Calculate the osmotic pressure in pascals exerted by a solution prepared by dissolving 1.0 g of polymer of molar mass 185,000 in 450 mL of water at 37°C.
ANSWER:
It is given that:
Volume of water, V = 450 mL = 0.45 L
Temperature, T = (37 + 273)K = 310 K
• π (pi) is the osmotic pressure (Pa)
• c is the molar concentration of the solute (mol/L)
• R is the gas constant (8.314 J/K*mol)
• T is the absolute temperature (K)
We are given the following information:
• Mass of polymer (m) = 1.0 g
• Molar mass (M) = 185,000 g/mol
• Volume of solution (V) = 450 mL = 0.45 L
• Temperature (T) = 37°C = 310 K (conversion to Kelvin)
Step 1: Calculate the molar concentration (c)
First, we need to find the number of moles of polymer dissolved in the solution. We can do this by dividing the mass of the polymer by its molar mass:
Then, we can calculate the molar concentration by dividing the number of moles by the volume of the solution in liters:
Step 2: Apply the van't Hoff equation
Now that we have all the necessary values, we can plug them into the van't Hoff equation:
= 30.97 pascals (Pa).
Osmotic pressure,
= 30.98 Pa