Mole Fraction & Solution Concentration Practice Problems - Chemistry
INSTRUCTOR: In this video, we're going to focus on calculating the mole fraction of a substance in a solution. So we have 25 grams of sodium chloride, and it's mixed with 200 grams of water. What is the mole fraction of NaF in that solution? So to find the mole fraction of sodium fluoride, we need to take the moles of sodium fluoride and divide it by the most of the solution, where the moles of the solution is the total number of moles.
That's the moles of sodium fluoride plus the moles of the solvent water. So let's convert 25 grams of sodium chloride into moles. So we've got to find the molar mass of NaF. Fluorine has an atomic mass of 19 and sodium has an atomic mass of 23, so the molar mass is 42 grams per mole. Now, make sure you set it up in such a way that the unit grams council. So it's going to be 25 divided by 42, and that's 0.595 moles.
Now, let's do the same thing for water. So let's start with 200 grams of H2O. And the molar mass of water is 18.016 grams. So therefore, we have 11.1 moles of water. So now we can use this equation to calculate the mole fraction. So it's going to be 0.595 divided by the sum of the two numbers. When typing this in, you can put this in parentheses. So the mole fraction is 0.051.
Number 2, the mass percent sodium hydroxide in water is 4.7%. What is the mole fraction of sodium hydroxide in the solution? So how can we find a small fraction, given the mass percent? So feel free to try this from. Take a minute and work it out. Now, recall that mass percent is basically the ratio of the mass of the solute divided by the mass of the solution times 100% And it's important to know that the solute plus the solvent is equal to the solution.
So therefore, what does it mean to have a 4.7% mass percent? What does that mean? The way I like to think of it is that there's 4.7 grams of solute-- which is sodium hydroxide-- for every 100 grams of solution, because if you take 4.7, divide by 100, and then multiply it by 100%, that will give you a mass of 4.7%. So I'm going to say there's 4.7 grams of solute for every 100 grams of solution.
So now that I have these two values, I could find the mass of the solvent, which is water. So 100 minus 4.7 is 95.3. So a mass percent of 4.7 tells me that I have 4.7 grams of sodium hydroxide for every 95.3 grams of water. So now that I have the mass of the solute and a solvent, I can now calculate the mole fraction.
So let's start with 4.7 grams of NaOH, let's convert it to moles. Sodium is 23. Oxygen is 16. Hydrogen's about 1. So the molar mass of sodium hydroxide is 40 grams per mole. So 4.7 divided by 40 is 0.1175 moles of sodium hydroxide. Now, let's start with 95.3 grams of H2O. The molar mass of H2O is 18.016 grams per mole. And so this is going to be 5.29 moles of water.
So now let's calculate the mole fraction. So the mole fraction of NaOH in this example is the moles of sodium hydroxide divided by the total moles of the solution, which is the moles of the solute and the solvent. So let's see what the final answer's is going to be. So you should get 0.0217. So that's the mole fraction of sodium hydroxide in water.
Number 3, the volume of methanol in water is 12%. Calculate the fraction of methanol in the solution. And we're given the density of methanol and the density of water. So the percent by volume is 12%. So that means that-- let's use milliliters-- for every 12 liters of solute, we're going to have 100 milliliters of solution, because 12 divided by 100 is 12%.
And so if we take 100 and subtract by 12, that means that we have 88 milliliters of the the solvent H2O. So now, using the volume and the density, we could find a mass. So we know that density is mass over volume. If we multiply both sides by volume, density times volume is equal to mass.
So let's start with 12 milliliters of methanol, and let's multiply it by its density, which is 0.792 grams of CH3OH per milliliter. Now, this will give us the mass, but our goal is to calculate the mole fraction. So we can go ahead and convert grams to moles using the molar mass. The molar mass of methanol is going to be-- carbon is 12.01, hydrogen is 1.008 times 4, plus oxygen, which is 16. So the molar mass is 32.042 grams per mole.
So it's going to be 12 times 0.792 divided by 32.042. So in this example, there are 0.2966 moles of methanol. Now, let's calculate the number of moles of water. So we have 88 milliliters of water. The density is 1 gram per milliliter. And the molar mass of water is 18.016 grams. So it's just 88 divided by 18.016.
And so this is going to work out to be 4.885 moles of H2O.
S now let's calculate the mole fraction. So the mole fraction of methanol-- it's going to be the moles of methanol on top, which is 0.2966, divided by the total moles. And so this is going to be 0.0572. So that's the mole fraction of methanol.