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?

Question

2.63 × 103 g/mol

28.5 g/mol

6.49 × 105 g/mol

8.88 × 104 g/mol

9.05 × 103 g/mol

Answer 1

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.