How can I adjust the pH of an HNO₃ solution by adding KOH?

How many moles of KOH(s) must be added to 200 mL of a 0.100 M solution of HNO₃to bring the pH to 2.00? Zaki

Since a strong base is reacting with a strong acid, this is a stoichiometry problem, and not an equilibrium problem. Follow these steps to solve it:

Pick out the target. You want moles of KOH.
List the given information. You have 200 mL of a 0.100 M nitric acid solution. The final solution will have a pH of 2.00, which is the same as a hydrogen ion concentration of 0.010 M.
Connect the given information with the target. It's best to work backwards from the target. If you had mol HNO₃ that reacted, you could calculate mol KOH required. Whenever the problem involves a connection between two different substances, you must have a mole-to-mole relationship between the two to solve the problem. Write and balance an equation for the reaction between KOH and nitric acid to get this relationship.

200 mL of 0.100 M HNO₃ initially
0.010 M H⁺ finally mol HNO₃ reacted mole-to-mole ratio
from balanced equation
mol KOH

Now you have to get moles of HNO₃ reacted. Moles reacted will be final moles minus initial moles. You know initial moles of HNO₃, since you know the volume and concentration of the initial HNO₃ solution. You can estimate final moles too- you have to have a pH of 2.00, which is a hydrogen ion concentration of 0.010 M, and also a nitric acid concentration of 0.010 M. If you assume that the added KOH doesn't increase the volume significantly, the final volume of the solution is about 200 mL.
Do the math. Set up a series of conversion factors so that units cancel to ultimately give you mol KOH.
Check the answer. mol KOH should be less than moles of HNO₃ present initially, since all of the acid wasn't neutralized.

Author: Fred Senese senese@antoine.frostburg.edu

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