Question

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

Answer 1

Hint: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.