Question

How many molecules are in $0.400$ moles of ${N_2}{O_5}$?

Answer 1

The mole concept is used for determining the number of molecules in a substance. A mole of substance contains a number equal to $6.023 \times {10^{23}}$ numbers of molecules.

Complete step by step answer:
Mole is used as a unit of measurement to express the amount of a substance present in a specific weight of the substance. By definition, a mole is equal to the amount of substance which is present in $6.023 \times {10^{23}}$ number of particles. The particles considered may be atoms or molecules or ions.
The term mole was given by a German chemist Wilhelm Ostwald in $1896$ who describes that a large number of molecules is present in a mole of a compound. The number is $6.023 \times {10^{23}}$ and called it as Avogadro’s number or constant denotes ${N_A}$ after the death of Amedeo Avogadro.
For example a mole of carbon contains $12g$ of carbon and has $6.023 \times {10^{23}}$ number of carbon atoms. A mole of water contains $18g$ of water and contains $6.023 \times {10^{23}}$ number of water molecules.
The number of moles of a substance is represented by the following formula:
$n = \frac{N}{{{N_A}}}$ where, $n$ is the number of moles of the substance, $N$ is the total number of molecules present in a substance, and${N_A}$ is the Avogadro constant.
The given compound is ${N_2}{O_5}$. So one mole of ${N_2}{O_5}$ contains $6.023 \times {10^{23}}$ numbers of molecules. Thus the $0.400$ moles of ${N_2}{O_5}$ contains a number of molecules =$0.400moles \times 6.023 \times {10^{23}}$.
$= 2.41 \times {10^{23}}molecules.$

Note:
A mole (mol) is the amount of a substance that contains $6.023 \times {10^{23}}$ representative particles of that substance. The mole is used as the SI unit for describing the amount of a substance.