Final answer:
To determine the molar mass of the polymer, the osmotic pressure is first converted from torr to atmospheres, and the temperature from Celsius to Kelvin. Then the number of moles is found using the osmotic pressure formula, and finally, molar mass is calculated by dividing the polymer's mass by the number of moles, resulting in a molar mass of approximately 1099 g/mol.
Step-by-step explanation:
To find the molar mass of the polymer from the osmotic pressure of the solution, we can use the formula for osmotic pressure (Π):
Π = (n/V)RT, where Π is the osmotic pressure in atmospheres, n is the amount of solute in moles, V is the volume of the solution in liters, R is the ideal gas constant (0.0821 L·atm/(mol·K)), and T is the temperature in Kelvin.
First, we need to convert the osmotic pressure from torr to atmospheres:
26.9 torr * (1 atm / 760 torr) = 0.0354 atm
Next, convert the temperature from degrees Celsius to Kelvin:
30.0 °C + 273.15 = 303.15 K
Now, rearrange the osmotic pressure equation to solve for the number of moles (n):
n = (ΠV) / RT
Substitute the values:
n = (0.0354 atm * 0.251 L) / (0.0821 L·atm/(mol·K) * 303.15 K)
Calculate the moles of the polymer:
n ≈ 0.000364 moles
Finally, to find the molar mass (M) of the polymer, we divide the mass of the polymer by the number of moles:
M = mass / n = 0.400 g / 0.000364 moles
M ≈ 1099 g/mol
The molar mass of the polymer is therefore approximately 1099 g/mol.