### Video Transcript

The pH of a solution is measured to be 4.15. What is the concentration of hydronium ions in this solution? Give your answer to two decimal places and in units of moles per cubic decimeter.

The pH is defined as the negative log of the concentration of hydronium ions. You’ll also often see the pH defined as the negative log of the concentration of hydrogen ions. This representation is simpler. However, hydrogen ions don’t exist in solution for very long as they easily react with water to form hydronium.

In this problem, we’re being asked to solve for the concentration of hydronium ions. So we’ll use this definition. The pH is a scale. Solutions with a pH of seven are neutral, solutions with a pH less than seven are acidic, and a solution is basic if its pH is greater than seven. The solution in this problem has a pH of 4.15. So we know the solution is acidic.

We need to focus on solving for the concentration of hydronium ions. We’ll need to rearrange this expression to solve for the concentration of hydronium. Let’s first multiply both sides by negative one. Now we need to remove the log on the right side of the equation. A base of 10 with an exponent that is a logarithmic expression returns the quantity inside the log. So, if we raise both sides of our expression to a power of 10, we can isolate the concentration of hydronium ions.

Now let’s flip that equation around so we have the concentration of hydronium ions on the left-hand side of the equation. Now let’s plug in the pH. This gives us about 7.07945 times 10 to the negative five. The problem told us to give our answer to two decimal places. So we can round our answer to 7.08 times 10 to the negative five. The problem also told us we should give our answer in units of moles per cubic decimeter. So the concentration of hydronium ions in a solution with a pH of 4.15 is 7.08 times 10 to the negative five moles per cubic decimeter.