Chapter 2, Problem 2.76QA

Interpretation Introduction

To find:

Moles and atoms of iron in the given compounds.

Answer to Problem 2.76QA

Solution:

a) 2.5 moles of wolframite - FeWO₄ contain 2.5 moles and 1.5 x 10²⁴ atoms of Iron_.

b) 2.5 moles of pyrite- FeS₂ contain 2.5 moles and 1.5 x 10²⁴ atoms of Iron

c) 2.5 moles of magnetite - Fe₃O₄ contain 7.5 moles and 4.5 x 10²⁴ atoms of Iron_.

d) 2.5 moles of hematite - Fe₂O₃ contain 5.0 moles and 3.0 x 10²⁴ atoms of Iron_.

Explanation of Solution

Calculations:

a) 2.5 moles of FeWO₄

In one molecule of FeWO₄, there is one atom of Fe. Therefore, we can say that the mole ratio between FeWO₄ and Fe is 1:1. Now, we have the mole to mole ratio and moles of FeWO_4. So, we can calculate the moles of Fe by using the dimensional analysis as below.

$2.5\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}\mathrm{W}{\mathrm{O}}_4\mathrm{ }\times \mathrm{ }\frac{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}}{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}\mathrm{W}{\mathrm{O}}_4}=2.5\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}$

So, 2.5 moles of FeWO₄ contain 2.5 moles of Fe.

Now, we convert moles into atoms. We know that in every 1 mol of substance, we have 6.023 x  10²³ molecules or atoms of given substance, which is equal to Avogadro’s number.

$1 moles of the Fe = 6.023 \times {10}^{23} atoms of Fe$

Using this conversion factor, we will convert 2.5 mol of Fe to atoms of Fe.

$2.5\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}\times \frac{6.023\mathrm{*}\mathrm{ }{10}^{23}\mathrm{ }\mathrm{ }\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{ }\mathrm{F}\mathrm{e}}{1\mathrm{ }\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}}= {1.5\times 0}^{24}\mathrm{ }\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}$

So, 2.5 moles of FeWO₄ contain 1.5 x 10²⁴ atoms of Fe.

b) 2.5 moles of FeS₂

In one molecule of FeS₂, there is one atom of Fe. Therefore, we can say that the mole ratio between FeS₂ and Fe is 1:1. Now, we have the mole to mole ratio and moles of FeS₂. So, we can calculate the moles of Fe by using dimensional analysis as below.

$2.5\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{\mathrm{F}\mathrm{e}\mathrm{S}}_2\times \frac{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}}{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{\mathrm{F}\mathrm{e}\mathrm{S}}_2}=2.5\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}$

So, 2.5 moles of FeS₂ contains 2.5 moles of Fe.

Now, we convert moles into atoms. We know that in every 1 mol of substance, we have 6.023 x 1023 molecules or atoms of the given substance, which is equal to Avogadro’s number.

$1 moles of the Fe = 6.023 \times {10}^{23} atoms of Fe$

Using this conversion factor, we will convert 2.5 mol of Fe to atoms of Fe.

$2.5\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}\mathrm{ }\times \frac{6.023\mathrm{*}\mathrm{ }{10}^{23}\mathrm{ }\mathrm{ }\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{ }}{1\mathrm{ }\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}}= {1.5\times 10}^{24}\mathrm{ }\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}$

So, 2.5 moles of FeS₂ contain 1.5 x 10²⁴ atoms of Fe.

c) 2.5 moles of Fe₃O₄

In one molecule of Fe₃O₄, there are three atoms of Fe. Therefore, we can say that the mole ratio between Fe₃O₄ and Fe is 1:3. Now, we have the mole to mole ratio and moles of Fe₃O₄. So, we can calculate the moles of Fe by using the dimensional analysis as below.

$2.5\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{{\mathrm{F}\mathrm{e}}_3\mathrm{O}}_4\times \frac{3\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}\mathrm{ }}{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{{\mathrm{F}\mathrm{e}}_3\mathrm{O}}_4}=7.5\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}$

So, 2.5 moles of Fe₃O₄ contains 7.5 moles of Fe.

Now, we convert moles into atoms. We know that in every 1 mol of substance, we have 6.023 x  10²³ molecules or atoms of given substance, which is equal to Avogadro’s number.

$1 moles of the Fe = 6.023 \times {10}^{23} atoms of Fe$

Using this conversion factor, we will convert 7.5 mol of Fe to atoms of Fe.

$7.5\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}\times \frac{6.023\mathrm{*}\mathrm{ }{10}^{23}\mathrm{ }\mathrm{ }\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}}{1\mathrm{ }\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}}= {4.5\times 10}^{24}\mathrm{ }\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}$

So, 2.5 moles of Fe₃O₄ contain 4.5 x 10²⁴ atoms of Fe.

d) 2.5 moles of Fe₂O₃

In one molecule of Fe₂O₃, there are two atoms of Fe. Therefore, we can say that the mole ratio between Fe₂O₃ and Fe is 1:2. Now, we have the mole to mole ratio and moles of Fe₂O₃. So, we can calculate the moles of Fe by using dimensional analysis as below.

$2.5\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{\mathrm{F}\mathrm{e}}_2{\mathrm{O}}_3\times \frac{2\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}}{1\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }{\mathrm{F}\mathrm{e}}_2{\mathrm{O}}_3}=5.0\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}$

So, 2.5 moles of Fe₂O₃ contains 5.0 moles of Fe.

Now, we convert moles into atoms. We know that in every 1 mol of substance, we have 6.023 x  10²³ molecules or atoms of given substance, which is equal to Avogadro’s number.

$1 moles of the Fe = 6.023 \times {10}^{23} atoms of Fe$

Using this conversion factor, we will convert 5.0 mol of Fe to atoms of Fe.

$5.0\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}\mathrm{ }\times \frac{6.023\mathrm{*}\mathrm{ }{10}^{23}\mathrm{ }\mathrm{ }\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}\mathrm{ }}{1\mathrm{ }\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}}= {3.0\mathrm{*}10}^{24}\mathrm{ }\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{F}\mathrm{e}$

So, 2.5 moles of Fe₂O₃ contains 3.0 x 10²⁴ atoms of Fe.

Conclusion:

a) 2.5 moles of wolframite - FeWO₄ contain 2.5 moles and 1.5 x 10²⁴ atoms of Iron_.

b) 2.5 moles of pyrite- FeS₂ contain 2.5 moles and 1.5 x 10²⁴ atoms of Iron

c) 2.5 moles of magnetite - Fe₃O₄ contain 7.5 moles and 4.5 x 10²⁴ atoms of Iron_.

d) 2.5 moles of hematite - Fe₂O₃ contain 5.0 moles and 3.0 x 10²⁴ atoms of Iron_.