Question 23 When 793. mg of a certain molecular compound X are dissolved in 85. g of cyclohexane C6H12, the freezing point of the solution is measured to be 4.7 °C. Calculate the molar mass of X. If you need any additional information on cyclohexane, 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.

102.7 g/mol is the molar mass for compound X

Explanation:

Colligative property of freezing point depression should be used here:

ΔT = Kf . m . i

We assume compound x is not ionic, so i = 1 (Van't Hoff)

Freezing T° of pure solvent - Freezing T° solution = Kf . molality . i

6.59°C - 4.7°C = 20.8 °C/m . m . 1

1.89°C / 20.8 m/°C = m → 0.0908 mol/kg

Molality refers the moles of solute that corresponds to 1 kg of solvent, but in this case our solvent's mass is 85 g.

We convert the mass to kg in order the know, the moles of solute:

85 g. 1kg/ 1000 g = 0.085 kg

0.0908 mol/kg . 0.085 kg =7.72×10⁻³ moles

These are the moles that corresponds to 0.793 g of compound

(793 mg . 1 g/1000mg = 0.793g)

Molar mass = g/mol → 0.793 g / 7.72×10⁻³ mol = 102.7 g/mol

The molar mass of compound X is 104.8 g/mol

Explanation:

Step 1: Data given

Mass of compound X = 793 mg = 0.793 grams

Mass of cyclohexane = 85 grams = 0.085 kg

freezing point of the solution = 4.7 °C

Freezing point cyclohexane = 6.5 °C

Freezing point depression constant cyclohexane = 20.2 °C/m

Step 2: Calculate molality

ΔT = i*Kf*m

⇒ΔT  = freezing point depression = 6.5 - 4.7 = 1.8 °C

⇒ i = the van't hoff factor = 1

⇒ Kf = Freezing point depression constant cyclohexane = 20.2 °C/m

⇒ m = the molality = ?

1.8 = 20.2 * m

m = 1.8 / 20.2

m = 0.0891 molal

Step 3: Calculate moles of compound X

molality = moles compound X / mass cyclohexane

0.0891 molal = moles compound X / 0.085 kg

moles compound X = 0.0891 molal * 0.085 kg

moles compound X = 0.00757 moles

Step 4: Calculate molar mass compound X

Molar mass = mass / moles

Molar mass = 0.793 grams / 0.00757 moles

Molar mass = 104.8 g/mol

The molar mass of compound X is 104.8 g/mol