The pH scale | Acids and bases | AP Chemistry | Khan Academy

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. 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 = -log[H⁺].

So, to find the pH of pure water, we just need to plug in the concentration of hydronium ions into our equation. Thus, pH = -log(1.0 × 10⁻⁷), which is equal to 7.00. So, the pH of pure water at 25 degrees Celsius is equal to 7.

Notice that there are two significant figures for the concentration, and there are two decimal places for the final answer. 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 the negative fourth molar. Since we have the concentration of hydronium ions, we can simply plug that concentration into the equation for pH. So, pH = -log(3.6 × 10⁻⁴), which is 3.44.

Notice that we have two significant figures for the concentration; therefore, we have two decimal places in our final answer. Plugging in -log(3.6 × 10⁻⁴) on your calculator 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 that 3.6 × 10⁻⁴ is between 1.0 × 10⁻⁴ and 10.0 × 10⁻⁴. Ten times ten to the negative fourth is the same as 1.0 × 10⁻³. If the concentration of hydronium ions is 1.0 × 10⁻³, you can find the pH of that without using a calculator if you know your logarithms; the pH would be equal to 3.

If the concentration of hydronium ions is 1.0 × 10⁻⁴, this is a log base 10 system, so the negative log of 1.0 × 10⁻⁴ would be equal to a pH of 4. Since 3.6 × 10⁻⁴ is between 1.0 × 10⁻⁴ and 1.0 × 10⁻³, the pH of this concentration must be between a pH of 4 and a pH of 3. 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 14. We can go ahead and plug in the concentration of hydroxide ions into the Kw equation. So that's 2.0 × 10⁻³, and we don't know what the concentration of hydronium ions is; we'll make that x.

So, we're going to solve for x, which is equal to 1.0 × 10⁻¹⁴. Solving for x, x = 5.0 × 10⁻¹², which is the concentration of hydronium ions. So, the concentration of hydronium ions is equal to 5.0 × 10⁻¹² molar.

Now that we know the concentration of hydronium ions in solution, we can plug that into our equation for pH. So, pH = -log(5.0 × 10⁻¹²), which gives 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 0 to 14; however, it is possible to go below zero or to go above 14. We calculated 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 with a pH of 7 is considered to be a neutral solution. An aqueous solution with a pH less than 7 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, making lemon juice acidic. 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 6 and another solution with a pH of 5, the solution with a pH of 5 is more acidic. Going back to our equation for pH, pH = -log[H₃O⁺]. This is log base 10. Therefore, the solution with a pH of 5 is 10 times more acidic than a solution with a pH of 6.

Because of the way the equation is written, the higher the concentration of hydronium ions in solution, the lower the value for the pH, and the lower the concentration of hydronium ions in solution, the higher the value for the pH. If an aqueous solution has a pH greater than 7, 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. 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 = -log[H₃O⁺], which you could also write as pH = -log[H⁺]. Writing 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.

pKw would be equal to -log[Kw]. Let's go back to the Kw equation, which says that the concentration of hydronium ions times the concentration of hydroxides 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 -log[H₃O⁺] + -log[OH⁻] = -log[Kw].

The negative log of the concentration of H₃O⁺ is just equal to pH, so we can write pH down here, plus -log[OH⁻] (that's equal to pOH) means we have pH + pOH = -log[Kw]. At 25 degrees Celsius, Kw is equal to 1.0 × 10⁻¹⁴. Therefore, -log[Kw] = -log(1.0 × 10⁻¹⁴), which is equal to 14.00.

So, we can plug in 14.00 for pKw, which gives us a very useful equation that says pH + pOH = 14.00, and this equation is true when the temperature is 25 degrees Celsius.