Final answer:
To find the polymer's molar mass, we convert the osmotic pressure to atm, the temperature to Kelvin, solve for molarity, and then calculate molar mass using the given mass and volume of the solution.
Step-by-step explanation:
To calculate the molar mass of the polymer we use the formula for osmotic pressure (Π = MRT) where Π is the osmotic pressure, M is the molarity of the solution, R is the ideal gas constant, and T is the temperature in Kelvin. The osmotic pressure is given as 8.63 mmHg which we convert to atm (1 mmHg = 0.001316 atm), and temperature is given in Celsius which we convert to Kelvin (K = °C + 273.15).
First, convert the osmotic pressure to atm and temperature to Kelvin:
- 8.63 mmHg × 0.001316 atm/mmHg = 0.01136 atm
- 21°C + 273.15 = 294.15 K
Then, solve for the molarity (M) using the osmotic pressure formula:
M = Π / (RT)
Next, calculate the number of moles of polymer:
moles = mass (g) / molar mass (g/mol)
Since mass of the polymer is given, we rearrange the molarity formula to find molar mass (M = moles / volume in liters), plug in the values, and solve for molar mass:
Molar mass = mass (g) / (M × volume (L))
Finally, calculate the molar mass of the polymer and present the answer. Don't forget to convert the solution volume from mL to L (1 mL = 0.001 L).