Video Transcript
A 0.2-gram solid mixture of KOH and KCl was titrated against a 0.1-molar solution of HCl. The addition of 20 milliliters of HCl resulted in complete neutralization. As a whole number, what was the percentage of KOH in the solid mixture? The molar mass of potassium is 39 grams per mole. The molar mass of oxygen is 16 grams per mole. The molar mass of hydrogen is one gram per mole. And the molar mass of chlorine is 35.5 grams per mole.
Titration is a quantitative analytical method used to determine the concentration of an analyte using a known concentration of a second solution. An analyte is the substance in a sample that’s being investigated. In this case, the analyte is KOH, or potassium hydroxide, that was in the solid mixture. We’re determining the percentage of our analyte in the solid mixture by titrating it with a known concentration of hydrochloric acid. As hydrochloric acid is an acid and potassium hydroxide is a base, when the hydrochloric acid is added, it will react with the base in a neutralization reaction, forming a salt, potassium chloride, and water. When the solution is completely neutralized, the moles of hydroxide that came from the potassium hydroxide will be equal to the moles of hydrogen ions that came from the hydrochloric acid that was added.
We can use this as the starting point for solving the problem. If we can calculate the amount of hydrogen ions, we will know the moles of hydroxide ions. From there, we can determine the amount of potassium hydroxide that was present in the solid mixture. From there, we can calculate the percentage of the mixture that was potassium hydroxide. We can calculate the amount of hydrochloric acid in moles by multiplying the concentration of hydrochloric acid by the volume of hydrochloric acid that was added. The concentration of hydrochloric acid is 0.1 molar, and 20 milliliters of hydrochloric acid was added. The units of molar are equivalent to moles per liter. So we need to convert the volume from units of milliliters to units of liters before we can continue.
One liter is equal to 1000 milliliters. We can convert from milliliters to liters if we use this relationship, making sure milliliters is on the bottom so that the units will cancel. Performing the calculation, we’ll find that 20 milliliters is equivalent to 0.02 liters. The liters cancel, leaving us in units of moles. So we added 0.002 moles of HCl. Hydrochloric acid dissociates in water to form hydrogen ions and chloride ions. Every one mole of hydrochloric acid produces one mole of hydrogen ions. So 0.002 moles of hydrochloric acid produce 0.002 moles of hydrogen ions.
As we said before, the moles of hydroxide ions are equal to the moles of hydrogen ions when the solution is completely neutralized. This means that we have 0.002 moles of hydroxide ions in the solution. Remember, these hydroxide ions came from the potassium hydroxide in the solid mixture, since one mole of hydroxide ions is formed when one mole of potassium hydroxide dissociates in water. The 0.002 moles of hydroxide ions came from 0.002 moles of potassium hydroxide originally. Now that we know the amount of potassium hydroxide in moles, we can calculate the mass. We’ll do this using the molar mass of potassium hydroxide.
The molar mass of potassium hydroxide will be equal to the molar mass of potassium plus the molar mass for oxygen plus the molar mass for hydrogen. Adding those together gives us 56 grams per mole for the molar mass of potassium hydroxide. The mass of a substance can be calculated by multiplying the amount of that substance in moles by the substance’s molar mass. So we’ll calculate the grams of potassium hydroxide by multiplying the moles by the molar mass. The moles cancel, and we’ll find the mass of potassium hydroxide is equal to 0.112 grams. So of the 0.2-gram solid mixture of potassium hydroxide and potassium chloride, 0.112 grams was potassium hydroxide.
So what is the percentage of potassium hydroxide in this mixture? The percentage of a component in a mixture by mass is equal to the mass of the component divided by the mass of the mixture multiplied by 100 percent. So the percentage of potassium hydroxide in the mixture by mass is the mass of potassium hydroxide, 0.112 grams, divided by the mass of the mixture, 0.2 grams. Then, we multiply by 100 percent. Performing the calculation gives us 56 percent, which is already expressed as a whole number. So our final answer and the percentage of potassium hydroxide in the solid mixture is 56 percent.
