Chapter 13, Problem 92IL

### 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

# In chemical research we often send newly synthesized compounds to commercial laboratories for analysis. These laboratories determine the weight percent of C and H by burning the compound and collecting the evolved CO2 and H2O. They determine the molar mass by measuring the osmotic pressure of a solution of the compound. Calculate the empirical and molecular formulas of a compound, CxHyCr, given the following information: (a) The compound contains 73.94% C and 8.27% H; the remainder is chromium. (b) At 25 °C, the osmotic pressure of a solution containing 5.00 mg of the unknown dissolved in exactly 100 mL of chloroform solution is 3.17 mm Hg.

Interpretation Introduction

Interpretation Empirical formula and molecular formula of the compound is 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

Osmotic pressure: The pressure created by the column of solution for the system at equilibrium is a measure of the osmotic pressure and is calculated by using the equation,

π=cRT

where,

c is the molar concentration

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

Numberofmole=GivenmassofthesubstanceMolarmass

Empirical formula: The simplest integer ratio of the element in a chemical formula. It can be obtained by reducing the ratio of elements to the simplest integer form of a molecular formula.

Explanation

Given,

â€‚Â Molar mass of carbon is 12.01â€‰g/mol

â€‚Â Molar mass of hydrogen is 1.01â€‰g/mol

â€‚Â Molar mass of chromium is 52.00â€‰g/mol

â€‚Â Râ€‰=â€‰0.082057â€‰L.atmÂ Kâˆ’1molâˆ’1Tâ€‰=â€‰250Câ€‰=â€‰(25â€‰+â€‰273.2)â€‰Kâ€‰=â€‰298.2â€‰K

â€‚Â Mass of the unknown compound is 5.00â€‰mgâ€‰=â€‰0.005â€‰g

â€‚Â Osmotic pressure,Ï€â€‰=â€‰3.17â€‰mmâ€‰Hg

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

â€‚Â Numberâ€‰ofâ€‰moleâ€‰=Givenâ€‰massâ€‰ofâ€‰theâ€‰substanceMolarâ€‰massâ€‰

â€‚Â Massâ€‰ofâ€‰Câ€‰=â€‰73.94â€‰100â€‰Ã—â€‰100â€‰gâ€‰=73.94â€‰gMassâ€‰ofâ€‰Hâ€‰=â€‰8.27â€‰100â€‰Ã—â€‰100â€‰gâ€‰=8.27â€‰gMassâ€‰ofâ€‰Crâ€‰=â€‰17.79â€‰100â€‰Ã—â€‰100â€‰gâ€‰=17.79â€‰gâ€‰

â€‚Â NumberÂ ofÂ molesâ€‰ofâ€‰Câ€‰=â€‰73.94â€‰g12.01â€‰g/mol=â€‰6.6â€‰mol

â€‚Â NumberÂ ofÂ molesâ€‰ofâ€‰Hâ€‰=â€‰8.27â€‰g1.01â€‰g/mol=â€‰8.2â€‰mol

â€‚Â NumberÂ ofÂ molesâ€‰ofâ€‰Crâ€‰=â€‰17.79â€‰g14.01â€‰g/mol=â€‰0.34â€‰mol

Empirical formula of the compound was determined.

â€‚Â C:H:Crâ€‰6.60.34:8.20.34:0

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