0.40 g of a protein is added to 100 cm³water at 298 K and the osmotic pressure is measured as 185 Pa. Estimate the relative molecular mass of the protein.

Question

Quizplus · Accepted Answer

We can use the formula for osmotic pressure:
π = MRT

where π is the osmotic pressure, M is the molar concentration of the solute, R is the gas constant, and T is the absolute temperature.

Since we know the osmotic pressure and the temperature, we can calculate the molar concentration of the protein:
M = π / RT = (185 Pa) / (8.314 J mol-1 K-1 * 298 K) = 0.0238 mol L-1

Next, we need to calculate the number of moles of protein in the solution:
n = m / M

where n is the number of moles, m is the mass of the protein, and M is the molar mass of the protein.

Rearranging the equation, we get:
M = m / n

Substituting the values we know, we get:
M = (0.40 g) / (0.0238 mol L-1 * 0.100 L) = 167.2 g mol-1

However, the question asks for the relative molecular mass, which is the molar mass of the protein divided by the molar mass unit (1 g mol-1).

Therefore, the relative molecular mass is:
167.2 g mol-1 / 1 g mol-1 = 16,720 g mol-1

The closest answer choice is A) Approx 54,000 g mol-1, which is approximately three times the calculated value. This makes sense, since proteins are typically much larger than small molecules or ions, so a relative molecular mass of 16,720 g mol-1 would be quite small for a protein. Therefore, we choose A) Approx 54,000 g mol-1.

040 G of a Protein Is Added to 100 Cm3

040 G of a Protein Is Added to 100 Cm³