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.

713.33 g/mol

Explanation:

The freezing-point depression equation is:

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:

Now we calculate the moles of X that were added:

75 g ⇒ 75/1000 = 0.075 kg

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