Question

A biomedical engineer is working in a lab that is isolating gene fragments. She dissolves a 10.0mg sample in enough water to make 30.0mL of solution. The osmotic pressure of the solution is 0.340torr at 25C. What is the molar mass of the gene fragment

Answer 1

Answer: The molar mass of the gene fragment is 5466021.2 g/mol

Explanation:

To calculate the molar mass of solute, we use the equation for osmotic pressure, which is:

$\pi=iMRT$

Or,

$\pi=i\times \frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Volume of solution (in mL)}}\times RT$

where,  

$\pi$ = osmotic pressure of the solution = 0.340 torr

i = Van't hoff factor = 1 (for non-electrolytes)

Mass of solute = 10.0 mg = 0.010 g    (Conversion factor:  1 g = 1000 mg)

Volume of solution = 30.0 mL

R = Gas constant = $62.364\text{ L. torr }mol^{-1}K^{-1}$

T = temperature of the solution = $25^oC=[273+25]=298K$

Putting values in above equation, we get:

$0.340torr=1\times \frac{0.010\times 1000}{\text{Molar mass of gene fragment}\times 300}\times 62.364\text{ L. torr }mol^{-1}K^{-1}\times 298K\\\\\text{Molar mass of gene fragment}=\frac{1\times 0.010\times 1000\times 62.364\times 298}{0.340}=5466021.2g/mol$

Hence, the molar mass of the gene fragment is 5466021.2 g/mol