Question

Calculate the mass of $6.022 \times {10^{23}}$ number of nitrogen molecules.

Answer 1

To solve this question, we must first know some basics of the mole concept and the formulae to find the number of moles. Then we need to calculate the number of moles in the given amount of sample and then find the mass of the given number of molecules by using the simple formula which we use to find the number of moles and then only we can conclude the correct answer.

Complete step-by-step answer: Before we move forward with the solution of this given question, let us first understand some basic concepts:
The mole is the unit of measurement for the amount of substance in the International System of Units (SI). A mole of a substance or a mole of particles is defined as containing exactly $6.02214076 \times {10^{23}}$ particles, which may be atoms, molecules, ions, or electrons.
The number $6.02214076 \times {10^{23}}$ is popularly known as the Avogadro constant and is often denoted by the symbol ${N_A}$ .
Step 1: In this step we will find the number of moles of nitrogen in given number of molecules:
Given, Number of molecules of Nitrogen = $6.022 \times {10^{23}}$
Number of moles of a substance in given number of molecules $= \frac{{number{\text{ }}of{\text{ }}molecules}}{{{N_A}}}$
$= \frac{{6.022 \times {{10}^{23}}}}{{6.022 \times {{10}^{23}}}} = \,\,1$
Step 2: In this step we will find the mass of given sample:
Let m be the required mass.
Since, we know that Number of moles $= \frac{{Given\,\,Mass}}{{Molecular\,\,Mass}}$
$1 = \,\frac{m}{{28}}$
$\Rightarrow m = 28g$

Therefore, the mass of $6.022 \times {10^{23}}$ number of nitrogen molecules is $28\,\,grams$.

Note: The total sum of the masses of the atoms or elements present in the molecule is termed as molecular mass. The molar mass of a substance is the mass of 1 mole of that substance, in multiples of the gram.