Answer:
11824 g/mol
Step-by-step explanation:
To calculate the molar mass of the polymer, we need to use the equation for osmotic pressure:
π = MRT
where π is the osmotic pressure, M is the molarity of the solution, R is the gas constant, and T is the temperature in Kelvin.
We can rearrange this equation to solve for the molarity of the solution:
M = π / RT
We can then use the molarity to calculate the number of moles of the polymer:
moles of polymer = molarity * volume
where volume is the volume of the solution in liters.
Finally, we can use the number of moles and the mass of the polymer to calculate the molar mass:
molar mass = mass of polymer / moles of polymer
Let's plug in the given values and solve for the molar mass:
π = 1.25 × 10^-2 atm
mass of polymer = 2.75 g
volume = 150.0 mL = 0.1500 L
R = 0.08206 L atm mol^-1 K^-1
T = 130 + 273.15 = 403.15 K
First, let's calculate the molarity:
M = π / RT = (1.25 × 10^-2 atm) / (0.08206 L atm mol^-1 K^-1 × 403.15 K) = 0.00155 M
Next, let's calculate the number of moles of the polymer:
moles of polymer = molarity × volume = (0.00155 mol/L) × 0.1500 L = 0.0002325 mol
Finally, let's calculate the molar mass:
molar mass = mass of polymer / moles of polymer = 2.75 g / 0.0002325 mol = 11824 g/mol
Therefore, the molar mass of the polymer is 11824 g/mol.
ALLEN