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## AP®︎/College Chemistry

### Course: AP®︎/College Chemistry > Unit 8

Lesson 1: Introduction to acids and bases# Worked examples: Calculating [H₃O⁺] and pH

In this video, we'll solve for [H₃O⁺] and pH in two different worked examples. First, we'll walk through the possible approaches for calculating [H₃O⁺] from pOH. Then, we'll find the pH of pure water at 50°C from the value of the autoionization constant at 50°C. Created by Jay.

## Want to join the conversation?

- So pH + pOH does not always sum to 14?(3 votes)
- Correct. That only applies at 25°C when the autoionization constant of water, Kw, is equal to 1.0 x 10^(-14). If we use Jay's example here at 50°C, then pH + pOH should equal ~13.28.

Hope that helps.(9 votes)

- so at the end (last problem), the PH value for neutral (equal concentration of H+ and OH-) water @ 50°C is 6.64. I've always assumed that only PH=7 is neutral. Does the neutral PH value of everything depend on temperature? In other words, does the [H+]=[OH-] concentration equilibrium change depending on the temperature?(2 votes)
- So no matter the temperature, the same rule applies for neutral water in that the number of hydronium ions equals the number of hydroxide ions. A pH (little p) of 7 only means neutral water at 25°C, but for other temperatures this means a pH above or below 7. This is due to the changing value of water's self-ionization constant, Kw, with temperature. At 25°C we know it to be 1.0 x 10^(-14), but at something like 50°C it's about 5.5 x 10^(-14). When we do the math using the Kw at 50°C to find the pH and pOH we find that they are both lower than 7, simply meaning that there more hydronium and hydroxide ions in neutral water at higher temperatures.

Hope that helps.(4 votes)

- So if the neutrality point depends on temperature, does that mean the entire pH scale depends on temperature?(1 vote)
- Yeah, exactly. A neutral pH is only true at 25°C because Kw 1.0x10^(-14). If the temperature changes then the Kw also changes which means what constitutes a neutral pH also changes. A neutral pH of 7 is used because 25°C is average room temperature in most places.

Hope that helps.(3 votes)

- Excuse me, how do you convert the 10^-4.75 to 1.8 x 10^-5? For reference, it's around the timestamp3:31. Thank you!(0 votes)
- If you mean how does he solve the equation around that time, he's using antilog. An antilog is how you would undo a logarithm by making both sides of the equation exponents to a number equal the value of the logarithm's base, in this case 10.

After that, 10^(-4.75) is just a math operation so we can have a calculator do for us.

Hope that helps.(3 votes)

- Why would you only use 10 for the -9.25 part?(1 vote)
- Jay is exponentiating the equation to solve it. Exponentiation undoes a logarithm since exponential and logarithmic functions are inverses of each other. Exponentiation involves making everything in the equation the exponent of a certain number we call the base. The base we choose for exponentiation depends on the base of the logarithm. In this case that is 10 (An unlabeled logarithm is assumed to have a base of 10). So exponentiating an equation by 10 which includes a logarithm of base 10 undoes the logarithm. This allows us to solve for the [H3O+] and makes it equal to a power of 10.

Hope that helps.(1 vote)

## Video transcript

- [Instructor] Here are some equations that are often used in pH calculations. For example, let's say a solution is formed at 25 degrees Celsius and the solution has a pOH of 4.75, and our goal is to
calculate the concentration of hydronium ions in solution, H3O+. One way to start this problem
is to use this equation, pH plus pOH is equal to 14.00. And we have the pOH equal to 4.75, so we can plug that into our equation. That gives us pH plus 4.75 is equal to 14.00. And solving for the pH, we get
that the pH is equal to 9.25. So we have the pH and our goal is to solve for the concentration of hydronium ions, and pH is equal to the negative log of the concentration of hydronium ions. So we can plug our pH
right into this equation. So that would give us the pH which is 9.25 is equal to the negative log of the concentration of hydronium ions. Next, we need to solve
for the concentration of hydronium ions. So we could move the negative
sign over to the left side, which gives us negative 9.25 is equal to the log of the
concentration of hydronium ions. And to get rid of that log,
we can take 10 to both sides. So that's gonna give us the
concentration of hydronium ions, H3O+, is equal to 10 to the negative 9.25. And 10 to the negative 9.25 is equal to 5.6 times
10 to the negative 10. So the concentration of hydronium ions in our solution at 25 degrees Celsius is equal to 5.6 times 10
to the negative 10th molar. Also notice that because
we had two decimal places for our pH, we have the
concentration of hydronium ions to two significant figures. There's another way to
do the same problem. Since we have the pOH, we could use the pOH equation
to find the concentration of hydroxide ions in solution. So we would just need to plug
in the pOH into this equation which gives us 4.75, which is the pOH, is
equal to the negative log of the concentration of hydroxide ions. Next, we can move the negative
sign over to the left side. So negative 4.75 is equal to
the log of the concentration of hydroxide ions. And to get rid of the log, we
just take 10 to both sides. 10 to the negative 4.75 is equal to 1.8 times 10
to the negative fifth. So the concentration of hydroxide ions is equal to 1.8 times 10 to
the negative fifth molar. So our goal is to find the concentration of hydronium ions in solution, and we have the concentration
of hydroxide ions in solution, so we can use the Kw equation because the concentration
of hydronium ions times the concentration of
hydroxide ions is equal to Kw, which is equal to 1.0 times
10 to the negative 14th at 25 degrees Celsius. So we can plug in the
concentration of hydroxide ions into our equation. That gives us 1.8 times
10 to the negative fifth times the concentration of hydronium ions, which we'll just write
as x in our equation is equal to Kw which is equal to 1.0 times
10 to the negative 14. Solving for x, we find the x is equal to 5.6
times 10 to the negative 10th. So the concentration of hydronium ions is equal to 5.6 times 10
to the negative 10th molar. So even though we used
two different equations from the first time we did this problem, we ended up with the same answer
that we did the first time, 5.6 times 10 to the negative 10th molar. So it doesn't really matter
which approach you take. Finally, let's look at an example where the temperature is
not 25 degrees Celsius. Let's say, we have a sample of pure water at 50 degrees Celsius, and our goal is to calculate the pH. Pure water is a neutral substance which means the concentration
of hydronium ions, H3O+, is equal to the concentration
of hydroxide ions, OH-. Right now, we don't know what
those concentrations are, but we know that the
concentration of hydronium ions times the concentration of hydroxide ions is equal to Kw. However, we have to be careful because Kw is only equal to 1.0
times 10 to negative 14th at 25 degrees Celsius. And at 50 degrees Celsius, Kw is equal to 5.5 times
10 to the negative 14th. So let's go ahead and write Kw is equal to 5.5 times
10 to the negative 14th. And if we make the concentration
of hydronium ions x, then the concentration of hydroxide ions would also have to be x
since the two are equal. So we would have x times x is equal to 5.5 times
10 to the negative 14th. So that gives us x squared is equal to 5.5 times
10 to the negative 14th. And if we take the square
root of both sides, we find that x is equal to 2.3 times 10 to the negative seventh. And since x is equal to the concentration of hydronium ions in solution, the concentration of hydronium ions is 2.3 times 10 to the
negative seventh molar. Now that we know the concentration of hydronium ions in solution, we can use our pH equation
to find the pH of water at 50 degrees Celsius. So we plug our concentration
of hydronium ions into our equation, and we take the negative log of that, and we get that the pH is equal to 6.64. Notice with two significant
figures for the concentration, we get two decimal places for our answer. If we had used Kw is equal to 1.0 times
10 to the negative 14th, we would've gotten a pH of 7.00, but that's only true
at 25 degrees Celsius. Since Kw is temperature dependent, if the temperature is something other than 25 degrees Celsius, the
pH of water will not be seven. So in this case, we
calculated it to be 6.64. The pH of pure water is
6.64 at 50 degrees Celsius. However, water is still
a neutral substance. The concentration of hydronium ions is equal to the concentration
of hydroxide ions.