What is the molecular weight of a polymer if 3.50 g are dissolved in enough water to give 252 mL of the solution and give a osmotic pressure of 28.52 mm Hg at 25°C?
2.63 × 103 g/mol
28.5 g/mol
6.49 × 105 g/mol
8.88 × 104 g/mol
9.05 × 103 g/mol
To find the molecular weight of the polymer, we can use the formula for osmotic pressure:
π = MRT
Where:
π = osmotic pressure
M = molecular weight of the polymer
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin (25°C + 273.15 = 298.15 K)
First, let's convert the osmotic pressure from mm Hg to atm:
28.52 mm Hg * 1 atm/760 mm Hg = 0.0375 atm
Now, let's rearrange the formula to solve for M:
M = π/RT
M = 0.0375 atm / (0.0821 L·atm/(mol·K) * 298.15 K)
M = 0.0375 / 24.4488
M = 0.001535 mol
Finally, we can calculate the molecular weight by dividing the mass by the number of moles:
Molecular weight = 3.50 g / 0.001535 mol ≈ 2275.42 g/mol
Therefore, the molecular weight of the polymer is approximately 2275.42 g/mol.
None of the given options match this result, so none of them are correct.