Chapter 4, Problem 95AE

(a)

Interpretation Introduction

Interpretation: The percent composition by mass of the compound is to be calculated.

Concept introduction: Composition relative to elements or components in their respective compoundsor samples can be evaluated through mass percentage. Through this quantity the individual component’s mass in entire sample’s mass can be estimated. Respective formulas of given compounds can then be predicted utilizing this mass composition.

Answer to Problem 95AE

The percent composition by mass of the compound is given as follows:

  $\begin{array}{c}\text{Co}:24.7\%\\ \text{Cl}:29.7\%\\ \text{H}:5.09\%\\ \text{O}:40.5\%\end{array}$

Explanation of Solution

The compound comprises of elements $\text{Co,}\text{Cl,}\text{H}$ and $\text{O}$ .

The given mass of the sample is $0.256\text{g}$ .

The mass of silver chloride $\left(\text{AgCl}\right)$ formed is $0.308\text{g}$ .

The molar mass of $\text{AgCl}$ is $143.32\text{g/mol}$ .

The number of moles of $\text{AgCl}$ can be calculated as follows:

  $\text{Moles}=\frac{\text{Given}\text{mass}}{\text{Molar}\text{mass}}$  (1)

Substitute the values in equation (1).

  $\begin{array}{c}\text{Moles}\text{of}\text{AgCl}=\frac{0.308\text{g}}{143.32\text{g/mol}}\\ =2.149\times {10}^{-3}\text{mol}\end{array}$

Since, $1$ mole of $\text{AgCl}$ contains $1$ mole of ${\text{Cl}}^{-}$ ions, the number of moles of ${\text{Cl}}^{-}$ ions will be equal to that of $\text{AgCl}$ that is $2.149\times {10}^{-3}\text{mol}$ .

The mass of chloride can be calculated as follows:

  $\text{Mass}=\text{Moles}\times \text{Molar}\text{Mass}$(2)

The molar mass of $\text{Cl}$ is $35.45\text{g/mol}$ .

Substitute the values in equation (2) to calculate mass of $\text{Cl}$ .

  $\begin{array}{c}\text{Mass}\text{of}\text{Cl}=2.149\times {10}^{-3}\text{mol}\times 35.45\text{g/mol}\\ =0.076\text{g}\end{array}$

The mass percent of element can be calculated as follows:

  $\text{Mass}\text{\%}=\frac{\text{Mass}\text{of}\text{element}}{\text{Total}\text{sample}\text{mass}}\times 100\%$(3)

Substitute the values in equation (3) to calculate mass percent of chloride ion.

  $\begin{array}{c}\text{Mass}\text{\%}\text{of}\text{Cl}=\frac{0.076\text{g}}{0.256\text{g}}\times 100\%\\ =29.7\%\end{array}$

The given mass of second sample of the compound is $0.416\text{g}$ .

The mass of cobalt (III) oxide $\left({\text{Co}}_2{\text{O}}_3\right)$ formed is $0.145\text{g}$ .

The molar mass of ${\text{Co}}_2{\text{O}}_3$ is $165.86\text{g/mol}$ .

The number of moles of ${\text{Co}}_2{\text{O}}_3$ can be calculated using equation (1) as follows:

  $\begin{array}{c}\text{Moles}\text{of}{\text{Co}}_2{\text{O}}_3=\frac{0.145\text{g}}{165.86\text{g/mol}}\\ =8.74\times {10}^{-4}\text{mol}\end{array}$

Since, $1$ mole of ${\text{Co}}_2{\text{O}}_3$ contains $2$ molesof $\text{Co}$ , the number of moles of $\text{Co}$ can be calculated as follows:

  $\begin{array}{c}\text{Moles}\text{of}\text{Co}=\text{Moles}\text{of}{\text{Co}}_2{\text{O}}_3\times \frac{2\text{mol}\text{Co}}{1\text{mol}{\text{Co}}_2{\text{O}}_3}\\ =\left(8.74\times {10}^{-4}\times 2\right)\text{mol}\\ =\text{1}\text{.75}\times {\text{10}}^{-3}\text{mol}\end{array}$

The molar mass of cobalt is $58.93\text{g/mol}$ .

The mass of $\text{Co}$ can be calculated using equation (2) as follows:

  $\begin{array}{c}\text{Mass}\text{of}\text{Co}=\text{1}\text{.75}\times {\text{10}}^{-3}\text{mol}\times 58.93\text{g/mol}\\ =0.103\text{g}\end{array}$

The mass percent of $\text{Co}$ can be calculated using equation (3) as follows:

  $\begin{array}{c}\text{Mass}\text{\%}\text{of}\text{Co}=\frac{0.103\text{g}}{0.416\text{g}}\times 100\%\\ =24.7\%\end{array}$

The mass percent of water in the sample can be calculated as follows:

  $\text{Mass}\text{\%}\text{of}{\text{H}}_2\text{O}=100\%-\left(\text{Mass}\text{\%}\text{of}\text{Co}+\text{Mass}\text{\%}\text{of}\text{Cl}\right)$ (4)

Substitute the values in equation (4).

  $\begin{array}{c}\text{Mass}\text{\%}\text{of}{\text{H}}_2\text{O}=100\%-\left(\text{24}\text{.7}\text{\%}+29.7\%\right)\\ =100\%-54.4\%\\ =45.6\%\end{array}$

The molar mass of ${\text{H}}_2\text{O}$ is $18.015\text{g/mol}$ . It means that in $1$ mole, $18.015\text{g}$ of ${\text{H}}_2\text{O}$ is present.

The ${\text{H}}_2\text{O}$ molecule contains $2$ moles of hydrogen and $1$ mole of oxygen. One mole hydrogen contains $2.015\text{g}$ and one mole oxygen contains $16.00\text{g}$ . It means that there is $2.015\text{g}$ of hydrogen $16.00\text{g}$ of oxygen in ${\text{H}}_2\text{O}$ .

The mass percent of $\text{H}$ in water can be calculated using equation (3) as follows:

  $\begin{array}{c}\text{Mass}\text{\%}\text{of}\text{H}=\frac{2.015\text{g}}{18.015\text{g}}\times 100\%\\ =11.18\%\end{array}$

The mass percent of $\text{O}$ in water can be calculated using equation (3) as follows:

  $\begin{array}{c}\text{Mass}\text{\%}\text{of}\text{O}=\frac{16.00\text{g}}{18.015\text{g}}\times 100\%\\ =88.81\%\end{array}$

The mass percent of $\text{H}$ in the compound can be calculated as follows:

  $\begin{array}{c}\text{Mass}\text{\%}\text{of}\text{H}=\frac{11.18}{100}\times 45.6\%\\ =5.09\%\end{array}$

The mass percent of $\text{O}$ in the compound can be calculated as follows:

  $\begin{array}{c}\text{Mass}\text{\%}\text{of}\text{O}=\frac{88.81}{100}\times 45.6\%\\ =40.5\%\end{array}$

Therefore, the percent composition of the compound is as follows:

  $\begin{array}{c}\text{Co}:24.7\%\\ \text{Cl}:29.7\%\\ \text{H}:5.09\%\\ \text{O}:40.5\%\end{array}$

(b)

Interpretation Introduction

Interpretation: The formula of the compound containing $1$ cobalt ion per formula unit is to be stated.

Concept introduction:Composition relative to elements or components in their respective compounds or samples can be evaluated through mass percentage. Through this quantity the individual component’s mass in entire sample’s mass can be estimated. Respective formulas of given compounds can then be predicted utilizing this mass composition.

Answer to Problem 95AE

The formula of the compound is ${\text{CoCl}}_2\cdot 6{\text{H}}_2\text{O}$ .

Explanation of Solution

The calculated number of moles of ${\text{Cl}}^{-}$ is $2.149\times {10}^{-3}\text{mol}$ .

The mass of the compound for first reaction is given as $0.256\text{g}$ .

The calculated mass percent of $\text{Co}$ is $24.7\%$ .

The mass of $\text{Co}$ in the compound can be calculated using equation (3) as follows:

  $\begin{array}{c}\frac{\text{24}\text{.7}}{100}=\frac{\text{Mass}\text{of}\text{Co}}{0.256\text{g}}\\ \text{Mass}\text{of}\text{Co}=\frac{\text{24}\text{.7}\times 0.256}{100}\text{g}\\ \text{Mass}\text{of}\text{Co}=\text{0}\text{.063}\text{g}\end{array}$

The number of moles of $\text{Co}$ can be calculated using equation (1) as follows:

  $\begin{array}{c}\text{Moles}\text{of}\text{Co}=\frac{\text{0}\text{.063}\text{g}}{58.93\text{g/mol}}\\ =1.07\times {10}^{-3}\text{mol}\end{array}$

The mass of water can be calculated as follows:

  $\text{Mass}\text{of}{\text{H}}_2\text{O}=\text{Mass}\text{of}\text{compound}-\left(\text{Mass}\text{of}\text{Co}+\text{Mass}\text{of}\text{Cl}\right)$ (5)

Substitute the values in equation (5).

  $\begin{array}{c}\text{Mass}\text{of}{\text{H}}_2\text{O}=0.256\text{g}-\left(0.063\text{g}+0.076\text{g}\right)\\ =0.256\text{g}-0.139\\ =0.117\text{g}\end{array}$

The number of moles of water can be calculated by using equation (1) as follows:

  $\begin{array}{c}\text{Moles}\text{of}{\text{H}}_2\text{O}=\frac{\text{0}\text{.117}\text{g}}{18.015\text{g/mol}}\\ =6.5\times {10}^{-3}\text{mol}\end{array}$

The ratio of elements in the compound can be calculated by dividing each of the element’s moles with the least number of moles that is by $1.07\times {10}^{-3}\text{mol}$ as follows:

  $\begin{array}{c}\text{Co}:\text{Cl}:{\text{H}}_2\text{O}\\ \frac{1.07\times {10}^{-3}\text{mol}}{1.07\times {10}^{-3}\text{mol}}:\frac{2.149\times {10}^{-3}\text{mol}}{1.07\times {10}^{-3}\text{mol}}:\frac{6.5\times {10}^{-3}\text{mol}}{1.07\times {10}^{-3}\text{mol}}\\ 1:2.008:6.07\\ 1:2:6\end{array}$

The formula of the compound becomes ${\text{CoCl}}_2\cdot 6{\text{H}}_2\text{O}$ .

Therefore, the formula of the compound is ${\text{CoCl}}_2\cdot 6{\text{H}}_2\text{O}$ .

(c)

Interpretation Introduction

Interpretation: The three balanced reactions for the given conditions are to be stated.

Concept introduction:Composition relative to elements or components in their respective compounds or samples can be evaluated through mass percentage. Through this quantity the individual component’s mass in entire sample’s mass can be estimated. Respective formulas of given compounds can then be predicted utilizing this mass composition.

Answer to Problem 95AE

The three balanced reactions are as follows:

  $\begin{array}{c}{\text{CoCl}}_2\cdot 6{\text{H}}_2\text{O}\left(aq\right)+2{\text{AgNO}}_3\left(aq\right)\to 2\text{AgCl}\left(s\right)+\text{Co}{\left({\text{NO}}_3\right)}_2\left(aq\right)+6{\text{H}}_2\text{O}\left(l\right)\\ {\text{CoCl}}_2\cdot 6{\text{H}}_2\text{O}\left(aq\right)+2\text{NaOH}\left(aq\right)\to \text{Co}{\left(\text{OH}\right)}_2\left(s\right)+2\text{NaCl}\left(aq\right)+6{\text{H}}_2\text{O}\left(l\right)\\ \text{4Co}{\left(\text{OH}\right)}_2\left(s\right)+{\text{O}}_2\left(g\right)\to 2{\text{Co}}_2{\text{O}}_3\left(s\right)+4{\text{H}}_2\text{O}\left(l\right)\end{array}$

Explanation of Solution

The three balanced reactions are as follows:

The balanced reaction of cobalt compound with silver nitrate is as follows:

  ${\text{CoCl}}_2\cdot 6{\text{H}}_2\text{O}\left(aq\right)+2{\text{AgNO}}_3\left(aq\right)\to 2\text{AgCl}\left(s\right)+\text{Co}{\left({\text{NO}}_3\right)}_2\left(aq\right)+6{\text{H}}_2\text{O}\left(l\right)$

The balanced reaction of ${\text{CoCl}}_2\cdot 6{\text{H}}_2\text{O}$ with $\text{NaOH}$ is as follows:

  ${\text{CoCl}}_2\cdot 6{\text{H}}_2\text{O}\left(aq\right)+2\text{NaOH}\left(aq\right)\to \text{Co}{\left(\text{OH}\right)}_2\left(s\right)+2\text{NaCl}\left(aq\right)+6{\text{H}}_2\text{O}\left(l\right)$

The balanced reaction of $\text{Co}{\left(\text{OH}\right)}_2$ with ${\text{O}}_2$ is as follows:

  $\text{4Co}{\left(\text{OH}\right)}_2\left(s\right)+{\text{O}}_2\left(g\right)\to 2{\text{Co}}_2{\text{O}}_3\left(s\right)+4{\text{H}}_2\text{O}\left(l\right)$

Therefore the three balanced reactions are as follows:

  $\begin{array}{c}{\text{CoCl}}_2\cdot 6{\text{H}}_2\text{O}\left(aq\right)+2{\text{AgNO}}_3\left(aq\right)\to 2\text{AgCl}\left(s\right)+\text{Co}{\left({\text{NO}}_3\right)}_2\left(aq\right)+6{\text{H}}_2\text{O}\left(l\right)\\ {\text{CoCl}}_2\cdot 6{\text{H}}_2\text{O}\left(aq\right)+2\text{NaOH}\left(aq\right)\to \text{Co}{\left(\text{OH}\right)}_2\left(s\right)+2\text{NaCl}\left(aq\right)+6{\text{H}}_2\text{O}\left(l\right)\\ \text{4Co}{\left(\text{OH}\right)}_2\left(s\right)+{\text{O}}_2\left(g\right)\to 2{\text{Co}}_2{\text{O}}_3\left(s\right)+4{\text{H}}_2\text{O}\left(l\right)\end{array}$