What is the mass percent of vitamin C and sucralose in the sample?

Question

A 1.335 g sample contains only vitamin C (C6H8O6) and sucralose (C12H19Cl3O8). When the sample is dissolved in water to a total volume of 44.3 mL, the osmotic pressure of the solution is 3.32 atm at 297 K. What is the mass percent of vitamin C and sucralose in the sample?

Answer 1

mass Vit C = X g

mass Suc = 1.335 g - X g

osmotic pressure = π = iMRT where i = van't Hoff factor; M = molarity; R = gas constant; T = temp in Kelvin

For VC:

i = 1; M = X g/176 g /0.0443 L; R = 0.0821 Latm/Kmol; T = 297K

For Suc:

i = 1; M = 1.335 g - X g / 398 g / 0.0443 L; R = 0.0821 Latm/Kmol; T = 297K

Total for both:

3.41 = (X/176 * 0.0443)(0.0821)(297) + (1.335 - X /398 * 0.0443)(0.0821)(293)

3.41 = (24.38 X / 7.80) + (32.55 - 24.38 X / 17.63)

3.41 = 3.13 X + 1.85 - 1.38 X

1.75 X = 1.56

X = 0.891 g = mass of vitamin C

1.335 g - 0.891 g = 0.444 g = mass of sucralose

mass % vitamin C = 0.891 g / 1.335 g (x100%) = 66.7%

mass % sucralose = 0.444 g / 1.335 g (x100%) = 33.3%