   Chapter 24, Problem 36IL

Chapter
Section
Textbook Problem

Insulin is a protein important in the metabolism of sugar. Its molar mass can be determined by means of an osmotic pressure experiment. A 50.0-mg sample of insulin was dissolved in enough water to make 100. mL of solution. This solution was determined to have an osmotic pressure of 21.8 mm H2O. What is the molar mass of insulin? (Hint: The density of mercury is 13.6 g/mL.)

Interpretation Introduction

Interpretation:

The molar mass of insulin has to be calculated.

Concept introduction:

Insulin is the protein which helps in metabolism of sugars. This is a hormone which regulate the blood sugar level in the body. After taking food, insulin is secreted in our body when blood glucose level is high.

Osmotic pressure is the colligative property. Osmotic pressure is minimum amount of pressure required to stop osmosis process.

The relation between osmotic presuure and concentration of the solution is given by following expression:

π = CRT

Here,

C=m (g)M (g.mol1)V (L)

Substitute the value of C,

π = (mMV)(RT)

Here,

π= Osmotic pressure in atm.

m= Mass of solute in g.

M= Molar mass in g.mol1.

R= Gas constant in Latmmol1K1.

T= Temprature in K.

V= Volume in L.

Explanation

Calculate the molar mass of insulin.

Given:

Osmotic pressure is 0.02868 atm.

Mass of solute is 0.050 g.

Gas constant is 0.0821 Latmmol1K1.

Temperature value at room temperature is 298 K.

Volume of the solution is 0.100 L.

The value of molar mass is calculated by using following expression,

π = (mMV)(RT)

Rearrange for the molecular mass M,

M= mRTπV

Subsitute the given values,

M=(0

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