When 551. mg of a certain molecular compound x are dissolved in 100 g of benzonitrile (ch, cn), the freezing point of the solution is measured to be 13.4 °c. calculate the molar mass of x. if you need any additional information on benzonitrile, use only what you find in the aleks data resource. also, be sure your answer has a unit symbol, and is rounded to the correct number of significant digits.

M1 = 49.04 g/mol

Explanation:

The pure benzonitrile has freezing point -12.8°C. By adding  a nonvolatile compound, the freezing point will be changed, a process called cryoscopy. The freezing point will be reduced. In this case, the new freezing point is -13.4°C. The variation at the temperature can be calculated by the equation:

ΔT = Kc*W*i

Where ΔT is the variation at the freezing temperature (without the solute less with the solute), Kc is the cryoscopy constant (5.34 for benzonitrile), W is the molality, and i the Van't Hoff correction factor, which is 1 for benzonitrile.

((-12.8-(-13.4)) = 5.34*W

5.34W = 0.6

W = 0.1124 mol/kg

W = m1/M1*m2

Where m1 is the mass of the solute (in g), M1 is the molar mass of the solute (in g/mol), and m2 is the mass of the solvent (in kg).

m1 = 0.551 g, m2 = 0.1 kg

0.1124 = 0.551/M1*0.1

0.01124M1 = 0.551

M1 = 49.04 g/mol

yes it is balanced