Question

How many number of moles of carbon and hydrogen atoms and also number of molecules of ethane present in $\text{3}\,\text{moles}$ of ethane $\text{(}{{\text{C}}_{\text{2}}}{{\text{H}}_{\text{6}}}\text{)}$?

Answer 1

Hint:A mole is the amount of a substance that contains as many atoms or molecule as there are atoms in exactly $\text{12}\,\text{gm}$ of the$\text{carbon-12}$. In a simple way one mole is the collection of $\text{6}\text{.022 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{23}}}\text{atom/molecule}$.
One mole of every substance contains $\text{6}\text{.022 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{23}}}\text{molecules}$and this is given a separate name and symbol known as ‘Avogadro constant’ denoted by${{\text{N}}_{\text{A}}}$.
In chemistry atoms, molecules and ions are subatomic particles and we count the number of atom or molecules by weighing the amount of substance. In a chemical reaction the moles of two substance reacts in a definite ratio, so we use following formula to calculate the number of moles in a reaction –
 $\text{mole}\,\text{atom = }\dfrac{\text{weight}}{\text{atomic}\,\text{weight}}....(i)$
$\text{mole}\,\text{molecules = }\dfrac{\text{weight}}{\text{molecular}\,\text{weight}}.....(ii)$
$\text{mole}\,\text{molecules =}\dfrac{\text{number}\,\text{of}\,\text{molecule}}{{{\text{N}}_{\text{A}}}}......(iii)$
In a chemical reaction stoichiometry of reacting substance represents the reacting moles of these chemical substances.

Complete step-by-step answer:Since, one mole of ethane gives two mole of carbon and six mole of hydrogen, so three moles of ethane gives six moles of carbon and eighteen moles of hydrogen.
                                                        \[\begin{align}
  & {{\text{C}}_{\text{2}}}{{\text{H}}_{\text{6}}}\to \,\text{2C}\,\text{+}\,\text{6H} \\
 & \text{3}{{\text{C}}_{\text{2}}}{{\text{H}}_{\text{6}}}\to \,\text{6C}\,\text{+}\,\text{18H} \\
\end{align}\]
(i) Six moles of carbon atom.
(ii) Eighteen moles of hydrogen atom.
(iii) After applying the equation (III) we will get the number of molecules present in the$\text{3}\,\text{moles}$of ethane.
 $\begin{align}
  & \text{mole}\,\text{molecules =}\dfrac{\text{number}\,\text{of}\,\text{molecules}}{{{\text{N}}_{\text{A}}}} \\
 & 3=\dfrac{\text{number}\,\text{of}\,\text{molecules}}{6.022\times {{10}^{23}}} \\
 & \text{number}\,\text{of}\,\text{molecule}s=\,3\times 6.022\times {{10}^{23}} \\
 & \text{number}\,\text{of}\,\text{molecule}s=\,18.06\text{6 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{23}}}\text{molecules} \\
 & =\,1.8066\times {{10}^{24}}\text{molecules}
\end{align}$

Note:Weight of one mole is the molecular weight in gram.
Equal moles of different substances contain the same number of constituent particles but equal weight of different substances does not contain the same number of constituent particles.