Solutions and cognitive properties

Question

A solution is made using 56.9g of toluene (MM=92.13g/mol) and 80.0 g of benzene( MM=78.11g/mol). What is the mol fraction of toluene in the solution?

Answer 1

To find the mole fraction of toluene, we must know two things:

1. The number of moles of toluene in 56.9 grams of toluene
2. The number of moles of benzene in 80.0 grams of benzene

Let's start by figuring out the number of moles of toluene. The question gives us the molar mass of toluene (MM = 92.13 g/mol). This means that there are 92.13 grams of toluene in 1 mole of toluene. So we need to find out how many moles of toluene are equal to 56.9 grams of toluene. In other words, we need to convert 56.9 grams of toluene to moles of toluene. We do this conversion like this:

56.9 grams of toluene x 1 mole of toluene

92.13 grams of toluene

Notice that "grams of toluene" appears on both the top and bottom, so it will cancel. We will be left with only "mole of toluene", which is exactly what we want. We solve this conversion by first doing 56.9 x 1. Of course, 56.9 x 1 = 56.9. Now we do 56.9 / 92.13. The calculator says that 56.9 / 92.13 = 0.6176. Thus, 56.9 grams of toluene is equal to 0.6176 moles. We have found the moles of toluene.

Next we need to find how many moles of benzene are in 80.0 grams of benzene. The question gives us the molar mass of benzene (MM = 78.11 g/mol). This means that there are 78.11 grams of benzene in 1 mole of benzene. We have 80.0 grams of benzene, and we need to convert the 80.0 grams to moles. We do this conversion like this:

80.0 grams of benzene x 1 mole of benzene

78.11 grams of benzene

We solve this by first doing 80.0 x 1. Of course, 80.0 x 1 = 80.0. Now we do 80.0 / 78.11. The calculator says that 80.0 / 78.11 = 1.024. Thus, 80.0 grams of benzene is equal to 1.024 moles of benzene.

Now we can finally find the mole fraction of toluene. The equation for finding the mole fraction of toluene is this:

Moles of toluene / Total moles

First let's find the total moles. We do this by adding the number of moles of toluene and the number of moles of benzene. So it looks like this:

Total moles = moles of toluene + moles of benzene

We know that we have 0.6176 moles of toluene. We also know that we have 1.024 moles of benzene. So we put these numbers into the equation for the total moles:

Total moles = 0.6176 + 1.024

And we add these numbers together. The calculator says that 0.6176 + 1.024 = 1.6416. Thus, we know that the Total moles = 1.6416 moles.

Now we have enough information to find the mole fraction of toluene. We know that there are 0.6176 moles of toluene, and the Total moles is equal to 1.6416.

So now we put these numbers in the mole fraction equation:

0.6176 / 1.6416

The calculator says that 0.6176 / 1.6416 = 0.3762. So the mole fraction of toluene is 0.3762. We should round this mole fraction to 3 significant figures because the numbers we were given in the problem (56.9 and 80.0) have 3 significant figures. If we round 0.3762 to 3 significant figures, we get 0.376. So the mole fraction of toluene is 0.376.