroxide concentration.
05:47
According to the balanced equation for the dissociation of water,
05:50
hydronium and hydroxide are formed at a 1:1 ratio,
05:54
so their equilibrium concentrations must be equal.
05:57
That means if we call the concentration of H3O+, for example ‘x’,
06:00
then the concentration of OH- must equal ‘x’ as well.
06:04
So the formula for the dissociation constant 1.0 x 10^-14 simplifies even further to x times x, or x squared.
06:11
Suddenly, it’s crazy easy.
06:13
The equilibrium concentration of each ion is just the square root of 1.0 x 10^-14.
06:19
Touch one key on the ‘ol calculator, and hello both concentrations equal
06:23
1.0 x 10^-7 moles per liter in equilibrium.
06:27
The pH then, is simply the negative log of that, which is 7.
06:30
This my friends, is the basis of the pH scale.
06:34
Water is neutral, so 7 is the center of the scale.
06:37
And I can prove it too.
06:38
This is a strip of paper that’s been infused with a chemical called litmus.
06:41
Litmus is a pH indicator, a chemical that turns different colors at different pHs.
06:46
There are many different indicators, with many different colors, but we’ll talk more about those next week.
06:51
For now, just know that litmus paper turns pink in acids, blue in bases, and a sorta light purple when it’s neutral.
06:57
But one thing you need to remember about the pH scale,
07:00
because pH is calculated from a negative logarithm, it turns everything backward.
07:04
When the hydrogen ion concentration goes up, the pH gets lower.
07:08
For instance, if a little acid, such as vinegar, were added to the water,
07:11
the concentration of hydronium ion might rise to say, 1.0 x 10^-4 moles per liter.
07:17
Which is a thousand times more than before.
07:20
That concentration would push the pH down to 4.
07:23
On the other hand, a base, such as ammonia,
07:25
would consume a lot of hydrogen ions if it were added to the water.
07:28
If the hydrogen ion concentration drops to 1.0 x 10^-11,
07:32
a thousandth of the equilibrium concentration, the pH would be eleven.
07:36
As you can see, the logs turn out to be a mathematical shorthand,
07:40
that saves us from dealing with very huge or very tiny numbers.
07:43
The pH scale then is normally written from 0 to 14.
07:47
With numbers below 7 representing acids, and numbers above 7 representing bases.
07:52
It could also below zero or above 14, but that only happens in super extreme cases,
07:57
that you are very unlikely to encounter.
07:59
At least I hope.
08:00
As with like hydrochloric or nitric acid, which ionize strongly, sometimes even completely.
08:04
Thus releasing a lot of protons, are called strong acids.
08:08
Because they raise the hydrogen concentration a lot, they also generally have very low pHs.
08:13
Weak acids, like citric acid, dissociation incompletely,
08:16
releasing much smaller amounts of hydrogen ions, and therefore they usually have higher pHs.
08:21
Generally considered in like the 4 to 6 range.
08:24
Strong bases meanwhile, like sodium hydroxide,
08:26
consume large amounts of hydrogen ions leaving the concentration very low, so they 10d to have very high pHs.
08:32
Weak bases, like sodium bicarbonate (baking soda), consume much less, and generally have pHs in the 8-11 range.
08:38
Neutral pH is technically just 7.0, but in a more practical sense, it’s usually considered to be between 6 and 8.
08:45
So if pH is based on the concentration of hydrogen, that is hydronium ions,
08:50
what about the concentration of hydroxide ions?
08:53
Just as we can calculate the pH of a substance from it’s hydrogen ion concentration, we can calculate the pOH.
08:58
The negative log of the hydroxide concentration.
09:00
This is easy because Kw never changes.
09:03
Although the concentrations of hydrogen and hydroxide are only equal in pure water, or perfectly neutral solutions,
09:10
the product of the 2 concentrations always equals 1.0 x 10^-14 in any aqueous solution.
09:18
So like orange juice, which is really just an aqueous solution of sugar and citric acid and a few other things,
09:22
say the hydrogen concentration in your OJ is 3.2 x 10^-4 moles per liter.
09:27
Just for the fun of it, let’s go ahead and calculate what the pH is at that point, which turns out to be 3.5.
09:32
But we can also use the Kw and the hydronium ion concentration
09:35
to do a very simple division problem and find the hydroxide concentration.
09:40
It works out to 3.1 x 10^-11 moles per liter.
09:43
Once we have the concentration we can take another step,
09:45
we can find the pOH of the solution which is similar to the pH, simply the negative log of the OH concentration.
09:51
The pOH in this case is 10.5.
09:54
And now for a tip that’s just more awesome and cooler than an ice cream corn dog,
09:57
the sum of the pH and the pOH is always 14.
10:01
In the example we just did, the pH was 5.4 and the pOH was 8.6, and yeah you add those together: 14! Surprise!
10:09
OK, maybe that’s only cool to me.
10:11
But that’s never stopped me before, I love this stuff!
10:14
And next week, I hope to really bend your mind by showing you how to make the pH of a solution hold steady,
10:18
even if you dump a strong acid or base in it.
10:21
In the meantime, thank you for watching this episode of Crash Course Chemistry.
10:24
If you paid attention, you learned
10:25
how pure water ionizes to form hydronium and hydroxide ions in reversible reactions.
10:31
And you learned about the equilibrium constant for that reaction,
10:34
which has a special name: the water dissociation constant.
10:37
You learned some examples of acids and bases and neutral substances,
10:40
as well as why some acids and bases are called strong and others are called weak.
10:45
You learned about logarithms and how you can use them to calculate the pH of a substance.
10:49
And a little bit about pOH, which can be calculated with logarithms, also with subtraction.
10:55
And finally, you learned about some cool mathematical connections between pH and pOH.
10:58
This episode was written by Edi González and edited by Blake de Pastino.
11:02
The chemistry consultant was Dr. Heiko Langner.
11:04
It was filmed, edited, and directed by Nicholas Jenkins. The script supervisor was Katherine Green.
11:08
Michael Aranda is our sound designer, and our graphics team is Thought Café.
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This post was previously published on YouTube.
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Photo credit: Screenshot from video