The normal freezing point of cyclohexane is 6.55 c. when 0.458 g of benzophenone is dissolved in 15.0 g of cyclohexane, the freezing point is found to be 3.19 c. what is the experimental molar mass of benzophenone? (kf cyclohexane = 20.0 c m^-1).
a) 182
b) 18.0
c) 89.3
d) 160
e) 360

The experimental molar mass of benzophenone is 182 g/m (option A)

Explanation:

ΔT = Kf . m . i

(i means the Van't Hoff factor,  since benzophenone is not electrolyte, the value for i is 1)

ΔT = T° - T' (Melting temp sv pure - Melting temp sv in sl)

Kf is data (the cryoscopic constant)

m is molality (moles from solute in 1kg of solvent)

6,55°C - 3,19°C = 20,0° C/m . m

3,36 °C = 20,0 C/m . m

3,36 °C /20,0 m/C = m

0,168 = m

We have 0,168 moles of benzophenone in 1 kg of cyclohexane but we don't have 1kg, we have just 15 g so, we need the rule of three.

1000 g 0,168 moles

15 g  (15 g . 0,168 m) / 1000 g = 0,00252 m

Now we can get the molar mass:

0,458 g of benzophenone / 0,00252 moles = 181,7 g/m