Question

If the molecular weights of $N{{H}_{3}}$and ${{H}_{2}}$ are 17 amu and 2 amu respectively, then the number of molecules of $N{{H}_{3}}$ in 17 gm of ammonia is :
(A)- less than the number of molecules of ${{H}_{2}}$ in 2 grams of hydrogen
(B)- equal to the number of molecules of ${{H}_{2}}$ in 2 grams of hydrogen
(C)- equal to the number of atoms of H in 2 grams of hydrogen
(D)- more than the number of molecules of ${{H}_{2}}$ in 2 grams of hydrogen

Answer 1

Hint: One mole of a substance is equal to $6.022\times {{10}^{23}}$ units of that substance (such as atoms, molecules, or ions). The number $6.022\times {{10}^{23}}$ is called Avagadro’s number or Avagadro’s constant.

Complete step by step answer:
-One mole of a substance is equal to the molecular weight of the substance and that is equal to Avagadro’s number.
$1\text{ mole}=\text{Molecular weight}=6.022\times {{10}^{23}}molecules$
-Molecular weight of $N{{H}_{3}}=14+3=17g$

-Therefore,
1 mole of $N{{H}_{3}}$= 17 g of $N{{H}_{3}}=6.022\times {{10}^{23}}molecules$
-Molecular weight of ${{H}_{2}}=1\times 2=2g$

-Therefore,
1 mole of ${{H}_{2}}$ = 2g of ${{H}_{2}}=6.022\times {{10}^{23}}molecules$
Since the number of molecules $N{{H}_{3}}$ is equal to the number of molecules ${{H}_{2}}$ .
So, the correct answer is “Option B”.

Note: The Avagadros number was coined in the year 1909 by the physicist Jean Perrin who defined it as the number of molecules which is exactly equal to the 32 grams of oxygen. The Avogadro constant represented by ${{N}_{A}},{{N}_{0}}$, N or L is the proportionality factor that relates the number of constituent particles, usually molecules, atoms, or ions present in a sample with the amount of substance in the sample. The SI unit of Avagadro’s number is the reciprocal of mole, which is $mo{{l}^{-1}}$. Avagadro’s number is a dimensionless quantity. Avagadro’s number is numerically equal to the average mass of one molecule of the compound in Daltons, where one Dalton being the $\dfrac{1}{12}$ of the mass of one carbon-12 atom, which is approximately equal to the mass of one nucleon. The Avagadro’s number also gives the relation of the molar volume of a substance to the average volume nominally occupied by one of its particles, when both of the units are expressed in the same units of volume.