What are the mole fractions of the components of the solution formed when 92 g glycerol is mixed with 90 g water?

Question

Peyton Adams · Accepted Answer

You can read how to calculate mole fractions in:
How do you calculate mole fractions?

In your problem,

#n_"glycerol"# = 92 g glycerol × #(1"mol glycerol")/(92.09"g glycerol")# = 0.9990 mol glycerol (2 significant figures + 2 guard digits)

#n_"water"# = 90 g water × #(1"mol water")/(18.02"g water")# = 4.994 mol water

#n_"total" = n_"glycerol" + n_"water"# = 0.9990 mol + 4.994 mol = 5.993 mol

The mole fraction #Χ# of glycerol is

#Χ_"glycerol" = n_"glycerol"/n_"total" = (0.9990"mol")/(5.993"mol")# = 0.17

The mole fraction of water is

#Χ_"water" = n_"water"/n_"total" = (4.994"mol")/(5.993"mol")# = 0.83

Note: The required answers can have only 2 significant figures, because that is all you gave for the masses of glycerol and water.

Hope this helps.

Xavier Avery · Answer

undefined To find the mole fractions of the components in the solution, first, calculate the number of moles of each component. Then, determine the total moles of the solution. Finally, divide the moles of each component by the total moles to find the mole fractions.

1. Calculate moles of glycerol:
   $ \text{Molar mass of glycerol (C3H8O3)} = 92.09 \, \text{g/mol} $
   $ \text{Moles of glycerol} = \frac{92 \, \text{g}}{92.09 \, \text{g/mol}} $

2. Calculate moles of water:
   $ \text{Molar mass of water (H2O)} = 18.02 \, \text{g/mol} $
   $ \text{Moles of water} = \frac{90 \, \text{g}}{18.02 \, \text{g/mol}} $

3. Total moles of the solution:
   $ \text{Total moles} = \text{moles of glycerol} + \text{moles of water} $

4. Mole fraction of glycerol:
   $ \text{Mole fraction of glycerol} = \frac{\text{moles of glycerol}}{\text{total moles}} $

5. Mole fraction of water:
   $ \text{Mole fraction of water} = \frac{\text{moles of water}}{\text{total moles}} $

Perform the calculations to find the mole fractions of glycerol and water in the solution.