What is the molar mass of a protein if a solution of 0.020 g of the protein in 25.0 mL of solution has an osmotic pressure of 0.56 torr at 25 ∘ C

26.5 kD  

Explanation:

Here we can apply the formula ∏ = iMRT, where ∏ = osmotic pressure = 0.56 - ( given ). This is only one part of the information we are given / can conclude in this case

i = van’t Hoff factor = 1 for a protein molecule,

R = gas constant = 62.36 L torr / K-mol,

T ( temperature in Kelvin ) = 25 + 273 - conversion factor C° + 273 = 298K

( Known initially ) ∏ = osmotic pressure = 0.56 torr

besides the part " M " in the formula, which we have no information on whatsoever, as we have to determine it's value.

Substitute derived / known values to solve for M ( moles / liter ) -

∏ = iMRT

⇒ 0.56 = ( 1 )( M )( 62.36 )( 298 )

⇒ 0.56 = M( 18583.28 )

⇒ M = 0.56 / 18583.28 ≈ 0.00003013461

We know that M = moles / liter, so we can use this to solve for moles, and hence calculate the molar mass by the formula molar mass = g / mol -

M = mol / l

⇒ 0.00003013461 = 0.020 / 25 mL ( 0.025 L ),

0.020 / 0.025 = 0.8 g / L

⇒ 0.8 g = 0.00003013461 moles,

molar mass = 0.8 g / 0.00003013461 moles = 26,548 g / mol = 26.5 kD  

the correct answer would be d. hope this !