Question

Vapor Pressure of pure ethanol is 40.0 torr at 19 degrees C

3.42g of sugar (C12H22O11, non-volatile, non-electrolyte) is added to 50.0 mL of ethanol (C2H6O, 0.79 g/mL, melting point = -114 degrees C, Kf = 1.99 degrees C/m)

a. Calculate the vapor pressure of the sugar/ethanol solution @ 19 degrees C.

b. Calculate the melting point of the sugar/ethanol solution.

Answer 1

Vapor Pressure of pure ethanol is 40.0 torr at 19 degrees C

3.42g of sugar (C12H22O11, non-volatile, non-electrolyte) is added to 50.0 mL of ethanol (C2H6O, 0.79 g/mL, melting point = -114 degrees C, Kf = 1.99 degrees C/m)

a. Calculate the vapor pressure of the sugar/ethanol solution @ 19 degrees C.

Use Raoult's Law:

Moles of sugar: 3.42 g / 342.2965 g/mol

= 0.01 moles sugar

Mass of ethanol = density * volume

= 0.79 g/mL * 50.0 ml

=39. 5g

Moles of ethanol = 39.5 g/ 46.06844 g/ mole

= 0.86 moles

Moles fraction of solvent ; ethanol = moles of ethanol / total moles

= 0.865/0.86+0.01

= 0.989

Here P°_solvent=40.0 torr

P_solution = (χ_solvent) (P°_solvent)

x = (0.989) (40.0 torr)

x = 39.54 torr

b. Calculate the melting point of the sugar/ethanol solution.

Molality:

The molality of solute is the ratio of mole of solute to the mass (in kilogram) of solvent.it is denoted by, and the unit of molality is .

   

Here, number of mole and mass of solvent in kilogram.

Moles of sugar: 3.42 g / 342.2965 g/mol

= 0.01 moles sugar

Mass of ethanol = density * volume

= 0.79 g/mL * 50.0 ml

=39. 5g = 0.0385 kg

Molality = 0.01/ 0.0395 kg

= 0.253 m

dT = Kf x m x i

dT = change in freezing point

Kf = freezing point depression constant of the solvent ;

= 1.99 degrees C/m
m = molality = moles solute / kg solvent; 0.253 m

i = van't hoff factor = number of ions each molecule of solute dissociates into for sucrose it is 1.

dT = 1.99 degrees C/m x 0.253 x 1

dT =0.504 degrees C

here melting point = -114 degrees C, Kf = 1.99 degrees C/m)

the melting point of the sugar/ethanol solution = T1+ dT

= -114 degrees +0.504 degrees C

=-113.5 degrees