Question

Sorbose, C6H12O6, is a carbohydrate used in the manufacture of vitamin C. A lab supervisor at Vital C Pharmaceuticals, Inc. suspected that an employee had sabotaged the production line by substituting xylitol, C5H12O5, a sweetener for "sugar-free" gum, for sorbose. Combustion analysis of the white powder found in the production line and in the employee's possession gave the following results: %C = 39.47; %H = 7.95; %O = 52.58 Was the employee guilty of sabotage and thus should the employee be fired for sabotage?

Answer 1

Let the 100 g of the sample is analyzed for its composition i.e. quantitative and qualitative analysis.

Analysis suggest the composition as, %C =39.47, %H = 7.95, %O = 52.58.

From this data let us find out the empirical formula for the unknown compound.

Step-1) Determination of relative number of atoms:

Divide the %composition by atomic mass of respective element.

Atomic mass of C = 12, %C = 39.47. so, Relative C atoms = 39.47/12 = 3.29

Atomic mass of H = 1,   %H = 7.95. so, Relative H atoms = 7.95/1 = 7.950.

Atomic mass of O = 16, %O =52.58. so,Relative O atoms = 52.58/16 = 3.29

Hence ratio of relative number of elements is,

C:H:O = 3.29 : 7.950 : 3.29.

Step-2) Determination of simplest ration:

Divide the above ratio by the smallest number among them,

C:H:O = (3.29/3.29) : (7.95/3.29) : (3.29/3.29)

C:H:O = 1 : 2.416 : 1

C:H:O = 1 : 2.4 : 1.

Hence the simplest atomic ratio is C:H:O = 1 : 2.4 : 1.

But all numbers must be whole number hence we will multiply whole ratio by the number till we get all whole number integer.

On trial and error basis we get that number as 5 (see only 2.4 is fractional and 2.4 = 12 a whole number we get)

Hence on multiplying by 5 to above atomic ratio we get the new ratio as,

C:H:O = 5 : 12 : 5

Hence the empirical formula is C₅H₁₂O₅.

Hence the presence of Xylitol confirmed and employee should be fired for sabotage.

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