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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.

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Answer:

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

The molar mass of compound X is 104.8 g/mol. This can be calculated by using freezing point depression.

Given:

Mass of compound X = 793 mg = 0.793 grams

Mass of cycl-ohexane = 85 grams = 0.085 kg

Freezing point of the solution = 4.7 [tex]^oC[/tex]

Freezing point cycl-ohexane = 6.5 [tex]^oC[/tex]

Freezing point depression constant cycl-ohexane = 20.2 [tex]^oC[/tex]/m

Freezing point depression:

ΔT = i* Kf *m

ΔT  = freezing point depression = 6.5 - 4.7 = 1.8 [tex]^oC[/tex]

Kf = Freezing point depression constant cycl-ohexane = 20.2 [tex]^oC[/tex]/m

To find:

m = molality = ?

On subsituting the values:

1.8 = 20.2 * m

m = 1.8 / 20.2

m = 0.0891 m

Calculation of moles:

Molality = moles compound X / mass cyclohexane

0.0891 molal = moles compound X / 0.085 kg

moles of compound X = 0.0891 molal * 0.085 kg

Moles of compound X = 0.00757 moles

Calculation of molar mass:

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.

Find more information about Freezing point depression here:

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