### Video Transcript

What is the pH of a solution with an H3O+ concentration of 3.98 times 10 to the negative two moles per cubic decimeter? Give your answer to one decimal place.

We’ve been given a concentration of hydronium. And we need to find the pH. The pH is defined as the negative log of the concentration of the hydronium ion. Often you’ll see the pH defined as the concentration of hydrogen ions as well. However, hydrogen ions don’t exist by themselves in water for very long, as the hydrogen ion reacts easily with water to form the hydronium ion. The pH is a scale. Neutral solutions have a pH of seven. If a solution has a pH less than seven, the solution is acidic. And solutions are basic if they have a pH greater than seven.

To calculate the pH of the solution in this question, we can simply plug in the concentration of hydronium. However, the concentration we plug in should be in units of molar. In this problem, we’ve been given a concentration with units of moles per cubic decimeter. Molarity is defined as moles per liter. One cubic decimeter is equal to a liter, so moles per cubic decimeter is also equal to moles per liter. So we can go ahead and plug in the concentration of hydronium. The log of 3.98 times 10 to the negative two is negative 1.4001. Of course, a negative times a negative gives us a positive.

The problem told us to express our answer with one decimal place, which gives us 1.4. If we refer to the pH scale, we’ll see a pH of 1.4 means our solution is acidic. So the pH of a solution with a hydronium concentration of 3.98 times 10 to the negative two moles per cubic decimeter is 1.4.