### Video Transcript

What is the concentration of OH− ions in a solution at 25 degrees Celsius with a pH of 12.45? Give your answer to two decimal places.

To answer this question, we need to calculate the concentration of OH− ions, or hydroxide ions, in a solution with a known pH. The pH of a solution is a way to represent the concentration of hydronium ions in the solution. But to answer this question, we need to calculate the concentration of hydroxide ions. As it turns out, for aqueous solutions at 25 degrees Celsius, the pH can be easily related to the quantity pOH, as the pH plus the pOH must equal 14 at 25 degrees Celsius. The pOH functions similarly to the pH as it is a way to represent the concentration of hydroxide ions. All in all, for solutions at 25 degrees Celsius, there are six equations that can relate the pH, pOH, hydronium ion concentration, and hydroxide ion concentration to one another.

Looking at this diagram, we can see that there are two different ways to solve for the hydroxide ion concentration from the pH. For this video, we’ll start by finding the pOH by using the equation pH plus pOH equals 14. After substituting the pH into the equation and rearranging to solve, we have determined that the pOH of the solution is 1.55. Now, we can calculate the hydroxide ion concentration using the equation hydroxide ion concentration equals 10 raised to the negative pOH. After substituting the pOH and performing the calculation, we get a numerical answer of 0.02818.

We should recognize that even though pOH is a unitless value, we solved for a concentration, so our answer should have the unit of molarity. The unit molarity is also equivalent to the unit moles per liter or moles per cubic decimeter. Hydronium and hydroxide ion concentrations are often reported in scientific notation. Thus, the hydroxide ion concentration is 2.818 times 10 to the negative second moles per decimeter cubed.

Lastly, the question tells us to give our answer to two decimal places. Rounding this value to two decimal places gives us a hydroxide ion concentration of 2.82 times 10 to the negative second moles per decimeter cubed. So the concentration of hydroxide ions in a solution at 25 degrees Celsius with a pH of 12.45 is 2.82 times 10 to the negative second moles per decimeter cubed.