John dissolves .5g of a white powder in 25g of benzene (FP 5oC) (kf benzene is 5.1) and finds the solution freezes at 3.7oC. Determine the MW of the compound!

Question

John dissolves .5g of a white powder in 25g ofbenzene (FP 5oC) (kf benzene is 5.1) and finds the solution freezes at 3.7oC. Determine the MW of the compound! 

Answer 1

Begin with the equation for for freezing point depression.

delta T_f = K_f x m

Because the solvent is benzene, we assume that the solute will produce 1 particle per mole when dissolved.

Step 1. Use the first equation to calculate the molality (m) of the solution.

m = delta T_f / K_f = (5.0 ⁰C - 3.7 ⁰C) / 5.1 ⁰C = 0.255 m

Now, recall the definition of molality, m = moles of solvent / kg of solvent

Now, calculate the moles of solute = 0.5 g/ MM, where MM is the molar mass of solute.

And the mass of solvent = 25 g / 1000 g/kg = 0.025 kg

Step 2. Use the value for molality from Step 1 to find the molar mass of solute.

m = 0.255 = (0.5 g/MM) / (0.025 kg)

Step 3. Calculate number of moles and sole for molar mass (MM).

MM = (0.5 g / MM) = 0.025 kg x 0.255 mol/kg = 0.00638 mol

So, MM = 0.5 g / 0.00638 mol = 78.4 g/ mol