The heat of fusion of pure nitric oxide (NO) is 2.30 kJ/mol at its freezing point of -164 oC (when pressure is 1 atm). Suppose you add 112 grams of a fully soluble, non-dissociating substance to 1000 g of nitric oxide. You measure the freezing point temperature of the solution to be 0.177 oC lower than the pure solvent freezing point temperature. What is the molar mas?

Where m is the molality of the solute in NO, Kf is the cryoscopic constant (in K·kg/mol), and i is 1 in this case (because the substance in non-dissociating).

We can calculate Kf of NO with the information given by the problem and the formula:

Kf = R * M * Tf² / ΔH

Where R is the universal gas constant (8.314 J·mol⁻¹·K⁻¹), M is the molar mass of NO (30 g/mol, or 0.03 kg/mol), T f is the freezing point of NO (in K), and ΔH is the heat of fusion.

Kf = 8.314 J·mol⁻¹·K⁻¹ * 0.03 kg/mol * (109.16 K)² ÷ 2300 J/mol = 1.292 K·kg/mol

Now we calculate the molality of the solute in NO:

ΔT = Kf * m * i

0.177 = 1.292 * m

m = 0.1370 m

Molality is equal to the moles of solute per kilogram of solvent:

0.1370 m = moles solute/ 1 kg NO

moles solute = 0.1370 moles

With the given mass of the solute we can calculate the molar mass:

112 g / 0.1370 moles = 817.66 g/mol