1(20%) A 2.0 L bottle of diet cola was analyzed for caffeine and sodium benzoate
ID: 1033372 • Letter: 1
Question
1(20%) A 2.0 L bottle of diet cola was analyzed for caffeine and sodium benzoate content. A 10.0 mL aliquot of soda was diluted to 250.0 mL in a volumetric flask. A sample of this solution was transferred to a 1.00-cmcell. The absorbance values at 225 nm and 270 nm were found to be 0.742 and 0.287, respectively. Beer's law was obeyed for b?h components at both wavelengths. Compound Sodium benzoate Caffeine ? @ 225 nm (M.1cm. 1) 7210 e@ 270 nm (M-1cm-1) 890 8790 Calculate the mass, in grams, of caffeine and sodium benzoate in the original 2.0 L bottle of diet cola.Explanation / Answer
Let the concentrations of sodium benzoate and caffeine in the 250.0 mL dilute solution be C1 and C2 respectively. Assume that the absorbances are additive; hence, we have
0.742 = (7210 M-1cm-1)*C1*(1.00 cm) + (5510 M-1cm-1)*C2(1.00 cm) …….(1)
0.287 = (890 M-1cm-1)*C1*(1.00 cm) + (8790 M-1cm-1)*C2(1.00 cm) ……..(2)
(1)*890 – (2)*7210 gives
0.742*890 – 0.287*7210 = (5510 M-1)*(890)*C2 – (8790 M-1)*(7210)*C2
======> -1408.89 = (-58472000 M-1)*C2
======> C2 = (-1408.89)/(-58472000) = 2.409*10-5 M ? 2.41*10-5 M.
The concentration of caffeine in the 250.0 mL solution is 2.41*10-5 M.
Put C2 = 2.41*10-5 M in (1) and obtain
0.742 = (7210 M-1cm-1)*C1*(1.00 cm) + (5510 M-1cm-1)*(2.41*10-5 M)*(1.00 cm)
======> 0.742 = (7210 M-1)*C1 + 0.132791
======> (7210 M-1)*C1 = 0.742 – 0.132791 = 0.609209
======> C1 = 0.609209/(7210 M-1) = 8.449*10-5 M ? 8.45*10-5 M.
The concentration of sodium benzoate in the 250.0 mL solution is 8.45*10-5 M.
10.0 mL of the sample solution was taken and diluted to 250.0 mL; therefore, the dilution factor is (250.0 mL)/(10.0 mL) = 25.0.
The concentration of sodium benzoate in the sample solution = (8.45*10-5M)*(dilution factor) = (8.45*10-5 M)*(25.0) = 2.1125*10-3 M.
The concentration of caffeine in the sample solution = (2.41*10-5 M)*(25.0) = 6.025*10-4 M.
Since we have 2.0 L sample solution, hence,
moles of sodium benzoate in the sample solution = (2.1125*10-3 M)*(2.0 L) = 4.225*10-3 mole.
moles of caffeine in the sample solution = (6.025*10-4 M)*(2.0 L) = 1.205*10-3 mole.
Molar mass of sodium benzoate = 144.11 g/mol.
Molar mass of caffeine = 338.299 g/mol.
Mass of sodium benzoate in the diet coke = (4.225*10-3 mole)*(144.11 g/mol) = 0.60886 g ? 0.6089 g (ans).
Mass of caffeine in the diet coke = (1.205*10-3 mole)*(338.299 g/mol) = 0.40765 g ? 0.4076 g (ans).
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