Final answer:
To find the osmotic pressure of bovine insulin solution, calculate the moles of insulin, volume in liters, molarity, and use the van 't Hoff equation incorporating the ideal gas constant and Kelvin temperature. The osmotic pressure for the insulin solution is 4.32 x 10^-3 atm.
Step-by-step explanation:
To calculate the osmotic pressure of a solution of bovine insulin with a molar mass of 5700 g/mol, we follow these steps:
- Calculate the number of moles of insulin in the solution using the molar mass and the mass provided.
- Convert the volume of the solution from mL to L.
- Use the van 't Hoff equation for osmotic pressure (Π = iMRT) where Π is the osmotic pressure, i is the van 't Hoff factor (which is 1 for insulin, a non-electrolyte), M is the molarity of the solution, R is the ideal gas constant (0.0821 L·atm/K·mol), and T is the temperature in Kelvin (add 273 to the given temperature in °C).
Now, let's do the calculation:
- Moles of insulin: 0.103 g / 5700 g/mol = 1.81 x 10-5 mol
- Volume in liters: 100.0 mL / 1000 mL/L = 0.1 L
- Molarity (M): 1.81 x 10-5 mol / 0.1 L = 1.81 x 10-4 M
- Temperature in Kelvin: 18 °C + 273 = 291 K
- Osmotic pressure: Π = (1)(1.81 x 10-4 M)(0.0821 L·atm/K·mol)(291 K)
Thus, the osmotic pressure is: Π = 1.81 x 10-4 M x 0.0821 L·atm/K·mol x 291 K = 4.32 x 10-3 atm
Think about your result: The answer represents the osmotic pressure in atmospheres and is reported with three significant figures.