Question

Number of atoms in \[4.25\text{ g}\]of $\text{N}{{\text{H}}_{3}}$ is approx.:
A.$1\times {{10}^{23}}$
B.$1.5\times {{10}^{23}}$
C.$2\times {{10}^{23}}$
D.$6\times {{10}^{23}}$

Answer 1

Hint: This problem can be solved from a knowledge of the mole concept and stoichiometry. One mole of a substance is defined to be equal to $6.022\times {{10}^{23}}$particles of that substance. Also the molecular weight of a compound is equal to one mole and also the atomic weight of an element is equal to one mole.

Complete step by step answer:
The molecular weight of $\text{N}{{\text{H}}_{3}}$=$17$\[\text{g/mol}\]=1 mole of $\text{N}{{\text{H}}_{3}}$=$6.022\times {{10}^{23}}$ molecules of $\text{N}{{\text{H}}_{3}}$
1 molecule of $\text{N}{{\text{H}}_{3}}$= 4 atoms $\left( \text{1 atom of N and 3 atoms of H} \right)$
So, $6.022\times {{10}^{23}}$molecules of $\text{N}{{\text{H}}_{3}}$= $4\times 6.022\times {{10}^{23}}$ atoms
Therefore, \[4.25\text{ g}\] of $\text{N}{{\text{H}}_{3}}$= $\dfrac{4\times 6.203\times {{10}^{23}}}{17}\times 4.25$ atoms = $6.022\times {{10}^{23}}$ atoms

Hence, the answer is option D.

Note:
The concept of mole was introduced to weigh the atoms and molecules as it is not possible to weigh them physically.
One mole of a substance is also known as “Avogadro’s Constant” and is denoted by the symbol “${{\text{N}}_{\text{A}}}$”.
One mole of a substance is defined as the amount of a substance that is equal to the mass of 12 g of carbon in a C-12 isotope.
The number of moles of a substance can be calculated from the weight and the molecular weight of the substance. $\text{n=}\dfrac{\text{w}}{\text{M}}$Where “w” is the weight and “M” is the molecular weight.
The word “mole” was introduced around the year 1896 by German chemist Wilhelm Ostwald, who derived the term from the Latin word meaning “a pile or a heap".