Question

14. Calculate the molecular weight of a small protein if a 0.24-g sample dissolved in 108 mL of water has an osmotic pressure of 9.5 mmHg at 22°C. (760 mmHg = 1 atm) A) 3.2 x 102 g/mol B) 4.3 x 103 g/mol C) 5.7 g/mol D) 1.8 x 102 g/mol E) 5.7 x 10–3 g/mol

Answer 1

We calculate the osmotic pressure, (pi), using the following equation:

Where:

M is the molar concentration of dissolved species (units of mol/L).
R is the ideal gas constant (0.08206 L atm mol^-1 K^-1, or other values depending on the pressure units).
T is the temperature on the Kelvin scale.

9.5 /760 atm = M * 0.08206 L atm mol-1K-1 * (273+22)

M = 9.5 /760 atm / 0.08206 L atm mol-1K-1 * (273+22)

M = 5.16* 10^-4 mol L-1

moles of protein = 5.16* 10^-4 mol L-1* 108mL = 0.5573* 10^-4 moles

molecular weight of protein = mass of protein / moles

           = 0.24/0.5573* 10^-4 = 4.3 * 10^3 g/mol

Hence, Answer is B)