Question

How many moles of chlorine gas will be required to react with sufficient iron to produce 14 moles of iron(III) chloride?
\[{\text{2Fe}}\left( {\text{s}} \right)\,{\text{ + 3C}}{{\text{l}}_{\text{2}}}\left( {\text{g}} \right) \to {\text{2FeC}}{{\text{l}}_3}\left( {\text{s}} \right)\]

Answer 1

Hint:Determine the yield means we have to determine the amount of the substance. In a chemical reaction, the yield is determined by using the stoichiometry between the reactants and the products.Stoichiometry is nothing but the mole ratio of reactants and products involved in the balanced chemical reaction.Here, the mole ratio is typically the ratio of integer numbers. In many chemical reactions, the stoichiometric relation is used to determine the amount that is the yield of the product.

Complete step-by-step solution:Here, in the question the reaction it is given that two moles of the solid iron reacts with three moles of the gaseous chlorine and produce two moles of the solid iron(III) chloride as follows:
\[{\text{2Fe}}\left( {\text{s}} \right)\,{\text{ + 3C}}{{\text{l}}_{\text{2}}}\left( {\text{g}} \right) \to {\text{2FeC}}{{\text{l}}_3}\left( {\text{s}} \right)\]
The mole ratio between the reactants and products is as follows:
\[{\text{Fe}}\,\,{\text{:}}\,\,{\text{C}}{{\text{l}}_{\text{2}}}\,\,{\text{:}}\,\,{\text{FeC}}{{\text{l}}_{\text{3}}}\]
\[{\text{2}}\,\,{\text{mol}}\,\,{\text{:}}\,\,{\text{3}}\,\,{\text{mol}}\,\,{\text{:}}\,\,{\text{2}}\,{\text{mol}}\]
The stoichiometric mole ratio indicates 3 moles of the chlorine gas are required to produce two moles of the iron(III) chloride.
\[{\text{C}}{{\text{l}}_{\text{2}}}\,\,{\text{:}}\,\,{\text{FeC}}{{\text{l}}_{\text{3}}}\]
\[{\text{3}}\,\,{\text{mol}}\,\,{\text{:}}\,\,{\text{2}}\,{\text{mol}}\]
Now, determine the moles of the chlorine gas required to react with iron to produce 14 moles of iron(III) chloride as follows:
\[{\text{C}}{{\text{l}}_{\text{2}}}\,{\text{ = }}\,{\text{FeC}}{{\text{l}}_{\text{3}}}\]
\[{\text{3}}\,\,{\text{mol}}\,\,{\text{C}}{{\text{l}}_2} = \,\,{\text{2}}\,{\text{mol}}\,\,{\text{FeC}}{{\text{l}}_3}\]
\[{\text{14}}\,{\text{mol}}\,\,{\text{FeC}}{{\text{l}}_3} = \dfrac{{{\text{14}}\,{\text{mol}}\,\,{\text{FeC}}{{\text{l}}_3} \times {\text{3}}\,\,{\text{mol}}\,\,{\text{C}}{{\text{l}}_2}}}{{{\text{2}}\,{\text{mol}}\,\,{\text{FeC}}{{\text{l}}_3}}}\]
\[{\text{14}}\,{\text{mol}}\,\,{\text{FeC}}{{\text{l}}_3} = 21\,\,{\text{mol}}\,\,{\text{C}}{{\text{l}}_2}\]
Thus, the moles of the chlorine gas required to produce 14 moles of the iron(III) chloride is 21 moles.

Note:The moles of the substance are calculated using the following formulae:
\[{\text{mole = }}\dfrac{{{\text{weight}}}}{{{\text{molar}}\,{\text{mass}}}}\]
The mole ratio obtained from the balanced chemical reaction is very useful to determine the amount of the species in the reaction.We can determine the amount of the product formed in the reaction or the amount of the reactant required to produce a specific amount of the products.Here, the given reaction is a balanced chemical reaction hence, use its mole ratio for determining the moles of the chlorine gas.