# A solution contains 180 g of glucose and 162 g of water. What is the mole fraction of glucose?

Aug 22, 2016

${\chi}_{\text{glucose}} = 0.10$

#### Explanation:

In order to find the mole fraction of glucose in this solution, you need to know

• the number of moles of glucose
• the total number of moles present in the solution

To find the number of moles of glucose present in $\text{180 g}$, use the compound's molar mass, which is equal to ${\text{180.16 g mol}}^{- 1}$.

Your sample of glucose will thus contain

180 color(red)(cancel(color(black)("g"))) * overbrace("1 mole glucose"/(180.16color(red)(cancel(color(black)("g")))))^(color(blue)("molar mass of glucose")) = "0.9991 moles glucose"

Now do the same for water, using the fact that its molar mass is equal to ${\text{18.015 g mol}}^{- 1}$

162 color(red)(cancel(color(black)("g"))) * overbrace("1 mole water"/(18.015color(red)(cancel(color(black)("g")))))^(color(purple)("molar mass of water")) = "8.9925 moles water"

The total number of moles present in this solution will be

${n}_{\text{total" = "0.9991 moles" + "8.9925 moles" = "9.9916 moles}}$

Now, the mole fraction of glucose is equal to the number of moles of glucose divided by the total number of moles present in solution.

In your case, this is equal to

chi_"glucose" = (0.9991 color(red)(cancel(color(black)("moles"))))/(9.9916color(red)(cancel(color(black)("moles")))) = 0.10

The answer is rounded to two sig figs, the number of sig figs you have for the mass of glucose.