The pH Scale: Calculating the pH of a Solution

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  • 0:06 pH Scale
  • 1:39 Calculating pH for…
  • 3:47 Calculating pH for…
  • 6:01 Calculating Hydronium…
  • 8:43 Lesson Summary
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Lesson Transcript
Instructor: Amy Meyers

Amy holds a Master of Science. She has taught science at the high school and college levels.

Learn the history of the pH scale, how to describe it and why it is used by scientists. Discover how to calculate the pH of an acid or base solutions given either the hydroxide ion concentration or the hydronium ion concentration. Learn how to start with the pH and calculate the hydroxide and hydronium ion concentrations.

pH Scale

Chemist Soren Sorensen developed the formula for measuring acidity.
Soren Sorensen

The idea of pH was proposed in 1909 by a Danish chemist named Soren Sorensen to solve an annoying problem chemists were having. Chemists had found that when they were working with acids and the concentration of hydronium ions, [H3O+], the numbers in the calculations involved negative exponents. Sorenson proposed using the negative logarithm of [H3O+] to measure acidity.

Sorenson called the new measurement pH. The p stands for power and the H for hydrogen, so pH stands for power of hydrogen. pH is just a value used to express how acidic or basic a solution is. The pH scale runs from 0 (the lowest possible value) to 14 (the highest possible value). Values from 0-6 are acidic, a value of 7 is neutral, and values from 8-14 are basic.

The pH scale shows how acidic or basic a solution is.
pH Scale Diagram

Here's a fun pH experiment you can do at home. Red cabbage is a natural pH indicator. Mix chopped cabbage with boiling water and allow the mixture to sit for 10 minutes to leach out the flavin (a pigment). After 10 minutes, pour out just the water. It should be a purple color. When the solution is purple, the pH is neutral. Divide the solution into different containers and start adding various household liquids to the containers. If the solution turns red, the solution you added was acidic. If it turns yellow/green, then the solution you added was basic.

Calculating pH for Acidic Solutions

To calculate the power of pH, the formula is -log [H3O+].

Although this sounds complicated, it really isn't. If you have a hydronium ion concentration [H3O+] of 1 x 10^-7, the pH is 7. -log [H3O+] = -log (1 x 10^-7) = 7

If the [H3O+] is 1 x 10^-1, the pH is 1.

If it is 1 x 10^-13, the pH is 13. See how that works?

In this pH formula example, the 13 is the pH of the solution.
pH Formula Example

The following problem is a bit harder because you are given the molarity of the solution and not the concentrations of the ions.

What is the pH of a 0.00010M solution of HNO3, a strong acid?

Because the problem told you that HNO3 is a strong acid, you know that it dissociates nearly 100%, so you know that the [H3O+] = 1 x 10^-4 M (.0001 = 1 x 10^-4).

pH = -log [H3O+] = -log (1 x 10^-4) = - (-4) = 4

Here's another one. You will need a calculator for this one.

Calculate the pH of a 0.2 M solution of a strong acid.

Strong acid - therefore the [H3O+] is the same as the molarity of the solution, or [H3O+] = 2 x 10^-1

pH = -log [H3O+] = -log (2 x 10^-1) = 0.7

Calculating pH for Basic Solutions

What is the pH of a 0.0136M solution of KOH, a strong base?

This one is a bit harder because you have the hydroxide ion concentration but not the hydronium ion concentration. Because you were told that the KOH is a strong base, you know it dissociates nearly 100% to form 1.36 x 10^-2 [OH-].

If you remember that the Kw, or auto-ionization constant of water, is calculated by the formula [H3O+] [OH-] = Kw = 1 x 10^-14, you can figure out the [H3O+] concentration.

[H3O+] = Kw / [OH-]

[H3O+] = 1 x 10^-14 / 1.36 x 10^-2

[H3O+] = 7.35 x 10^-13

Now that you know [H3O+], you can figure out the pH.

pH = -log [H3O+] = -log (7.35 x 10^-13)

pH = 12.13

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