1.0 g of a protein is dissolved in 100 ml of distilled water. The resulting solution has an osmotic pressure of 0.001 atm at room temperature. What is the molecular weight of the protein?

The molar mass of the protein is 244678.2 g/mol

Explanation:

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

where,

= osmotic pressure of the solution = 0.001 atm

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

c = molarity of solute = ?

R = Gas constant =

T = temperature of the solution =

Putting values in above equation, we get:

To calculate the molecular mass of solute, we use the equation used to calculate the molarity of solution:

We are given:

Molarity of solution =

Given mass of protein = 1.0 grams

Volume of solution = 5.00 mL  

Putting values in above equation, we get:  

Hence, the molar mass of the protein is 244678.2 g/mol

the ideal gas law equation is as follows

pv = nrt

where p - pressure

v - volume

n - number of moles

r - universal gas constant

t - temperature

so if the pressure, volume and temperature are already known

we are left with n and r

since r is the universal gas constant that has a known fixed value then r too is known

so we are left with 'n'

once we know temperature volume and pressure

we can find the number of moles of gas present using the ideal gas law equation

this is not my own answer, this is an answer for the same question by the user blahblahmali. i do not claim ownership of this account.