Question

If there are $7.44 \times [10^{23}$ atoms of gold, how many moles of gold are there?

Answer 1

We know that the $1\,g$ of an atom will be equal to $1$ mole.
In equation;
$1\,g$ of atom $= \,\,1\,$ mole
Since, $1$ mole contains Avogadro’s number (${N_A}$ ) of molecule
So, $1\,mole\, = \,6.022\, \times \,{10^{23}}\,atoms$
Therefore, for $1$ molecule will be;
$1\,\,atoms\, = \,\dfrac{1}{{6.022\, \times \,{{10}^{23}}}}\,g\,\,atoms$
So, the answer will be;
$1\,atoms\, = 1.66\, \times \,{10^{ - 24}}\,g\,atoms$

Complete step-by-step answer: $1$ mole gold contains Avogadro’s number (${N_A}$ ) of molecules.
Given values are,
The number of atoms of gold $= \,7.44 \times {10^{23}}$ atoms
Since, $1\,mole\,{\text{of}}\,{\text{Au}}\, = \,6.022\, \times \,{10^{23}}\,atoms$ of Au
From the given equivalence, we can derive that;
$\dfrac{{1\,mol\,Au}}{{6.022\, \times \,{{10}^{23}}\,atoms\,Au}}$ or $\dfrac{{6.022\, \times \,{{10}^{23}}\,atoms\,Au}}{{1\,mol\,Au}}$
$= \,7.44\, \times \,{10^{23}}\,atoms\,Au\, \times \,\dfrac{{1\,mol\,Au}}{{6.022\, \times \,{{10}^{23}}\,atoms\,Au}}$
$= \,\,\dfrac{{ = \,7.44\, \times \,{{10}^{23}}\,mol\,Au}}{{6.022\, \times \,{{10}^{23}}\,}}$
$= \,1.24\,mol\,Au$

Additional information: Gold ($Au$) is a chemical element. In Latin it is named as aurum. The atomic number is $79$ which makes it one of the higher atomic number elements that occur naturally. In a pure form, it is a bright, soft, slightly reddish yellow, ductile malleable, and dense metal. Chemically, gold is a transition metal and it belongs to the group $11$ element. Gold is one of the least reactive chemical elements which is also solid under standard conditions. Gold occurs in a solid solution series with the native element silver which is naturally alloyed with other metals like copper $(Cu)$ and palladium $(Pd)$ and also as mineral inclusions such as within pyrite.
Number of moles is calculated by using below given formula;
$n\,\, = \,\,\dfrac{{mass}}{{molar\,mass}}$
where $n$ is the amount in moles $(mol)$ , mass in grams $\;(g)$ , and molar mass in grams per mole $\;(g/mol)$ .

Note: A mole is a unit measurement for the amount of substance in the international system of units i.e., SI unit. A mole of a particle or a mole of a substance is defined as $6.02214076 \times {10^{23}}$ of a chemical unit, that can be ions, atoms, molecules, etc. Originally it was defined as the number of atoms in $12{\text{ }}g$ of carbon-12.