Question

Caffeine has a molecular weight of 194. If it contains 28.9% by mass of nitrogen, the number of atoms of nitrogen in one molecule of caffeine is:
(A) $4$
(B) $6$
(C) $2$
(D) $3$

Answer 1

Hint: The number of atoms of a given element in a particular compound can be calculated by knowing its weight percentage in the compound or empirical formula. The empirical formula is the simplest whole number ratio of all the atoms in a compound.
Formula used: The formula used can be written as:
$Number\,of\,atoms\,of\,any\,element = \dfrac{{Weight\,of\,element\,in\,molecule}}{{Atomic\,mass\,of\,the\,element}}$

Complete step by step answer:
The given quantities can be written as:
Molecular weight of caffeine $ = 194g$
Mass percent of nitrogen $ = 28.9\% $
Atomic weight of nitrogen $ = 14g$
Thus, mass of nitrogen element in one mole of caffeine $ = 28.9\% \,of\,194g = \dfrac{{28.9}}{{100}} \times 194g = 56.06g$
Number of nitrogen atoms in caffeine can be calculated by dividing the mass of nitrogen in a molecule of caffeine with the atomic mass of nitrogen.
Number of nitrogen atoms in one molecule of caffeine$ = \dfrac{{56.06}}{{14}} = 4$ .
Hence, option ‘A’ is the correct answer.
Additional information: It is very interesting that the empirical formulae of different compounds can be same for example the empirical formula of sulphur monoxide $SO$ and sulphur dioxide ${S_2}{O_2}$ is same i.e. SO. Empirical formula is the simplest ratio of atoms which combine to form a molecule of a compound. When the chemical formula of the compound is the simplest ratio in which the constituent atoms can combine then it is the same as its empirical formula. The empirical formulae only give the knowledge about the constituent elements of the compound.
Note:
The molecular and atomic weights are in grams always. The number of atoms cannot be in decimal, they are always an integer. And talking about caffeine ,Caffeine is a central nervous system stimulant of the methylxanthine class. It is the world's most widely consumed psychoactive drug.