What is the approximate pH of the solution resulting from adding 0.0080 mole of HBr and 0.0096 mole of KOH to water to make one liter of solution? (A) Two, (B) three, (C) seven, (D) 11, or (E) 13.
In this question, we’re adding HBr and KOH together to make a solution. Hydrobromic acid is an acid, and potassium hydroxide is a base. That means that when we mix these two chemical species together to create a solution, they’ll make a salt, in this case potassium bromide, and water. We want to find the pH of the solution after these two chemical species react. The pH is defined as the negative log of the concentration of hydrogen ions in the solution.
The problem tells us that we have 0.0080 moles of hydrobromic acid and 0.0096 moles of potassium hydroxide. Potassium hydroxide and hydrobromic acid react one to one. So since we have less of the hydrobromic acid in the solution, we’re going to run out of that first. So let’s figure out how much of each chemical species we’ll have once the reaction is finished. Since everything here reacts one to one, we can do that by subtracting 0.0080 moles from each of the amounts of the reactants and adding that amount to the products. So when the reaction is finished, we’ll have no HBr remaining, 0.0016 moles of potassium hydroxide, and we’ll have formed 0.0080 moles of potassium bromide.
Now that we know what’s remaining in the solution after these two chemical species react, we need to figure out what the pH of the solution is. But the pH of the solution is defined as the negative log of the concentration of hydrogen ions. And we just have the amount of base. Well, in any aqueous solution, water will react with itself to form hydrogen ions and hydroxide ions. This is an equilibrium reaction, the equilibrium expression for which is the concentration of hydrogen ions times the concentration of hydroxide ions. The equilibrium constant for this expression is equal to 1.0 times 10 to the minus 14 at 25 degrees Celsius.
We can use this to create an expression that we can use to solve for the concentration of hydrogen ions that are in our solution. The equilibrium constant is equal to 1.0 times 10 to the minus 14. So now, we just need the concentration of hydroxide in our solution, which is equal to the moles of hydroxide ions divided by the volume of the solution. The volume of the solution is one liter. And the moles of hydroxide ions will be equal to the moles of potassium hydroxide because one mole of potassium hydroxide dissociates in water to form one mole of hydroxide ions. So the concentration of hydroxide ions in the solution is 0.0016. To help us with the math, let’s go ahead and convert this number into scientific notation. This would give us 1.6 times 10 to the minus three.
Now, let’s take care of these exponents. When we have exponents in the numerator and denominator that have the same base, we can subtract their exponents. Negative 14 minus negative three gives us negative 11 for our remaining exponent. Now, we can divide 1.6 into one or we can just recognize that we’re only looking for the approximate pH here. Rounding this off to an even one times 10 to the minus 11 for the sake of easy math is not going to affect the final value that much since our answer choices are fairly spread out.
Now we can finally solve for the pH by taking the negative log of the concentration of hydrogen ions that we just found. We can use log rules here to figure out the pH easily. We can use log rules here to figure out the pH easily, since logs undo exponents. So the log of 10 to the minus 11 is minus 11. So the pH of our solution is approximately 11. If we didn’t round to find the concentration of the hydrogen ions in our solution, we would’ve found that the pH is 11.2, which is pretty close to what we got.
Either way, this matches answer choice (D). The pH of our solution resulting from mixing HBr and KOH is 11.