Please show all work Thanks 1 When a 491 g sample of an unkn

Please show all work. Thanks!

1. When a 49.1 g sample of an unknown compound is dissolved in 500. g of benzene, the freezing point of the resulting solution is 3.77 degrees C. The freezing point of pure benzene is 5.48 Degrees C and Kf for benzene is 5.12 degrees C/m. Calculate the molar mass of the unknown compound.

2. A metal crystallizes with a face centered cubic lattice. The edge of the unit cell is 395 pm. The diameter of the metal atom is:?

3. How many grams of ice would be melted by the energy obtained as 16.2g of steam is condensed at 100 degrees C and cooled to 0 degrees C?

specific heat (ice)= 2.10 J/g*C

specific heat (water)= 4.18 J/g*C

heat of fusion= 333 J/g

heat of vaporization= 2258 J/g

Solution

1. Decrease in freezing point= 5.48-3.77 = 1.71

Let molality of compound= m

Kf = 5.12/m

DeltaTf = i*Kf*m

m = deltaTf/i*Kf

m = 1.71/1*5.12/m = 0.328m

Molality = moles of compound/Mass of solvent in kg

Moles of unknown compound = 0.328m*0.5kg = 0.164moles

Molar mass = mass/moles = 49.1g/0.164moles

Molar mass = 299.39g/mol