# Video: Calculating the pH of a Solution of KOH of Known Volume and Concentration

What is the pH value of 0.5 L of 0.2 M KOH? [A] Zero [B] between 0 and 7 [C] 7 [D] between 7 and 10 [E] greater than 10

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### Video Transcript

What is the pH value of 0.5 liters of 0.2 molar KOH? A) Zero, B) between zero and seven, C) seven, D) between seven and 10, or E) greater than 10.

pH is defined as the negative log of the concentration of hydrogen ions in a solution. And we want to find the pH of a solution containing KOH, which is potassium hydroxide. When potassium hydroxide dissolves in water, it dissociates into K⁺ or potassium ions and OH⁻ or hydroxide ions. Since potassium hydroxide produces OH⁻ ions and water, that makes it a base. With the information that’s given in the problem, we would be able to find the amount of potassium hydroxide and therefore the amount of hydroxide in the solution. But to find the pH, we need the concentration of hydrogen ions, not the concentration of hydroxide ions.

In any aqueous solution, water reacts with itself in a process known as autoionization or self-ionization to form hydrogen ions and hydroxide ions. This is an equilibrium reaction with the equilibrium expression equal to the concentration of hydrogen ions times the concentration of hydroxide ions. The hydroxide ions from the potassium hydroxide solution will participate in this equilibrium reaction. So we’ll be able to use this to find the concentration of hydrogen ions and therefore find the pH of our solution.

The equilibrium constant for this expression Kw is equal to one times 10 to the minus 14 at 25 degrees Celsius. So the only thing we need to find in order to solve for the concentration of hydrogen ions is the concentration of hydroxide ions. Concentration is, of course, defined as the amount of a substance in moles per liter of solution. According to our balanced chemical equation, every one mole of potassium hydroxide dissociates to form one mole of hydroxide ions.

Since the amount of potassium hydroxide and the amount of hydroxide ions must be equal to each other and they’re both dissolved in the same volume of solution, the concentration of potassium hydroxide and the concentration of hydroxide ions must be equal to each other. So the concentration of hydroxide ions in our solution is also 0.2 molar.

Now, we can solve for the concentration of hydrogen ions in our solution by dividing both sides of the equilibrium expression for the autoionization of water by the concentration of hydroxide ions. So we can plug everything in. To make the math a little bit easier to solve, let’s convert the concentration of hydroxide ions into scientific notation, which would be two times 10 to the minus one.

Whenever you’re dividing exponents that are the same base. In this case, both of our exponents are a power of 10. You can make the math easier by subtracting the value in the exponents. We can separate out the math of the exponents and the other numbers. So one divided by two is one-half or 0.5 and then 14 minus a minus one gives us negative 13. So the concentration of hydrogen ions in the solution must be 0.5 times 10 to the minus 13.

Now, we can find the pH by taking the negative log of the concentration that we just found. This math gets a little bit tricky to do in our heads. But luckily, most of the answer choices are ranges of pHs. So we might be able to approximate here. So instead of finding the pH for a concentration of 0.5 times 10 to the minus 13, let’s just find the pH for a concentration of one times 10 to the minus 13 or just 10 to the minus 13.

If you see a log whose base is unspecified, you can assume that it’s log base 10. Since logs have the ability to undo exponents, the log base 10 of something raised to a power of 10 will just be the value in the exponent. So the log of 10 to the minus 13 is just minus 13. So our pH is approximately equal to 13. Since this pH is greater than 10, this matches answer choice E.

So the pH of our potassium hydroxide solution is greater than 10.