An artificial cell containing 200 mL of an aqueous urea solution is placed in a 0.05 M aqueous solution of CaCl ₂ at 300 K . The initial net osmotic pressure developed across the semipermeable membrane is 1.245 bar and the initial flow of water is observed to be into the artificial cell. Assuming complete dissociation of CaCl ₂ , the mass of urea present in the artificial cell is x 10⁻¹ g . The value of x is ________

Step-by-step solution

For CaCl ₂ , assuming complete dissociation, the van't Hoff factor i = 3 . The effective concentration of the CaCl ₂ solution is: C_ eff = i C = 3 0.05 M = 0.15 M The net osmotic pressure is given by: = C RT 1.245 = C 0.083 300 C = 1.245 24.9 = 0.05 M Since water flows into the artificial cell, the urea solution inside must be hypertonic compared to the outside CaCl ₂ solution. Thus, the concentration of urea is: C_ urea = C_ eff + C = 0.15 + 0.05 = 0.20 M The moles of urea in 200 mL of solution are: n = M V = 0.20