Main content

## MCAT

### Course: MCAT > Unit 9

Lesson 1: Acid/base equilibria- Acid/base questions
- Acid-base definitions
- Chemistry of buffers and buffers in our blood
- Ka and acid strength
- Autoionization of water
- Definition of pH
- Strong acid solutions
- Strong base solutions
- Weak acid equilibrium
- Weak base equilibrium
- Relationship between Ka and Kb
- Acid–base properties of salts
- pH of salt solutions
- Common ion effect and buffers
- Buffer solutions
- Buffer solution pH calculations

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Definition of pH

## Want to join the conversation?

- How can you do this logarithmic calculation in your head- because the MCAT does not allow for calculators?(82 votes)
- Here's an even better explanation: If you see a number that has 1.0 times 10 to an exponent (let's take 1.0 x 10^-4 as an example), the pH is simply the exponent of the power of 10 without the negative sign. So in the example I gave, the pH is 4. You will only get the pH to be the EXACT exponent value ONLY IF you're multiplying by 1.0.

Now, what if the first number isn't 1.0? To give you an idea, take this example: 2.4 x 10^-6. In a case like this, the exponent is 6, but that is NOT your pH! The rule here is that you subtract ONE HALF from the exponent when you have a number other than 1.0 in the mantissa (I believe that's what the position is called?). So we have 6 - 0.5, and you'll have a pH of somewhere between 5.5 and 6.0. Check your answer choices on the MCAT to see what answer falls within that range and you're good to go. The MCAT will NOT have answers looking like 5.5, 5.7, 5.8, etc. They will be more wide spread than that (2.0, 4.3, 5.7, 8.0, etc.). So without even using a calculator, you would select 5.7 out of those answer choices.

Simple, right? Hopefully, this is one of those golden tips whereby if you know what I just stated above, you should never get a pH question wrong on the MCAT....ever.(222 votes)

- Without a calculator follow these steps;

-log(1.5x10^-4)

step 1) divide 1.5 by 10 to get 0.15

step 2) deduct 0.15 from 4 i.e. 4-0.15 = 3.85

Answer on calculator is 3.82 as per video.

Hope this helps.(11 votes) - How do you calculate anti-logs w/out a calculator? I learned how to calculate the pH, but how would you do the anti-logs ?(8 votes)
- To find the concentration of H30 or OH, depending on the question, is to take the same basic principle as finding the PH. Looking at the example, he gave in the video of a pH of 3.82 when raising to this power you can immediately see that the answer will be ten raised to the negative 4 (if the pH were 5.21, it would be raised to the negative 6). So you can immediately remove any solution that doesn't have the exponent at -4. As for the answer of 1.51, There is one trick to know. Know that the half way point for pH is at 0.3. So at pH 3.3, the concentration of H3O would be 5.0 x 10^-4. So anything over 0.3 is going to be closer to the exponent value.(3 votes)

- At2:34he states that 3.82 gives you two significant figures. This is incorrect right? Because 3.82 is three sig figs. Shouldn't it just be 3.8 because we only need two sig figs and 3.8 is 2 significant figures. I don't know if this was a mistake or maybe I need to brush up on significant figures but I am pretty sure 3.82 has 3 significant figures.(4 votes)
- In logarithmic calculation like this, 3 isn't a significant figure. 3 was originally an exponent. It seemingly looks like a significant figure, but it is not. Exponents are excluded in counting significant figures. In 3,82, the significant figure is just ".82". But if 3.82 is just the case not having an exponent, 3.82 has 3 significant figures.(5 votes)

- Is there any difference in H3O+ or H+?(2 votes)
- H⁺ does not actually exist in water because it complexes with water.

So, H⁺ (aq) and H₃O⁺ (aq) are different ways of describing the same thing: the hydronium ion (also called hydroxonium).

In reality H⁺ complexes with more than one molecule of water, but the exact number varies with the conditions of the solution, so it is customary just to depict one molecule of water complexing with the H⁺ ion.(8 votes)

- At5:41, I'm confused as to why he is using the Kw of H2O in order to calculate the [H3O+] for an aqueous NH3 solution. Wouldn't the equilibrium constant for an NH3 solution be different than the Kw for H20 at 25 degrees celsius?(3 votes)
- Yes, Kb for NH₃ is quite different from the Kw for water.

But the value of [OH⁻] must satisfy both equilibrium constant expressions.

Thus, if you know [OH⁻] from the Kb calculation, you can then use it in the Kw expression to calculate [H₃O⁺].(3 votes)

- At6:33how should you get the concentration of H3O+ without using a calculator.(4 votes)
- for the calculations, can you please help me with scientific calculator? I don't know how to apply looking for the hydroxide ion. like when we have to divide the scienfic notation over a scientific notation to get a scienfic notation. please help.(3 votes)
- Are there any examples of solutions with a pH less than 0 or greater than 14?(2 votes)
- Isn't it important to distinguish that neutral isn't defined as a pH of 7, rather it's when the concentration of OH- and H3O+ are equal? At7:35he says that because the pH is 11.32 and greater than 7 it's basic, but don't we need to know the temperature and equilibrium constant to really decide what's basic, neutral, or acidic?(1 vote)
- Yes, that is correct. But for the normally encountered laboratory situations, true neutrality does not vary from pH 7 all that much. But for hot water or very cold water the pH of neutral water will vary noticeably from pH 7.

But, at this level of study, we don't usually get into such finer details, which do require more sophisticated mathematical models.

But this goes for any equilibrium constant -- they are all, to varying extents, dependent on temperature. Thus, we have to specify the temperature the K is valid for. If It is not specified, it is assumed to be one of the standard temperatures. For Kw, the standard temperature usually used is 298.15 K.(3 votes)

## Video transcript

- [Voiceover] pH is defined
as the negative log base 10 of the concentration of hydronium ions. Let's say we want to find the pH of water. To find the pH of water, we
would take the negative log of the concentration of hydronium ions. For water, at 25 degrees Celsius, the concentration is 1.0 times 10 to the negative seven molar. To find the pH, if you know logarithms, you can do this in your head. But if you don't, I'll get out the calculator here and show you what to do on the calculator. You would press negative log of 1.0 times 10 to the negative seven, and we seven here for our answer. So a pH of seven. If you're concerned with
significant figures, you would have to write 7.00. That's because we had
two significant figures for our concentration, one and two. When you're dealing with logarithms, the only significant
figures in a logarithm are the digits to the
right of the decimal point. Here's out decimal point, and we have two significant figures to the right of our decimal point, matching the number we had here. So water has a pH of seven, and we know that water is neutral. Let's compare water to another example. Let's say we have some orange juice. Let's say we're trying to calculate the pH of our orange juice. And I'll just make up a number. Let's say we measure the
hydronium ion concentration to be about 1.5 times 10 to the negative four molar. So what is the pH of our
orange juice solution? The pH is equal to the negative log of the concentration of our hydronium ion, which is 1.5 times 10
to the negative four. Let's get out the calculator and let's do this calculation here. We have negative log of 1.5 times 10 to the negative four. So we get 3.82. Notice how I'm rounding that. 3.82, if I write 3.82 for our answer here, that gives us two significant figures to the right of our decimal point, which is how many we had
to account for right here. So a pH of 3.82 is lower
than seven, obviously. Whenever your pH is lower than seven, you're talking about an
acidic solution here. So our orange juice solution is acidic. All right. Let's talk
about going in reverse. Let's say they gave you the pH and asked you for the
concentration of hydronium ions. Let's say they gave you ... We'll just use 3.82, just to make things a little bit easier. They give you the pH and ask you to solve for the
hydronium ion concentration. You take the pH is equal
to the negative log of the hydronium ion concentration. The negative log of H three O plus. So we could put the negative
sign on the left here. So we get negative 3.82 is equal to the log of H three O plus. To solve for the concentration
of H three O plus, we need to take the antilog, right, the antilog of the negative pH. That's just 10 to the negative 3.82. Let's get out the calculator and let's do 10 to the negative 3.82. That's going to give us 1.5. 1.5, because we have to round to 1.5 here if we're concerned about
significant figures, times 10 to the negative four. Let's go ahead and write that. 1.5 times 10 to the negative four is the concentration of hydronium ions. All right? So if we get two
significant figures here, we need two significant
figures for our answer. Obviously, we know this is the correct concentration
of hydronium ions because it's the same
problem as up here, right? So that's the concentration that we had. If you're trying to find the concentration of hydronium ions, all you need to do is take
10 to the negative pH. All right. So we found the pH for water and we found the pH for orange juice. Let's do the pH of ammonia. Let's look at this next problem here. Calculate the pH of an
aqueous ammonia solution with a hydroxide ion concentration of 2.1 times 10 to the
negative third molar. They want us to find the pH, and pH is equal to negative log of the concentration of hydronium ions. But they gave us the
concentration of hydroxide ions. So we need something that relates H three O plus to OH minus. This is the equation we talked about in an earlier video. The concentration of hydronium ions times the concentration of hydroxide ions is equal to KW, which is 1.0 times 10 to the negative 14. If we plug this number in here for the hydroxide ion concentration, we could say the hydronium
ion concentration is x. X times 2.1 times 10 to the negative third is equal to 1.0 times 10 to the negative 14. Simple math, we solve for x. X represents the concentration
of hydronium ions. We can get out the calculator and do this calculation here. 1.0 times 10 to the negative 14, and we need to divide 2.1 times 10 to the negative third. So we get 4.8 times 10 to the negative 12. So I write 4.8 times 10 to the negative 12, which is the molar concentration
of hydronium ions here. So we can take this number and plug it into here to calculate the pH. The pH of our solution is equal to negative log of 4.8 times 10 to the negative 12. Let's look at the calculator and let's do this calculation here. Negative log of 4.8 times 10 to the negative 12. Let's think about rounding that. We need to round that to two
digits past decimal point, so 11.32. The pH of our solution is 11.32. Once again, we had two
significant figures here so we have two significant figures to the right of our decimal point. So this pH is greater than seven. If your pH is greater than seven, greater than seven ... This is like a "greater
than" symbol here ... We're talking about a basic solution. So our ammonia solution is basic. All right. There's another
way to do this problem, but first we have to talk about pOH. All right? So pH is equal to negative log of H three O plus+. Or you could say, pH is equal to negative log of H plus, whichever way you want to do it. We're talking about pOH. That would be the
negative log of OH minus, so the negative log of the concentration of hydroxide ions. Let's calculate the pOH for water. The pOH of water is equal to negative log ... Well, at 25 degrees Celsius, the concentration of hydroxide ions is also 1.0 times 10 to the negative seven, so the pOH would be equal to seven, right? It's the same calculation
that we did above for the pH of water. Once again, if you're concerned about significant figures, I'll write 7.00. All right. So the pH of water was seven, and the pOH of water is also seven. The pH of water plus the pOH of water, that's seven plus seven. That's 14. That's another equation that you can use when you're doing acid-base
calculations here. All right, so let's do the problem again. Let's calculate the pH of
our ammonia solution again, this time using pOH, because we're given the concentration of hydroxide to be 2.1 times
10 to the negative third molar. We could plug that into here and calculate the pOH. Let's do that. The pOH would be equal to
the negative log of ... Let's plus in our concentration, 2.1 times 10 to the negative third, so the pOH is equal to ... Let's get out the calculator and do the math. We have negative log of 2.1 times 10 to the negative third. We get 2.68 after we round that. So the pOH is 2.68. Once again, two significant figures here, so we put two here. So the pOH is 2.68. We could plug that into here, and solve for the pH. The pH plus the pOH, which is 2.68, is equal to 14. 14 minus 2.68 gives us 11.32, which obviously is the same pH that we got when we
calculated it a different way. It does not matter how you do it. You're going to get the
same answer either way. All right. Let's look at a ... Let's look at a pH scale here, and let's put in some of the things we talked about in this video. We talked about water having a pH of seven. Water has a pH of seven. I'm putting seven right here. And we said this was neutral. So neutral, this was water. Next, we calculated the pH of an orange juice solution. Let's see what we got. I don't remember what
we got for our pH here. So for our orange juice, we got a pH of 3.82, so less than seven. Let's go ahead and put that in here. 3.82. Let's say that's about 3.82 right there. This represents our orange juice solution. And when your pH is less than seven, you're talking about an acidic solution. Anything below seven, you're talking about an acidic solution. Then we calculated the pH
of our ammonia solution as 11.32. Let's say that's about 11.32 here for our ammonia solution. When the pH is greater than seven, we're talking about a basic solution. So to the right of water, we're talking about a base here. Normally for your pH scale, usually you see zero to 14. Most things are probably going to fall between zero and 14. But it's possible to have, for example, a pH less than zero, right? It just depends on what your
concentration of hydronium is. That's the idea of a pH scale, looking at things compared to water, thinking about if a
solution is acidic or basic.