The formula for freezing point depression is:
ΔT = Kf * m --->1
Where,
ΔT = change in temperature = 2.88 degrees Celcius
Kf = freezing point molar constant of solvent
m = molality (moles solute/mass solvent)
First we calculate for molality since we are given the mass of solute and solvent.
Molar mass of pentane = 72.15 g / mol
molality m= (0.123 g / 72.15 g / mol) / (2.493 x 10^-3 kg)
m = 0.684 molal
Going back to equation 1:
ΔT = Kf * m
2.88 = Kf * 0.684
Kf = 4.21 degC / molal
Value for Kf in question 1 given that m = 0. 829 mol/kg:
2.88 = Kf * 0.829
Kf = 3.47 degC / molal