Main content

# Definition of pH

## 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.