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## AP®︎/College Chemistry

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

Lesson 1: Introduction to acids and bases# The pH scale

The pH scale is a convenient way to represent the acidity or basicity of a solution. We can calculate the pH of a solution by taking the negative logarithm of the hydronium ion concentration, or pH = -log[H₃O⁺]. At 25°C, a solution with pH < 7 is acidic, a solution with pH > 7 is basic, and a solution with pH = 7 is neutral. Created by Jay.

## Want to join the conversation?

- This might sound extremely stupid, but is there such thing as imaginary pH? We know that the log of something negative is imaginary, and it seems to me that according to E=mc^2, a sufficiently negative amount of potential energy can result in a negative mass. Dividing this negative mass by the molar mass gives us a negative amount of moles, resulting in an imaginary pH.(7 votes)
- Mathematically it's possible to generate an imaginary pH from a negative molarity, however this has no use to us in a chemistry context. A negative molarity would require either a negative volume of solution or solute moles, both of which are physical impossibilities.

Hope that helps.(7 votes)

- how does x equal 5.0x10-12?(3 votes)
- If the equation is (x)(2.0x10^(-3)) = 1.4x10^(-14), then we have to divide both sides by 2.0x10^(-3) to solve for x. (1.4x10^(-14))/ (2.0x10^(-3)) = x = 5.0x10^(-12).(3 votes)

- wait if the conc of 0H- and H30+ are diff, then why can you interchangeably plug in -log[H30+] and -log[0H-]? you get diff answers(2 votes)
- nvm im trippin(4 votes)

- If we are looking for the ph of [OH], why did we use the equation pH= -log[H30] and use that value for the ph of OH?(1 vote)
- The video was asking for the pH of a solution which contained both hydronium, H3O^(+), and hydroxide, OH^(-), ions. Aqueous solutions, even very acidic or basic, have both of those ions present at all times, but in different amounts. We can relate the concentration of hydroxide to hydronium through the autoionization of water reaction.

H2O(l) + H2O(l) → H3O^(+)(aq) + OH^(-)(aq)

Where the equilibrium expression, Kw, is: Kw = [H3O^(+)][OH^(-)], and Kw is equal to 1.0x10^(-14) at 25°C.

So if we know the hydroxide concentration then we can solve for the hydronium concentration. If [OH^(-)] is 2.0x10^(-3) M then Kw = [H3O^(+)][OH^(-)] becomes:

1.0x10^(-14) = (2.0x10^(-3))*x, where x is the hydronium concentration, [H3O^(+)]. Dividing both sides by 2.0x10^(-3) means x is 5.0x10^(-12) M.

Now we can use the equation pH = -log([H3O^(+)]) to solve for the pH.

Hope that helps.(1 vote)

- I've been trying to understand logs for a long time and it's always confusing to me so sorry if this is a simple question. at2:00minutes you took the negative log of hydronium to get 3.44. If I do this in my calculator without the negative sign at the beginning of the log I then get -3.44. If I do it with the negative sign then I get the same answer as you did. Can you explain the underlying concept of this? Am I correct in saying that this is a log law at work here?

I just don't seem to understand the negative sign in front of the log. Thanks in advance!(1 vote)- The negative sign is just multiplication by -1. So -log(3.6x10^(-4)) is really meant to be -1 x log(3.6x10^(-4)). This is why the answer of log(3.6x10^(-4)) is -3.44 and -log(3.6x10^(-4)) is 3.44; we simply multiplied -3.44 by -1.

Hope that helps.(1 vote)

- sorry if it is a stupid question, but why do we still use water's Kw of 1.0 x 10^(-14) when we're measuring pH of something that's not water/pure water?(0 votes)
- These solutions are still aqueous, which means the solvent is water. And as the solvent the majority of the molecules are water. So we have the acid or base doing its reaction, but alongside those reactions in the same solution we also have water still continuing to do its autoionization. So we have at least two reactions in solution with two different equilibriums coexisting. Both of these reactions want to move to equilibrium so the autoionization of water and Kw is still valid for determining the concentration of hydronium and hydroxide.

Hope that helps.(0 votes)

## Video transcript

- [Instructor] For a sample of pure water at 25 degrees Celsius, the
concentration of hydronium ion is equal to 1.0 times 10 to
the negative seventh molar. Because the concentrations
are often very small, it's much more convenient
to express the concentration of hydronium ion in terms of pH. And pH is defined as the negative log of the concentration of hydronium ion. Since H+ and H3O+ are used
interchangeably in chemistry, sometimes you'll see the
pH equation written out as pH is equal to the negative log of the concentration of H+ ion. So to find the pH of pure water, we just need to plug in the concentration of hydronium ions into our equation. So the pH is equal to the negative log of 1.0 times 10 to the negative seventh which is equal to 7.00. So the pH of pure water
at 25 degrees Celsius is equal to seven. Notice that there are
two significant figures for the concentration and there are two decimal
places for the final answer. And that's because for a logarithm, only the numbers to the
right of the decimal point are significant figures. Therefore, two significant
figures for a concentration means two decimal places. Let's say we have a sample of lemon juice and the measured concentration
of hydronium ions in solution is 3.6 times 10
to negative fourth molar. Since we have the concentration
of hydronium ions, we can simply plug in that concentration into the equation for a pH. So the pH is equal to the negative log of the concentration of 3.6
times 10 to the negative fourth which is 3.44. Notice that we have
two significant figures for the concentration therefore we have two decimal
places in our final answer. So plugging in negative
log of 3.6 times 10 to the negative fourth on your calculator, it gives you 3.44 for the answer. However, there's a way
of estimating the pH without using a calculator. The first step is to say 3.6
times 10 to the negative fourth is between one times 10
to the negative fourth and 10 times 10 to the negative fourth. 10 times 10 to the negative fourth is the same thing as one times
10 to the negative third. If the concentration of hydronium ions is one times 10 to the negative third, you can find the pH of that
without using a calculator if you know your logarithms. The pH would be equal to three. And if the concentration of hydronium ions is one times 10 to the negative fourth, this is a log base 10 system, so the negative log of one
times 10 to the negative fourth would be equal to a pH of four. Since 3.6 times 10 to the negative fourth is between one times 10
to the negative fourth and one times 10 to the negative third, the pH of this concentration
must be between a pH of four and a pH three. And we saw that with our calculator. The pH came out to be 3.44. Let's say we have some cleaning
solution at room temperature which is 25 degrees Celsius and the cleaning solution
has some ammonia in it. The concentration of hydroxide
ions in solution is measured to be 2.0 times 10 to
the negative third molar. And our goal is to calculate
the pH of the solution. The first step is to use the Kw equation which says that the
concentration of hydronium ions times the concentration of
hydroxide ions is equal to Kw which at 25 degrees Celsius is equal to 1.0 times
10 to the negative 14th. We can go ahead and plug
in the concentration of hydroxide ions into the Kw equation. So that's 2.0 times 10
to the negative third. And we don't know the
concentration of hydronium ions is, we'll make that X and so
we're gonna solve for X. And this is equal to one
times 10 to the negative 14th. Solving for X, X is equal to 5.0 times 10 to the negative 12 and this is the equal to the concentration of hydronium ions. So the concentration of
hydronium ions is equal to 5.0 times 10 to the negative 12 molar. Now that we know the
concentration of hydronium ions in solution, we can plug that
into our equation for pH. So the pH is equal to
the negative log of 5.0 times 10 to the negative
12 which gives a 11.30. Notice since we have
two significant figures for the concentration, we need two decimal places
for our final answer. Now that we've calculated the pH of three different substances, let's find where they rank on
what's called the pH scale. The pH scale normally
goes from zero to 14. However, it is possible to go
below zero or to go above 14. We calculate that a sample of pure water at 25 degrees Celsius has a pH of 7.00. That puts it right in the
middle of the pH scale. And we say that water
is a neutral substance. An aqueous solution has a pH of seven is considered to be a neutral solution. An aqueous solution with
a pH less than seven is considered to be an acidic solution. So for lemon juice, we
calculated the pH to be 3.44 which is right about here on our pH scale so lemon juice is acidic. And as you go to the left on the pH scale, you increase in acidity. For example, if we had a
solution with a pH of six and another solution with a pH of five, the solution with a pH
of five is more acidic. And going back to our equation for pH, pH is equal to the negative log of the concentration of hydronium ions. This is log based 10. Therefore the solution with the pH of five is 10 times more acidic than
a solution with a pH of six. And because of the way
the equation written, the higher the concentration
of hydronium ions in solution, the lower the value for the pH. And the lower the concentration
for the hydronium ions in solution, the higher
the value for them pH. And if an aqueous solution
has a pH greater than seven, we say that aqueous solution is basic. For example, our cleaning
solution with some ammonia in it had a pH of 11.30 so that's right about
here on the pH scale. So we would consider that
cleaning solution with ammonia to be a basic solution. As you move to the right on the pH scale, you increase in the
basicity of the solution. So we've seen that pH is
equal to the negative log of the concentration of hydronium ions which you could also write pH is equal to the negative log of H+. Running it this way on the
right makes it easier to see how the pattern works
for other situations. For example, pOH is
defined as the negative log of the concentration of hydroxide ions. So we have the pOH here and then we have the
concentration of hydroxide ions over here, the same way we wrote pH with the concentration
of H+ ions over here. And also pKw would be equal
to the negative log of Kw. Let's go back to the Kw equation which says that the
concentration of hydronium ions times the concentration of hydroxide ions is equal to Kw. If we take the negative log
of both sides of this equation and we use our log properties, we get that the negative
log of the concentration of H3O+ plus the negative
log of the concentration of OH- is equal to the negative log of Kw. The negative log of the
concentration of H3O+ is just equal to the pH, so we can write the pH down here, plus the negative log of the concentration of hydroxide ions,
that's equal to the pOH. So we have pH plus pOH is
equal to the negative log of Kw is equal to pKw. At 25 degrees Celsius, Kw is equal to 1.0 times 10 to the negative 14. Therefore the negative log of
Kw is the negative log of 1.0 times 10 to the negative
14 which is equal to 14.00. So we can plug in 14.00 in for pKw which gives us a very useful equation that says that the pH plus
the pOH is equal to 14.00. And this equation is true when the temperature
is 25 degrees Celsius.