### Video Transcript

What is the hydronium ion concentration of a solution at 25 degrees Celsius that has a pOH of 4.1? Give your answer to two decimal places and in scientific notation.

The pOH of a solution is a way to represent the concentration of hydroxide ions in solution. But to answer this question, we need to determine the hydronium ion concentration, not the hydroxide ion concentration. We are told in the question that the solution is at 25 degrees Celsius. As it turns out, for aqueous solutions, at 25 degrees Celsius, the concentration of hydronium ions times the concentration of hydroxide ions equals a constant: one times 10 to the negative 14th. This allows us to relate the concentrations of hydroxide and hydronium ions in solution.

In addition, just as the hydroxide ion concentration can be represented as a pOH, the hydronium ion concentration can be represented as a pH. These four quantities, pOH, pH, hydroxide ion concentration, and hydronium ion concentration, can be related to one another via six different equations so long as the temperature of the solution is 25 degrees Celsius. From this diagram, we should be able to see that there are two different methods to convert the pOH to the hydronium ion concentration. For this video, we’ll start by converting the pOH to the pH using the equation pH plus pOH equals 14.

We are told in the question that the pOH of the solution is 4.1. After substituting this value into the equation and rearranging to solve, we have determined that the pH of this solution is 9.9. Now we can convert the pH to the hydronium ion concentration using the equation hydronium ion concentration equals 10 to the negative pH. After substituting the pH and performing the calculation, we get a numerical answer of 1.2589 times 10 to the negative 10th. We should recognize that even though pH is a unitless value, we solved for a concentration. So our answer should be reported in moles per liter.

We are told in the question to give our answer to two decimal places and in scientific notation. Our answer is already in scientific notation, so we just need to round appropriately. Rounded to two decimal places, the hydronium ion concentration of a solution at 25 degrees Celsius that has a pOH of 4.1 is 1.26 times 10 to the negative 10th moles per liter.