Calculate the molar mass of the protein

Question

488 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 0.107atm

at 25.0°C.

Calculate the molar mass of the protein. Round your answer to 

3 significant digits.

Answer 1

Hi Amani, I can give this one a try.

Ok, so first I would start off by converting the mass from mg to g, the volume from ml to L, and the temperature from C to K. We don't want the mass in mg, we want it in in g, we don't want the volume in ml, we want it in L, and we don't want the temperature in C, we want it in K:

m = 488 mg => m = 488 mg*(1 g/1,000 mg) = 0.488 g

m = 0.488 g

V = 5 ml => V = 5 ml*(1 L/1,000 ml) = 0.005 L

V = 0.005 L

T = 25.0°C => T = (25.0°C + 273.15)K

T = 298.15 K

Let M be the molar of the unknown protein and let n be the number of moles of the unknown protein:

n = m/M

Using this equation, the concentration of the solution can be represented as:

C = n/V, or C = m/M*V

We are given the osmotic pressure: 0.107 atm.

We need to use the following formula, and rearrange to solve for M:

Π = CRT, or equivalently Π = (m/M*V)RT

Substituting our values in, we get:

0.107 atm = (0.488 g/M*0.005 L)(0.08206 L*atm/K*mol)*(298.15 K)

Using a bit of algebra, we should get that M = 0.488 g/0.0000219 mol = 2.228*10^4 g/mol

Thus, the molar mass rounded to 3 significant figures is 2.23*10^4 g/mol.