Question

When 10.5g of a certain molecular compound X are dissolved in 75g of benzonitrile(C6H5CN) , the freezing point of the solution is measured to be -13.8°C. Calculate the molar mass of x.

Answer 1

713.33 g/mol

Step-by-step explanation:

The freezing-point depression equation is:

• ΔT = Kf * m

Where ΔT is the difference in temperature. The freezing point of pure benzonitrile is -12.75 °C, so ΔT = -12.75 - (-13.8) = 1.05 °C

Kf is the cryopscopic constant, which is 5.35 °C/m (as reported by the CRC Handbook).

m is the molality (moles compound X/kg benzonitrile).

So first we calculate the molality:

• ΔT = Kf * m

• 1.05 °C = 5.35 °C/m * m

• m = 0.196

Now we calculate the moles of X that were added:

75 g ⇒ 75/1000 = 0.075 kg

• 0.196 m = mol X / 0.075 kg

• mol X = 0.0147 mol X

Finally we calculate the molar mass of X, using the added mass:

• 10.5 g / 0.0147 mol = 713.33 g/mol