Question

Solution of 12 g of non-electrolyte (A) prepared by dissolving it in 1000 mL of water exerts the same osmotic pressure as that of 0.05 M glucose solution at the same temperature. The empirical formula of A is CH₂O. The molecular mass of A is ____ g. (Nearest integer)

Answer 1

Correct Answer: 240

To find the molecular mass of compound A, which has the empirical formula CH₂O, we use the concept of osmotic pressure. Osmotic pressure, π, can be given by the formula: π = iCRT, where i is the van 't Hoff factor (i=1 for non-electrolytes), C is the concentration in molarity, R is the gas constant, and T is the temperature in Kelvin. Given that both solutions exert the same osmotic pressure:

1. Calculate the molarity of A using its mass and volume:

M of glucose = 0.05 mol/L.

Moles of A = 12 g / M_A, where M_A is the molecular mass of A.

Molarity of A, C_A = (12 / M_A) M/L (since volume = 1 L = 1000 mL).

2. Set the osmotic pressures equal:

π_glucose = π_A

(0.05)(R)(T) = ((12 / M_A)(R)(T))

⇒ M_A = 12 / 0.05 = 240 g/mol

3. Verify the range: As calculated, M_molecule = 240 g/mol, which is within the range [240,240]. Therefore, the molecular mass of A is confirmed to be 240 g/mol.