A 1.167 g sample contains only vitamin C (C6H8O6) and sucralose (C12H19Cl3O8). When the sample is dissolved in water to a total volume of 35.9 mL, 35.9 mL, the osmotic pressure of the solution is 3.67 atm 3.67 atm at 285 K. 285 K. What is the mass percent of vitamin C and sucralose in the sample?

Mass % Vitamin C: 73.3%

Mass % sucralose: 26.7%

Explanation:

The mass of Vitamin C (a) + Sucralose (b) is 1.167g. Thus, it is possible to write:

a + b = 1.167g (1)

The osmotic pressure formula in solution is:

π = i×M×R×T

Where π is osmotic pressure (3.67atm), i is Van't Hoff factor (1 for Vitamin C and Sucralose),M is molarity of solution (moles / 0.0359L), R is gas constant (0.082atmL/molK) and T is temperature (285K). Replacing:

3.67atm = 1 × moles / 0.0359L × 0.082atmL/molK × 285K

0.00564 = moles of solution (Moles of Vitamin C + Sucralose)

These moles can be written as:

0.00564 mol = a× (1mol / 176.12g) + b×(1mol / 397.64g) (2)

Where 176.12 is molar mass of vitamin C and 397.64 is molar mass of sucralose

Replacing (1) in (2)

0.00564 = (1.167 - b) / 176.12 + b / 397.64

0.000986 = 0.003163 b

0.312g = b. → Mass of sucralose.

Mass of Vitamin C → 1.167g - 0.312g = 0.855g

Thus, Mass percent is:

Mass % Vitamin C: 0.855g / 1.167g ×100 = 73.3%

Mass % sucralose: 0.312g / 1.167g ×100 = 26.7%

Explanation:

Mass of sucrose and sucralose = 1.167 g

Molar mass of sucrose = (C6H8O6)

= (12×6) + (8×1) + (6×16)

= 176 g/mol

Molar mass of = C12H19Cl3O8

= (12×12) + (19×1) + (35.5×3) + (16×8)

= 397.5 g/mol

Pressure, P = 3.67 atm

Volume, V = 35.9 ml

Temperature, T = 285 K

Using PV = nRT

nt = (3.67 × 35.9 × 10^-3)/(285 × 0.08205)

= 0.00563 moles.

Molar mass = mass/number of moles

let x be the mass of sucralose

nt = n1 + n2

0.00563 = (1.167 - x)/176 + x/397.5

0.00563 = 0.00663 - 0.0057x + 0.00252x

0.001 = 0.00318x

x = 0.3145 g

Mass % = mass of sample/total mass × 100

Sucralose mass % = 0.3145/1.167 × 100

= 26.95%

Sucrose mass % = (1.167 - 0.3145)/1.167 × 100

= 73.05%

the ideal gas law equation is as follows

pv = nrt

where p - pressure

v - volume

n - number of moles

r - universal gas constant

t - temperature

so if the pressure, volume and temperature are already known

we are left with n and r

since r is the universal gas constant that has a known fixed value then r too is known

so we are left with 'n'

once we know temperature volume and pressure

we can find the number of moles of gas present using the ideal gas law equation

this is not my own answer, this is an answer for the same question by the user blahblahmali. i do not claim ownership of this account.

i have no clue hope you find the answer