To determine the freezing point of the solution, we can use the formula for freezing point depression:
∆Tf=i⋅Kf⋅mWhere:
∆Tf is the freezing point depression
i is the van '
t Hoff factor (since propane is a non-electrolyte,
i=1 )
Kf is the freezing point depression constant
(5.12∘C∕m. for benzene)
m is the molality of the solution
The molality
(m) is given by the formula:
m=‌| ‌ moles of solute ‌ |
| ‌ kilograms of solvent ‌ |
First, we need to calculate the moles of propane. The molar mass of propane
(C3H8) is:
3×12.01g∕mol+8×1.01g∕mol=44.09g∕molThus, the moles of propane are:
‌=0.4536‌moles Next, we need to convert the mass of benzene from grams to kilograms:
400g=0.4‌kgNow, we can calculate the molality (m) of the solution:
m=‌=1.134‌mol∕kg Now, we can calculate the freezing point depression:
∆Tf=1×5.12∘C∕m×1.134‌mol∕kg=5.804∘C
Finally, we can determine the new freezing point of the solution by subtracting the freezing point depression from the normal freezing point of benzene:
Freezing point of solution
=5.48∘C−5.804∘C=−0.324∘CThus, the closest answer to our calculated value is:
Option A:
−0.34∘C