Strong base solutions | Acids and bases | AP Chemistry | Khan Academy

When dissolved in water, a strong base like potassium hydroxide will dissociate completely in solution to form hydroxide ions. Potassium hydroxide is an example of a group 1A metal hydroxide. Other examples include lithium hydroxide and sodium hydroxide. Group 2A metal hydroxides are also considered to be strong bases; for example, calcium hydroxide is a group 2A metal hydroxide, and so is strontium hydroxide.

Let's do a problem with a group 1A metal hydroxide, sodium hydroxide. Let's say the pH of the solution is 13.00, and our goal is to calculate the initial concentration of sodium hydroxide. First, we write out the dissolution equation. Solid sodium hydroxide dissociates completely in water to form sodium cations and hydroxide anions in solution.

Looking at the balanced equation, there's a one in front of sodium hydroxide and a one in front of hydroxide ions; therefore, the concentration of hydroxide ions is equal to the initial concentration of sodium hydroxide. We can find the concentration of hydroxide ions in solution from the pH. At 25 degrees Celsius, the pH plus the pOH is equal to 14.00.

So we can plug the pH into our equation, which gives us 13.00 plus the pOH is equal to 14.00. So the pOH of the solution is equal to 1.00, and the pOH is equal to the negative log of the concentration of hydroxide ions. We can plug the pOH into this equation, which gives us 1.00 is equal to the negative log of the concentration of hydroxide ions.

To solve for the concentration of hydroxide ions in solution, first we move the negative sign to the left side, which gives us negative 1.00 is equal to the log of the concentration of hydroxide ions. To get rid of the log, we take 10 to both sides, so the concentration of hydroxide ions in this solution is equal to 10 to the negative 1.00, which is equal to 0.10 molar.

Because sodium hydroxide is a strong base that dissociates completely in solution to form hydroxide ions, if the concentration of hydroxide ions in solution is 0.10 molar, so is the initial concentration of sodium hydroxide.

Now let's do a problem with a group 2A metal hydroxide. Let's say the initial concentration of a solution of calcium hydroxide is 0.0010 molar, and our goal is to find the pH of the solution at 25 degrees Celsius. Calcium hydroxide is a strong base that dissociates completely in solution to form calcium 2 plus ions and hydroxide anions.

Looking at the mole ratios in this dissolution equation, there's a one in front of calcium hydroxide, a one in front of calcium 2 plus, and a two in front of hydroxide ions. Since the mole ratio of calcium hydroxide to calcium is one to one, if the initial concentration of calcium hydroxide is 0.0010 molar, that's also the concentration of calcium ions, so it's 0.0010 molar in solution.

The mole ratio of calcium hydroxide to hydroxide ions is one to two. So if the initial concentration of calcium hydroxide is 0.0010 molar, the concentration of hydroxide ions in solution is twice that concentration. So two times 0.0010 molar is equal to 0.0020 molar.

Now that we know the concentration of hydroxide ions, we can calculate the pH of the solution. One way to calculate the pH is to first find the pOH of the solution, and pOH is equal to the negative log of the concentration of hydroxide ions. We can plug in the concentration of hydroxide ions into our equation, which gives us the pOH of the solution is equal to the negative log of 0.0020.

When you do the calculation, the pOH is equal to 2.70. Notice that since we have two significant figures for the concentration, we need two decimal places for pOH. To find the pH, we know that pH plus pOH is equal to 14.00 at 25 degrees Celsius.

So we can plug in the pOH of 2.70, and that gives us pH plus 2.70 is equal to 14.00. So the pH of the solution is equal to 11.30.