Question

How many moles are there in \[1.5{\text{ }}g\] of ethanol, \[C{H_3}C{H_2}OH\] ?

Answer 1

Hint: A mole is a unit measurement for amount of substance in the international system of units i.e., SI unit. A mole of a particle or a mole of a substances 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.

Formula used: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 \[\;(g/mol)\] .

Complete step-by-step answer:\[1\] mole \[C{H_3}C{H_2}OH\] contains \[6.02214076 \times {10^{23}}\] atoms
Let’s calculate the number of moles of ethanol i.e., \[C{H_3}C{H_2}OH\]
Mass of \[C{H_3}C{H_2}OH\] = \[1.5{\text{ }}g\]
To find the molar mass of ethanol;
There are two Carbon atoms and carbon molar mass is \[\left( {12.011{\text{ }}g/mol} \right)\],
Six Hydrogens atoms and hydrogen’s molar mass is\[\left( {1.008{\text{ }}g/mol} \right)\]
and one Oxygen atom and the oxygen’s molar mass is \[\left( {15.999{\text{ }}g/mol} \right){\text{ }}\]

The molar mass of \[C{H_3}C{H_2}OH\];
\[\left( {2{\text{ }} \times {\text{ }}12.011{\text{ }}g/mol{\text{ }}C} \right){\text{ }} + {\text{ }}\left( {6{\text{ }} \times {\text{ }}1.008{\text{ }}g/mol{\text{ }}H} \right){\text{ }} + {\text{ }}\left( {1{\text{ }} \times {\text{ }}15.999{\text{ }}g/mol{\text{ }}O} \right){\text{ }}\]
\[ = {\text{ }}46.07{\text{ }}g/mol{\text{ }}{C_2}{H_5}OH\]
Number of moles of \[C{H_3}C{H_2}OH\] ;
\[n\,\, = \,\,\dfrac{{mass}}{{molar\,mass}}\]
where \[n\] is the amount in moles \[(mol)\] , mass in grams \[\;(g)\] , and molar mass in grams per mole \[\;(g/mol)\] .

\[n\,\, = \,\,\dfrac{{1.5\,g}}{{46.07\,gmo{l^{ - 1}}}}\,\,\]
\[\Rightarrow n\,\, = \,\,0.0326\,\,mol\] of \[C{H_3}C{H_2}OH\]
But here, the question says about total atoms are in \[1.5{\text{ }}g\]of\[C{H_3}C{H_2}OH\]
\[n\,\, = \,\,0.0326\,\,mol\]of \[C{H_3}C{H_2}OH\]

Additional information:Ethanol is also known as ethyl alcohol, grain alcohol, spirits, drinking alcohol or simple alcohol.
Ethanol is produced naturally by the fermentation of sugars using yeasts. There is other method using petrochemical processes such as ethylene hydration. It is having medical applications such as an antiseptic and disinfectant. It is also used as a chemical solvent and used in the synthesis of organic compounds. Ethanol is also an alternative fuel source.

Note: The \[1\,g\] of 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 atoms
So, \[1\,mole\, = \,6.022\, \times \,{10^{23}}\,atoms\]
Therefore, for \[1\] atom will be;
\[1\,atom\, = \,\dfrac{1}{{6.022\, \times \,{{10}^{23}}}}\,g\,atoms\]
So, the answer will be;
\[1\,atom\, = 1.66\, \times \,{10^{ - 24}}\,g\,atoms\]
\[1\] mole \[C{H_3}C{H_2}OH\] contains Avogadro’s number (\[{N_A}\] ) of atoms.