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 1.2 g `mL^(-1)`, then what shall be the molarity of the solution?

Explanation

Mass of solution = 100 g
Mass of glucose = 10 g
Mass of solvent (water) `=100-10=90g = 0.09kg`
Molar mass of glucose,
`C_(6)H_(12)O_(6)=6xx12+12xx1+6xx16=180"g mol"^(-1)`
Molarity `=("No. of moles of solute")/("Mass of solvent (in kg)")`
`=("Mass of solute")/("Molar mass of solute") xx (1)/("Mass of solvent in kg")`
`=(10)/(180xx0.09)=0.617m`
Number of moles of glucose `=(10)/(180) =0.055`
Number of moles of water`=(90)/(18)=5.0`
Mole fraction of glucose, `x_(B)=(0.055)/(5+0.055)=0.0108`
Mole fraction of water, `x_(A)=1-x_(B)=1.0-0.0108=0.9892`
Density of solution `=1.2"g mL"^(-1)`
Volume of solution `=("Mass")/("Density")=(100)/(1.2)=83.33mL`
Molarity `=("No. of moles of solute")/("Volume of solution (mL)") xx 1000 = (10xx1000)/(180xx83.33)`
`=0.67M`