Question

A 0.588 g sample of a nonvolatile, yellow crystalline solid dissolves in 11.5 g of benzene, producing a solution that freezes at 5.02 oC. Find the molar mass of the yellow solid. The following may be useful: The freezing point of benzene is 5.51 oC and the freezing point depression constant, kf, is 4.90 oC/m.

Answer 1

The molar mass of the solid is 511.3 g/mol

Step-by-step explanation:

Step 1: Data given

Mass of the sample = 0.588 grams

Mass of benzene = 11.5 grams

The solution freezes at 5.02 °C

The freezing point of benzene is 5.51 °C

The freezing point depression constant, kf = 4.90 °C/m

Step 2: Determine the temperature change

Δt = 5.51 - 5.02 = 0.49°C

Step 3: Determine number of moles

Δt = i*Kf*m

⇒ with i = the number of dissolved particles the solute produces = 1

⇒ with Kf = the molal freezing point depression constant Kf = 4.90 °C*Kg/mol

⇒ with m = the molality of the solute

0.49 °C = (1) (4.90 °C kg/mol) (x / 0.01150 kg)

x = 0.00115 mol

Step 4: Calculate molar mass

0.588 grams / 0.00115 mol = 511.3 g/mol

The molar mass of the solid is 511.3 g/mol