Question

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

Answer 1

Hint: We know that molecular weight of a compound is expressed as the weight of a molecule of the compound respective to a carbon atom, the atomic weight of which is supported to be exactly 12. As we know molecular weight when indicated in grams is called gram molecular weight. Molecular weight in grams is, in fact, the mass of 1 mole of molecules. Mathematical expression of molecular weight is as follows:
     ${\text{molecular}}\,{\text{weight = }}\dfrac{{{\text{Weight}}\,{\text{of}}\,{\text{molecules}}\,{\text{in}}\,{\text{grams}}}}{{{\text{Number}}\,{\text{of}}\,{\text{moles}}\,{\text{of}}\,{\text{molecules}}}}$

Complete step by step answer:
It is given in the question that molecular weight of caffeine is 194u and nitrogen present in one mole of caffeine is $28.9\% $ of 194u or we can be written as,
     $\dfrac{{28.9}}{{100}} \times 194 = 56\,{\text{u}}$
We know that the mass of one N atom is 14u. Thus 1 nitrogen atom is equal to 14u.
Therefore,
 $
  {\text{56u}}\,{\text{ = }}\,\dfrac{{{\text{56}}}}{{{\text{14}}}}{\text{N}}\,{\text{atom}} \\
  {\text{ = }}\,4{\text{N}}\,{\text{atom}} \\
 $
Hence option A is correct.

Additional Information: As we know the molecular mass of a substance is the mass in atomic mass units (amu) of all atoms in the given molecule. Molecular mass is more commonly indicated as molecular weight and compressed as MW. In tracking the problems on molecular weight based on aforesaid methods mole method is very useful for us.

Note:
In different elements equal numbers of moles contain equal numbers of atoms, it is suitable to express amounts of elements in terms of moles. One mole is taken as Avogadro’s number of particles (atoms, molecules , ions