The pH scale

0:00- [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.

0:17And 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.

0:43So 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.

1:04And 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.

1:27Since 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.

1:51So 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.

2:1410 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.

2:31And 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.

3:00And 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.

3:19And 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.

3:37We 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.

3:58Solving 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.

4:20So 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.

4:42The 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.

5:06An 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.

5:26And 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.

5:46This 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.

6:17And 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.

6:36As 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.

6:57For 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.

7:19Let'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.

7:43The 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.

8:07At 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.

8:42And this equation is true when the temperature is 25 degrees Celsius.