A solution of glucose in water is labelled as 10% w/w, what would be the molality and mole fraction of each component in the solution? If the density of solution is 1.2 g mL–1, then what shall be the molarity of the solution?

Step-1

What is given in problem?

In this problem mass of glucose is 10%w/w

So take mass of total solution = 100 g

Then mass of glucose will = 10% of 100 g = 10 grams

Mass of water will = 100 – 10 = 90 grams

And density = 1.2gmL-1

Step-2

find molality

Molality = number of moles of solute / mass of solvent in Kg   ……(1)

Here have to find number of moles and mass of solvent in Kg both

mass of solute  = mass of glucose / molar mass of glucose  …..(2)

Molar mass of glucose (C6H12O6)  = 6*C +  12*H + 6*O

= 6*12 + 12*1 +  6*16

=180 g /mol

Plug the value back in equation (2) we get

Number of moles =  10/180  = 0.0556 moles

We have mass of solvent (H2O)  =  90 g

Mass in Kg  = 90 g* 1 Kg / 1000 g    = 0.09 Kg

Plug the value in equation (1) we get

Molality  =  0.0556/0.09   = 16.7M

Step – 3 

Find molar fraction

Molar fraction of glucose  = number of moles of glucose / total number of moles

Molar mass of water (H2O) = 2*H+ O  = 2*1 + 16  = 18 g/ mol

Number of moles of water  = 90/18 = 5 moles

Plug the value in formula we get

 Mole fraction  = 0.0556/(0.0556+ 5)  = 0.01

It is binary solution because it has 2 component only so molar fraction of

Water  =1 – mole fraction of glucose

            = 1-0.01  =0.99

Step – 4

Find the molarity ,

molarity = number of moles of solute / volume of solution in liter        ……….(1)

Volume = mass / density

            = 100 g / 1.2 g/ ml  = 83.33 ml

Mass in liter  = 83.33 * 1 liter /1000 ml   = 0.0833liter

Plug the value back equation (1) we get

Molarity = 0.0556/ 0.0833

               = 0.67 M