Problem PageQuestion114.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 0.0355atm at 25.0°C.Calculate the molar mass of the protein. Round your answer to 3 significant digits.

To solve this problem, we will use the formula for osmotic pressure:

Π = n/V * R * T

Where: Π is the osmotic pressure, n is the number of moles of the solute, V is the volume of the solution, R is the ideal gas constant, and T is the temperature in Kelvin.

First, we need to convert the temperature from Celsius to Kelvin. The formula to convert Celsius to Kelvin is K = °C + 273.15. So, T = 25.0°C + 273.15 = 298.15 K.

Next, we rearrange the formula to solve for n (the number of moles of the solute):

n = Π * V / (R * T)

We know that Π = 0.0355 atm, V = 5.00 mL = 0.00500 L (since 1 L = 1000 mL), R = 0.0821 Latm/(Kmol) (the value of the ideal gas constant), and T = 298.15 K. Substituting these values into the formula gives:

n = 0.0355 atm * 0.00500 L / (0.0821 Latm/(Kmol) * 298.15 K) = 0.0000072 mol

Finally, we can find the molar mass of the protein by dividing the mass of the protein by the number of moles. The mass of the protein is given as 114 mg = 0.114 g (since 1 g = 1000 mg). So, the molar mass is:

Molar mass = mass / n = 0.114 g / 0.0000072 mol = 15833.33 g/mol

Rounding to three significant figures gives a molar mass of 15800 g/mol.