Chapter 13, Problem 44PS

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# Anthracene, a hydrocarbon obtained from coal, has an empirical formula of C7H5. To find its molecular formula, you dissolve 0.500 g in 30.0 g of benzene. The boiling point of pure benzene is 80.10 °d whereas the solution has a boiling point of 80.34 °C. What is the molecular formula of anthracene?

Interpretation Introduction

Interpretation: The molecular formula of anthracene has to be determined.

Concept introduction:

Colligative properties: Properties of solutions which having influence on the concentration of the solute in it. Colligative properties are,

• Decrease in the vapor pressure
• Increase in the boiling point
• Decline in the freezing point
• Osmotic pressure

Change in boiling point is calculated by using the equation,

ΔTbp=Kbpmsolute

where,

Kbp is the molal boiling point elevation constant.

The number of moles of any substance can be determined using the equation

Numberofmole=GivenmassofthesubstanceMolarmass

Explanation

The molecular formula of anthracene is determined.

Given,

â€‚Â Î”Tâ€‰=â€‰(80.340Câ€‰âˆ’â€‰80.100Câ€‰)â€‰=â€‰0.240C

â€‚Â Mass of orange crystalline compound is 0.500â€‰g

â€‚Â Mass of benzene is 30â€‰gâ€‰=â€‰0.03â€‰kg

â€‚Â Molal boiling point elevation constant of benzene is 2.530C/m

Change in boiling point is calculated by using the equation,

â€‚Â Î”Tbpâ€‰=â€‰Kbpâ€‰msolute

Hence,

The concentration is calculated by,

â€‚Â Concentration,msolute=â€‰Î”TbpKbp=â€‰(â€‰0.240C)(2.530C/m)=â€‰0.09486â€‰m

The amount of compound dissolved is,

â€‚Â (0.09486â€‰m1â€‰kg)â€‰(0.03â€‰kg)=â€‰2

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