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How many molecules are in \[0.400\] moles of \[{N_2}{O_5}\]?

Last updated date: 13th Jun 2024
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Hint: 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.$

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.