Carbohydrates are compounds containing only carbon, hydrogen and oxygen having the atomic ratio of `H : O` as `2 : 1`. When heated in the absence of air, these compounds decompose to form carbon and water.
a. If `310 g` of a carbohydrates leaves a residue of `124 g` of carbon on heating in absence of air, what is the empirical formula of the carbohydrate?
b. If 0.0833 mole of the carbohydrate contains `1.0 g` hydrogen , what is the molecular formula of the carbohydrate?

Explanation

Step I. Calculation of the empirical formula of carbohydrate
Percentage of carbon `= ("Mass of carbon")/("Mass of carbohydrate")xx100=(("124 g"))/(("310 g"))xx100=40`
Percentage of water `= 100-40=60`
`{:("Element/Compound","Percentage","Atomic mass (Molar mass)","Atomic ratio (Molar ratio)","Simplest whole no. ratio"),("Carbon (C)",40,12,(40)/(12)=3.3,1),("Water"(H_(2)O),60,18,(60)/(18)=3.33,1):}`
Empirical formula : `C_(1)(H_(2)O)_(1) or CH_(2)O`
Step II. Calculation of the molecular formula of carbohydrate
0.0833 mole of carbohydrate contains H = 1.0 g or 1 atom
1 mole of carbohydrate contains H atom `= (("1 atom"))/(("0.0833 mol"))xx"1 mol"=12` atoms
Thus, 1 mole and also one molecule of carbohydrade contain hydrogen atoms = 12
Since hydrogen and oxygen are present in the ratio of 2 : 1 therefore,
1 molecule of carbohydrate contain oxygen atoms = 6
`:.` Molecular formula of carbohydrate `= (CH_(2)O)xx6 = C_(2)H_(12)O_(6)`.