Question

How many moles of ammonia contain ${{1}}{{.51 \times 1}}{{{0}}^{{{24}}}}{{ N}}{{{H}}_{{3}}}$ molecules?

Answer 1

In the above question, we have to find the number of moles present in ${{1}}{{.51 \times 1}}{{{0}}^{{{24}}}}{{ N}}{{{H}}_{{3}}}$ molecules. So, here we are going to use the Avogadro number concept. Avogadro number is the number of atoms present in ${{12g}}$ of carbon-12 which is nearly equal to $6.022 \times {10^{23}}$ which comprises 1 mole of a substance.

Formula Used: ${{moles}} = \dfrac{{{\text{number of particles}}}}{{{{{N}}_{{A}}}}}$

Complete step by step solution
We know that 1 mole of any substance will contain $6.022 \times {10^{23}}$ particles.
So, $6.022 \times {10^{23}}$ molecules of ${{N}}{{{H}}_{{3}}}$ will contains 1 mole of ${{N}}{{{H}}_{{3}}}$ .
We are interested to find out the number of moles present in ${{1}}{{.51 \times 1}}{{{0}}^{{{24}}}}$ molecules of ${{N}}{{{H}}_{{3}}}$ , we will get:
${{1}}{{.51 \times 1}}{{{0}}^{{{24}}}}$ molecules of ${{N}}{{{H}}_{{3}}}$ will contain $\dfrac{{{{1}}{{.51 \times 1}}{{{0}}^{{{24}}}}}}{{{{6}}{{.022 \times 1}}{{{0}}^{{{23}}}}}}{{ = 2}}{{.5}}$ moles of ${{N}}{{{H}}_{{3}}}$ .
Hence, ${{2}}{{.5}}$ moles of ${{N}}{{{H}}_{{3}}}$ are present in ${{1}}{{.51 \times 1}}{{{0}}^{{{24}}}}$ molecules of ${{N}}{{{H}}_{{3}}}$ .

Additional Information
Avogadro’s number is used in chemistry to deal with large numbers. It is the basis of the mole unit of measurement. It is a simple way of conversion between mole, mass and number of molecules. Suppose, to get the number of particles present in a substance, first, we have to find the number of moles present in it and then by using Avogadro’s number we can find the number of particles present inside it.

Note
Avogadro’s number is kind of generalized number, hence, we can write:
1 mole = $6.022 \times {10^{23}}$ atoms, or molecules, or protons, or electrons etc.
In short, it is the number of particles in a mole.
Hence, in order to solve these types of questions, we have to first decide which quantity (electron, proton, atom) is equivalent to Avogadro’s number.
At STP, one mole of any gas occupies a volume of ${{22}}{{.4}}$ L.