Chapter 13, Problem 39PS

### 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

# An aqueous solution containing 1.00 g of bovine insulin (a protein, not ionized) per liter has an osmotic pressure of 3.1 mm Hg at 25 °C. Calculate the molar mass of bovine insulin.

Interpretation Introduction

Interpretation: The molar mass of bovine insulin has to be determined if the solution has an osmotic pressure of 3.1mmHg at 25°C.

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 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

Explanation

Given,

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 bovine insulin is 1.00â€‰g

â€‚Â Osmotic pressure,Ï€â€‰=â€‰3.1â€‰mmâ€‰Hg

The osmotic pressure of the solution is,

â€‚Â Ï€â€‰=â€‰cRT

Hence,

The concentration is calculated by,

â€‚Â Concentration,câ€‰=â€‰Ï€RT=â€‰(3.1â€‰mmâ€‰Hg)(1â€‰atm760â€‰mmâ€‰Hg)(0.082057â€‰â€‰L.atmâ€‰Kâˆ’1â€‰molâˆ’1)(298.2â€‰K)=â€‰1.6669â€‰Ã—â€‰10âˆ’4â€‰mol/L

The amount of bovine insulin dissolved in one liter of water is,

â€‚Â 1

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