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Complete the table Element Mole Mass Cr 0.00432 _____ Fe _____ 87.0mg Ti 1.175 10 - 3 _____...

Question:

Complete the table

Element Mole Mass
Cr 0.00432 _____
Fe _____ 87.0mg
Ti 1.175{eq}\times 10^{-3} {/eq} _____

Hg _____ 1.54Kg

Molar mass

Number of moles of any element is calculated by the ratio of mass and its molar mass. The molar mass of an element is expressed in grams per mole which is mathematically equal to the atomic mass unit of element in amu.

Answer and Explanation:

Given Data:

  • {eq}\begin{align*} {{\rm{Element}}}&&{{\rm{Mole}}}&&{{\rm{Mass}}}\\ {{\rm{Cr}}}&&{0.00432}&{}\\ {{\rm{Fe}}}&{}&&&{87.0\;{\rm{mg}}}\\ {{\rm{Ti}}}&&{{\rm{1}}{\rm{.175}} \times {{10}^{ - 3}}\;}&{}\\ {{\rm{Hg}}}&{}&&&{1.54\;{\rm{kg}}} \end{align*} {/eq}


Number of moles of any element is calculated by using the expression shown below.

{eq}{\rm{Number}}\;{\rm{of}}\;{\rm{moles}} = \dfrac{{{\rm{Mass}}}}{{{\rm{Molar}}\;{\rm{Mass}}}} \cdot \cdot \cdot \cdot \cdot \cdot \left( {\rm{I}} \right) {/eq}

In the first case, the given number of moles is equal to 0.0432.

The molar mass of Cr is 52 g/mol.

Substitute all the values in the equation (I) to calculate the mass of Cr in 0.00432 mol.

{eq}\begin{align*} 0.0432{\rm{ mol}} &= \dfrac{{{\rm{Mass}}}}{{{\rm{52}}\;{\rm{g/mol}}}}\\ {\rm{Mass}} &= 0.00432{\rm{ mol}} \times {\rm{52}}\;{\rm{g/mol}}\\ &= 0.{\rm{224}}\;{\rm{g}} \end{align*} {/eq}

Therefore, the mass of Cr is {eq}\underline {0.{\rm{224}}\;{\rm{g}}}. {/eq}

In the second case, the given mass is equal to 87.0 mg.

The conversion of mass into grams is done as shown below.

{eq}\begin{align*} {\rm{Mass}} &= {\rm{87}}\;{\rm{mg}} \times \dfrac{{{{10}^{ - 3}}{\rm{g}}}}{{1\;{\rm{mg}}}}\\ &= {\rm{87}} \times {10^{ - 3}}{\rm{g}} \end{align*} {/eq}

The molar mass of Fe is 55.8 g/mol.

Substitute all the values in the formula (I) to calculate number of moles.

{eq}\begin{align*} {\rm{Number}}\;{\rm{of}}\;{\rm{moles}}&= \dfrac{{{\rm{87}} \times {{10}^{ - 3}}{\rm{g}}}}{{{\rm{55}}{\rm{.8}}\;{\rm{g/mol}}}}\\ &= {\rm{1}}{\rm{.56}} \times {10^{ - 3}}\;{\rm{mol}} \end{align*} {/eq}

Therefore, the number of moles of Fe is {eq}\underline {{\rm{1}}{\rm{.56}} \times {{10}^{ - 3}}\;{\rm{mol}}\;}. {/eq}

In the third case, the given number of moles is equal to {eq}{\rm{1}}{\rm{.175}} \times {10^{ - 3}}\;{\rm{mol}}\;. {/eq}

The molar mass of Ti is 47.88 g/mol

Substitute all the values in the equation (I) to calculate the mass of Ti in {eq}{\rm{1}}{\rm{.175}} \times {10^{ - 3}}\;{\rm{mol}}\;. {/eq}

{eq}\begin{align*} {\rm{1}}{\rm{.175}} \times {10^{ - 3}}\;{\rm{mol}}\; &= \dfrac{{{\rm{Mass}}}}{{{\rm{47}}{\rm{.88}}\;{\rm{g/mol}}}}\\ {\rm{Mass}} &= {\rm{1}}{\rm{.175}} \times {10^{ - 3}}\;{\rm{mol}}\; \times {\rm{47}}{\rm{.88}}\;{\rm{g/mol}}\\ &= {\rm{56}}{\rm{.26}} \times {10^{ - 3}}{\rm{g}} \end{align*} {/eq}

Therefore, the mass of Ti is {eq}\underline{{\rm{56}}{\rm{.26}} \times {{10}^{ - 3}}{\rm{g}}} . {/eq}

In the fourth case, the given mass is equal to 1.54 kg.

The conversion of mass into grams is done as shown below.

{eq}\begin{align*} {\rm{Mass}} &= {\rm{1}}{\rm{.54}}\;{\rm{kg}} \times \dfrac{{{{10}^{ - 3}}{\rm{g}}}}{{1\;{\rm{kg}}}}\\ &= {\rm{1}}{\rm{.54}} \times {10^{ - 3}}{\rm{g}} \end{align*} {/eq}

The molar mass of Hg is 200.6 g/mol.

Substitute all the values in the formula (I) to calculate number of moles.

{eq}\begin{align*} {\rm{Number}}\;{\rm{of}}\;{\rm{moles}}&= \dfrac{{{\rm{Mass}}}}{{{\rm{Molar mass}}}}\\ &= \dfrac{{{\rm{1}}{\rm{.54}} \times {{10}^{ - 3}}{\rm{g}}}}{{{\rm{200}}{\rm{.6}}\;{\rm{g/mol}}}}\\ &= 7.68\;{\rm{mol}} \end{align*} {/eq}

Therefore, number of moles of Hg is {eq}\underline {7.68\;{\rm{mol}}\;} . {/eq}

So, the given table is completed as shown below.

{eq}\begin{align*} {{\rm{Element}}}&&{{\rm{Mole}}}&&{{\rm{Mass}}}\\ {{\rm{Cr}}}&&{0.00432}&&{\underline {0.{\rm{224}}\;{\rm{g}}} }\\ {{\rm{Fe}}}&&{\underline {{\rm{1}}{\rm{.56}} \times {{10}^{ - 3}}\;\;} }&&{87.0\;{\rm{mg}}}\\ {{\rm{Ti}}}&&{{\rm{1}}{\rm{.175}} \times {{10}^{ - 3}}\;}&&{\underline {{\rm{56}}{\rm{.26}} \times {{10}^{ - 3}}{\rm{g}}} }\\ {{\rm{Hg}}}&&{\underline {7.68\;} }&&{1.54\;{\rm{kg}}} \end{align*} {/eq}


Learn more about this topic:

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What is Molar Mass? - Definition, Formula & Examples

from General Studies Science: Help & Review

Chapter 27 / Lesson 24
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