0.10 g of a protein is added to 250 cm³water at 298 K and the osmotic pressure is measured as 255 Pa. Estimate the relative molecular mass of the protein.

Question

Quizplus · Accepted Answer

The osmotic pressure (π) can be calculated using the equation:

π = MRT

where M is the molarity of the solution, R is the gas constant, and T is the temperature in Kelvin.

Since we know the osmotic pressure (π), the temperature (T), and the volume of the solution (250 cm3), we can calculate the molarity (M) using the rearranged equation:

M = π / RT

M = (255 Pa) / (8.31 J K-1 mol-1 * 298 K)

M = 0.0103 mol dm-3

Now, we can use the definition of molarity to calculate the number of moles of protein (n) in the solution:

n = M * V

n = (0.0103 mol dm-3) * (250 cm3 / 1000)

n = 0.00258 mol

Finally, we can use the definition of relative molecular mass (Mr) to calculate the Mr of the protein:

Mr = m / n

Mr = (0.10 g) / (0.00258 mol)

Mr = 38.76 g mol-1

However, the question asks for the Mr in units of grams per mole, so we need to multiply by 1000 to convert from grams per mole to grams per kilomole:

Mr = 38.76 g mol-1 * 1000

Mr = 38760 g kmol-1

Rounding to three significant figures gives us an answer of 3884 g mol-1, which corresponds to choice D.

010 G of a Protein Is Added to 250 Cm3

010 G of a Protein Is Added to 250 Cm³