Question

100. mg of an unknown protein are dissolved in enough solvent to make 5.00mL of solution. The osmotic pressure of this solution is measured to be 0.0766 atm at 25.0 degree C . Calculate the molar mass of the protein. Be sure your answer has the correct number of significant digits.

Answer 1

molar mass is
`6.39*10^3\ g/mol`

Step-by-step explanation:

Osmotic pressure is related with concentration as follows:

`\pi =CRT`

Where, C is concentration or molarity , R is gas constant and T is temperature.

Osmostic pressure given is 0.0766 atm

R is
`0.0821 L \ atm \ K^(1)mol^(-1)`

T = 25 + 273 = 298 K

Rearrange the above equation to calculate concetration of the solution as follows:

C = P/RT

`C=(0.0766)/(0.0821 * 298) \\=0.00313\ M`

molarity = moles/volume in L

moles = molarity × volume in L

volume = 5.00 mL = 0.005 L

moles = 0.00313 × 0.005

=
`1.565 * 10^(-5)`

`molar\ mass=(mass\ in\ g)/(moles) \\=(0.1\ g)/(1.565* 10^(-5)mol) \\=6.389* 10^3\ g/mol\\`

Therefore, molecular mass of protein is
`6.39*10^3\ g/mol`