Respuesta :
To know the answer, determine first the mass of the copper
used:
Copper used = 100 pennies x 3.0g Cu per penny = 300.0 g Cu
then, determine the pathway and molar ratio from Cu formed back to CuFeS2 required
using the balanced reactions:
1 Cu2S from 2 CuS; 2Cu from 1 Cu2S; 2CuS from 2CuFeS2
Therefore 2Cu from 2CuFeS2, they are in a one to one molar ratio.
then, convert g Cu to moles and g of CuFeS2:
= 300.0 g Cu * 1 mol Cu/63.546g Cu * 2 mol CuFeS2/2 moles Cu
= 4.72 moles CuFeS2
chalcopyrite had to be mined = 4.72 moles CuFeS2 * 183.54 g CuFeS2/1 mole
CuFeS2 = 866.49 g CuFeS2
The amount of chalcopyrite that had be mined to produce 100 pennies is [tex]\boxed{{\text{866}}{\text{.49g}}}[/tex].
Further explanation:
Stoichiometry of a reaction is used to determine the amount of species present in the reaction by the relationship between the reactants and products. It can be used to determine the moles of a chemical species when the moles of other chemical species present in the reaction is given.
Consider the general reaction,
[tex]{\text{A}}+2{\text{B}}\to3{\text{C}}[/tex]
Here,
A and B are reactants.
C is the product.
One mole of A reacts with two moles of B to produce three moles of C. The stoichiometric ratio between A and B is 1:2, the stoichiometric ratio between A and C is 1:3 and the stoichiometric ratio between B and C is 2:3.
The elemental copper that exists in its native state can be mined from its naturally occurring oxide or sulfide minerals. To extract copper from chalcopyrite certain reactions sequence is followed. First, the chalcopyrite is converted to its copper sulfide by the following reaction:
[tex]2{\text{CuFe}}{{\text{S}}_2}+3{{\text{O}}_2}\to2{\text{CuS}}+2{\text{FeO}}+2{\text{S}}{{\text{O}}_2}[/tex]
In the second step, the ferrous oxide thus formed is then treated with silica as follows:
[tex]2{\text{FeO}}+{\text{Si}}{{\text{O}}_2}\to2{\text{FeSi}}{{\text{O}}_3}[/tex]
In the third step, the copper sulfide decomposes as shown below:
[tex]2{\text{CuS}}\to{\text{C}}{{\text{u}}_2}{\text{S}}+{\text{S}}[/tex]
In the final sequence of the reaction, the [tex]{\text{C}}{{\text{u}}_2}{\text{S}}[/tex] formed undergoes following oxidation to form elemental copper.
[tex]{\text{C}}{{\text{u}}_2}{\text{S}}+{\text{S}}\to{\text{2Cu}}+2{\text{S}}{{\text{O}}_2}[/tex]
From these reactions, it is the evident that 2 moles of [tex]{\text{CuFe}}{{\text{S}}_2}[/tex] forms 2 moles of elemental copper. Therefore the molar ratio of the combination of Cu and [tex]{\mathbf{CuFe}}{{\mathbf{S}}_{\mathbf{2}}}[/tex] is 1:1.
Since one penny contains 3 g of Cu hence the mass of copper in 100 pennies is calculated as follows:
[tex]\begin{gathered}{\text{Mass of Cu}}=\left({\frac{{3\;{\text{g}}}}{{1\,{\text{penny}}}}}\right)\left({100\;{\text{pennies}}}\right)\\=300\;{\text{g}}\\\end{gathered}[/tex]
Using the mass of copper and the molar mass we would determine the number of moles of copper by applying the following formula.
[tex]{\text{Number of moles}}=\frac{{{\text{Given mass}}}}{{{\text{Molar mass}}}}[/tex] …… (1)
The given mass is [tex]300{\text{g}}[/tex].
The molar mass is [tex]{\text{63}}{\text{.546g/mol}}[/tex].
Substitute the values in equation (1).
[tex]\begin{gathered}{\text{Number of moles}}=\frac{{300.0{\text{g}}}}{{{\text{63}}{\text{.546g/mol}}}}\\=4.72099{\text{mol}}\\\end{gathered}[/tex]
The molar ratio of combination of Cu and [tex]{\text{CuFe}}{{\text{S}}_2}[/tex] is 1:1, so the number of moles of [tex]{\mathbf{CuFe}}{{\mathbf{S}}_{\mathbf{2}}}[/tex] is 4.72099 mol.
The moles of [tex]{\text{CuFe}}{{\text{S}}_2}[/tex] calculated can be used to determine the corresponding mass in grams. The formula to calculate the mass is as follows:
[tex]{\text{Mass of CuFe}}{{\text{S}}_2}=\left({{\text{moles of CuFe}}{{\text{S}}_2}}\right)\left({{\text{molar mass of CuFe}}{{\text{S}}_2}}\right)[/tex] …… (2)
The moles of [tex]{\text{CuFe}}{{\text{S}}_2}[/tex]is [tex]4.72099{\text{ mol}}[/tex].
The molar mass of [tex]{\text{CuFe}}{{\text{S}}_2}[/tex]is[tex]183.54{\text{g/mol}}[/tex].
Substitute the values in equation (2).
[tex]\begin{gathered}{\text{Mass of CuFe}}{{\text{S}}_2}=\left({4.72099{\text{ mol}}}\right)\left({183.54{\text{g/mol}}}\right)\\=866.49{\text{g}}\\\end{gathered}[/tex]
Learn more:
1. Statement about subatomic particle: https://brainly.com/question/3176193
2. The net ionic equation for the reaction of [tex]{\text{MgS}}{{\text{O}}_{\text{4}}}[/tex] with [tex]{\text{Sr}}{\left({{\text{N}}{{\text{O}}_3}}\right)_2}[/tex] : https://brainly.com/question/4357519
Answer details:
Grade: College
Subject: Chemistry
Chapter: Mole concept and stoichiometry
Keywords: copper, penny, pennies, CuFeS2, stoichiometry, O2, moles, mass, S and Cu2S.
