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## AP®︎/College Chemistry

### Course: AP®︎/College Chemistry>Unit 12

Lesson 1: Acids, bases, and pH

# Definition of pH

Introduction to pH and the pH scale. Examples of calculating pH of pure water, bleach, and orange juice.

## Want to join the conversation?

• Is there a maximum or minimum pH?
(72 votes)
• But on a normal ph scale, the lowest is 0 and the highest is 14, with a 7 or rear being neutral
(23 votes)
• Thank you Mr. Khan, I learn a lot from your videos.
I've got a question. In the video, the pH of the orange juice was 4. Then does that mean that in a cup of orange juice, there are 1x10^(-4) moles/liter of Hydrogen? does 1x10^(-4) refer to the amount of Hydrogen in the orange juice?
Thank you :D
(35 votes)
• It means, in every 1 litre of orange juice, there are 10^(-4) moles of H+.
Which means 10^(-4) x 6.02x10^23 = 6.02x10^19 H+ ions. (approx)
(16 votes)
• Why is the conventional pH scale from 0 to 14 and not from 1 to 14? How can you raise a number to an exponent such that you get 0?
(17 votes)
• It is a logarithmic scale, not an exponential scale. A pH of 0 corresponds to an H⁺ concentration of 1 M.
(26 votes)
• How does bleach have less hydrogen ions than water?Is most of it then hydroxide?
(6 votes)
• bleach is basically a solution of sodium HypoChlorite, or NaClO. This is a salt that contains the anion of the weak acid HClO, hypochlorous acid, and the cation of the strong base, NaOH. Because NaOH is a strong base, it fully dissociates into Na+ ions and OH- ions. However, the HClO is weak and does not fully dissociate. Therefore, there is more OH- ions inside the solution and less H+ ions. This makes a Basic Solution.
(9 votes)
• I got confused how we can calculate -log[proton] on the calculator.
Some people says log on calculator always has base 10, but some other people say the base is e. Isn't the log base e is equal to ln?
Same to writing, I saw physics teachers write log and they say in physics, its base is e, but my chemistry teacher says the base is 10.
How can we know whether the base is 10 or e?
(9 votes)
• The difference is:
*If you just have "log" (without a base underneath) it means it is base 10, it is implied.
*On the other hand if you have "ln", it is implied that you have a base of "e" (Euler's constant).

Logarithms are largely used in a lot of different fields of study, and their base depends on the phenomenon that you are referring to (basically, you use the one that helps you the best to explain that certain phenomenon), that's why sometimes you might even find bases even different than e or 10, although these are the ones that are used the most.
(6 votes)
• how do you measure the hydrogen ion concentration in a liquid? with a microscope?
(3 votes)
• If you want an accurate measurement you will typically use a device called a pH meter§.

There are also chemicals called pH indicators that can be used.

These chemicals are often bound onto small strips called pH paper than change color to give you an estimate of the pH.

Note that only a very few microscopes (e.g. Scanning tunneling electron microscopes — STMs) are capable of seeing individual atoms and even they can't resolve a single proton (hydrogen ion).

Also, STMs work best with the sample in a vacuum and require the atoms to be attached to a surface, so you couldn't look at ions within a liquid sample.

Finally, even if you could make this work you would have to count thousands or millions of molecules and ions to get an accurate concentration and that would be very challenging!

Does that help?

§Note: If you want to know the details of how pH meters work I recommend these sources:
https://www.explainthatstuff.com/how-ph-meters-work.html
https://en.wikipedia.org/wiki/PH_meter (gets very technical)
(8 votes)
• Consider a given amount of water. If we add n equivalents of an acid ((H sub y) x), y being the number of hydrogen ions in one molecule of the acid and x being some other element or ion...
In this case, the amount of H+ ions in the water will increase because of the donation of H+ ions by the acid. So, we can calculate the pH of this acid. But what if this acid was not dissolved in water, how would we calculate the pH of the acid in that case because the acid will not donate any protons to anything because of the absence of its solution (or in other words because of the absence of water) and hence the concentration of H+ ions would not change anywhere?
Is the pH not defined in that case, or is it just that we cannot calculate it but it does exist, or can we calculate it (if yes then how, if i may ask)?
Thank- you and sorry for the question being so long.
(6 votes)
• Your suspicion is correct - pH is only relevant to solutions, though they apparently do not need to be aqueous.

For example you can calculate the pH of a solution where ammonia is the solvent - in this case protons are taken up by ammonia molecules to form ammonium. This is analogous to formation of hydronium ions in aqueous solutions.

see:
http://chemistry.stackexchange.com/a/7000
(4 votes)
• : Stomach acid is just HCl right?
(4 votes)
• That is correct. HCl (hydrochloric acid) is the acid formed by the stomach during digestion.
(4 votes)
• Who created the mathematical term molar, and why did he/she make it so exact?
(2 votes)
• The term "molar" in chemistry was not created by a specific individual, but rather emerged from the development of the field over time. The concept of the mole, which is the basis for the term "molar," was introduced by the chemist and physicist Amedeo Avogadro in the early 19th century.

Amedeo Avogadro proposed Avogadro's law, which states that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules. He hypothesized that gases could be measured and compared based on the number of molecules they contained rather than their mass.

The term "mole" was coined in 1897 by the German chemist Wilhelm Ostwald, who derived it from the German word "Molekül" (molecule). It was later adopted internationally to represent the unit of measurement for the amount of substance in chemistry.
Hope it helps you.
(7 votes)
• If given 1M solution of HCL then what will be its pH(0?) and what does negative pH mean??
(3 votes)
• Yes if [HCl] = 1M then the pH = 0.

Negative pHs indicate an acidic solution with a [H₃O⁺] > 1M — you can just plug the values in to the equation to find out an exact answer for any value.

I also recommend reading this short article:
https://pubs.acs.org/doi/pdf/10.1021/ed083p1465

Does that help?
(4 votes)

## Video transcript

- [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.