### Video Transcript

An acidic solution was found to have a pH of one. Upon the addition of a small volume of a base, the pH changed to three. By what factor has the concentration of H+ ions changed?

Acidic means having the properties of or containing an acid. An acid is a substance that does or can lose protons in a reaction, where protons can be represented by hydrogen ions or H+. More specifically, this type of acid is called a Brønsted–Lowry acid. A Brønsted–Lowry base is a substance that does or can gain protons in a reaction.

The question tells us that we have an acidic solution, and we know that acids lose protons. If an acid, represented by HA, is added to water, then it can lose its protons, leaving A-. The protons react with the water molecules, forming H3O+ or hydronium ions. We can consider the hydronium ions to be equivalent to hydrogen ions.

The question tells us that a small volume of base is added to this acidic solution. We know that a base gains protons. So if we add a small volume of base, represented by the letter B, to the acidic solution, then it can gain protons from the hydronium ions, and the hydronium ions will become water. So the addition of base has decreased the number of hydronium ions in solution. As the hydronium ions are equivalent to hydrogen ions, the addition of base has caused a decrease in hydrogen ion concentration.

So we now know that the hydrogen ion concentration has decreased, but the question asks us, “By what factor?” To do this, we need to use the pHs. The acidic solution has a pH of one. And upon the addition of a small volume of base, the pH changed to three. The pH is a number that indicates the acidity or basicity of a solution. The hydrogen ion concentration also does this, but the hydrogen ion concentration can be very small and have a lot of decimal places. The pH is a more convenient measure.

It’s important to note that as the hydrogen ion concentration decreases, the pH increases. This is because the pH and hydrogen ion concentration are related via a negative logarithm. A logarithm tells us how many times we multiply something by itself to get a particular number. For example, if we multiply 10 by itself three times, we get 1000. So log base 10 of 1000 equals three. But when the base is 10, the 10 can be omitted. As there is no base in this formula, we can assume that it’s base 10.

Since pH is a logarithmic scale, a one-unit change in pH means that the ion concentration changes by a factor of 10. So a change in pH from one to two means that the hydrogen ion concentration will decrease by a factor of 10. The same is true going from pH two to pH three. The hydrogen ion concentration will decrease by a factor of 10. The question refers to a pH change from one to three. When the pH changes from one to three, the hydrogen ion concentration decreases by a factor of 10 twice. So it decreases by a factor of 10 times 10, which equals 100. So the answer to the question “By what factor has the concentration of H+ ions changed?” is it has decreased by a factor of 100.