Chapter 2, Problem 2.91P

The scvcn most abundant ions in seawater make up more than 99% by mass of the dissolved compounds. Here are their abundances in units of mg ion/kg seawater: chloride 18,980; sodium 10,560; sulfate 2650; magnesium 1270; calcium 400; potassium 380; hydrogcn carbonate 140.

(a) What is thc mass % of each ion in seawater?

(b) What çcrccnt of the total mass of ions is sodium ion?

(c) How does the total mass % of alkaline earth metal ions compare with the total mass % of alkali metal ions?

(d) Which make up the larger mass fraction of dissolved compon ents, anions or cations?

Interpretation Introduction

Interpretation:Mass $\%$ of each ion in seawater is to be calculated.

Concept introduction:Mass $\%$ is a method of representation of concentration of an element in a compound or a component mixture.

Calculation of mass $\%$ is done as follows:

  $\text{Mass}\%\text{of}\text{a}\text{component}\text{in}\text{a}\text{mixture}=\left(\frac{\text{Mass}\text{of}\text{that}\text{component}\text{in}\text{mixture}}{\text{Total}\text{mass}\text{of}\text{mixture}}\right)\left(100\right)\%$

Answer to Problem 2.91P

Mass $\%$ of chloride in seawater is $1.898\%$ .Mass $\%$ of sodium in seawater is $1.056\%$ .Mass $\%$ of sulfate in seawater is $0.265\%$ .Mass $\%$ of magnesiumin seawater is $0.127\%$ . Mass $\%$ of calciumin seawater is $0.04\%$ . Mass $\%$ of potassiumin seawater is $0.038\%$ . Mass $\%$ of hydrogen carbonatein seawater is $0.014\%$ .

Explanation of Solution

Given Information: In $1\text{kg}$ seawater mass of chloride ion is $18980\text{mg}$ , mass of sodium ion is $10560\text{mg}$ , mass of sulfate ion is $2650\text{mg}$ , mass of magnesium ion is $1270\text{mg}$ , mass of calcium ion is $400\text{mg}$ , mass of potassium $380\text{mg}$ , and mass of hydrogen carbonate is $140\text{mg}$ .

Mass $\%$ is a method of representation of concentration of an element in a compound or a component mixture.

Formula to calculate the mass $\%$ is as follows:

  $\text{Mass}\%\text{of}\text{a}\text{component}\text{in}\text{a}\text{mixture}=\left(\frac{\text{Mass}\text{of}\text{that}\text{component}\text{in}\text{mixture}}{\text{Total}\text{mass}\text{of}\text{mixture}}\right)\left(100\right)\%$

Total mass of seawater is $1\text{kg}$ or ${10}^6\text{mg}$ .

Formula to calculate the mass $\%$ of chloride ion is as follows:

  $\text{Mass}\%\text{of}\text{chloride}\text{ion}\text{in}\text{seawater}=\left(\frac{\text{Mass}\text{of}\text{chloride}\text{ion}}{\text{Total}\text{mass}\text{of}\text{seawater}}\right)\left(100\right)\%$

Mass of chloride ion is $18980\text{mg}$ .

Total mass of seawater is ${10}^6\text{mg}$ .

Substitute the values in above formula.

  $\begin{array}{c}\text{Mass}\%\text{of}\text{chloride}\text{ion}\text{in}\text{seawater}=\left(\frac{\text{Mass}\text{of}\text{chloride}\text{ion}}{\text{Total}\text{mass}\text{of}\text{seawater}}\right)\left(100\right)\%\\ =\left(\frac{18980\text{mg}}{{10}^6\text{mg}}\right)\left(100\right)\%\\ =1.898\%\end{array}$

Formula to calculate the mass $\%$ of sodium ion is as follows:

  $\text{Mass}\%\text{of}\text{sodium ion}\text{in}\text{seawater}=\left(\frac{\text{Mass}\text{of}\text{sodium ion}}{\text{Total}\text{mass}\text{of}\text{seawater}}\right)\left(100\right)\%$

Mass of sodium ion is $10560\text{mg}$ .

Total mass of seawater is ${10}^6\text{mg}$ .

Substitute the values in above formula.

  $\begin{array}{c}\text{Mass}\%\text{of}\text{sodium}\text{ion}\text{in}\text{seawater}=\left(\frac{\text{Mass}\text{of}\text{sodium}\text{ion}}{\text{Total}\text{mass}\text{of}\text{sea}\text{water}}\right)\left(100\right)\%\\ =\left(\frac{10560\text{mg}}{{10}^6\text{mg}}\right)\left(100\right)\%\\ =1.056\%\end{array}$

Formula to calculate the mass $\%$ of sulfate ion is as follows:

  $\text{Mass}\%\text{of}\text{sulfate ion}\text{in}\text{seawater}=\left(\frac{\text{Mass}\text{of}\text{sulfate ion}}{\text{Total}\text{mass}\text{of}\text{sea}\text{water}}\right)\left(100\right)\%$

Mass of sulfate ion is $2650\text{mg}$ .

Total mass of seawater is ${10}^6\text{mg}$ .

Substitute the values in the above formula.

  $\begin{array}{c}\text{Mass}\%\text{of}\text{sulfate ion}\text{in}\text{seawater}=\left(\frac{\text{Mass}\text{of}\text{sulfate ion}}{\text{Total}\text{mass}\text{of}\text{sea}\text{water}}\right)\left(100\right)\%\\ =\left(\frac{2650\text{mg}}{{10}^6\text{mg}}\right)\left(100\right)\%\\ =0.265\%\end{array}$

Formula to calculate the mass $\%$ of magnesium ion is as follows:

  $\text{Mass}\%\text{of}\text{magnesium ion}\text{in}\text{seawater}=\left(\frac{\text{Mass}\text{of}\text{magnesium ion}}{\text{Total}\text{mass}\text{of}\text{sea}\text{water}}\right)\left(100\right)\%$

Mass of magnesium ion is $1270\text{mg}$ .

Total mass of seawater is ${10}^6\text{mg}$ .

Substitute the values in the above formula.

  $\begin{array}{c}\text{Mass}\%\text{of}\text{magnesium ion}\text{in}\text{seawater}=\left(\frac{\text{Mass}\text{of}\text{magnesium ion}}{\text{Total}\text{mass}\text{of}\text{sea}\text{water}}\right)\left(100\right)\%\\ =\left(\frac{1270\text{mg}}{{10}^6\text{mg}}\right)\left(100\right)\%\\ =0.127\%\end{array}$

Formula to calculate the mass $\%$ of calcium ion is as follows:

  $\text{Mass}\%\text{of}\text{calcium ion}\text{in}\text{seawater}=\left(\frac{\text{Mass}\text{of}\text{calcium ion}}{\text{Total}\text{mass}\text{of}\text{sea}\text{water}}\right)\left(100\right)\%$

Mass of calcium ion is $400\text{mg}$ .

Total mass of seawater is ${10}^6\text{mg}$ .

Substitute the values in the above formula.

  $\begin{array}{c}\text{Mass}\%\text{of}\text{calcium ion}\text{in}\text{seawater}=\left(\frac{\text{Mass}\text{of}\text{calcium ion}}{\text{Total}\text{mass}\text{of}\text{sea}\text{water}}\right)\left(100\right)\%\\ =\left(\frac{400\text{mg}}{{10}^6\text{mg}}\right)\left(100\right)\%\\ =0.04\%\end{array}$

Formula to calculate the mass $\%$ of potassium ion is as follows:

  $\text{Mass}\%\text{of}\text{potassium ion}\text{in}\text{seawater}=\left(\frac{\text{Mass}\text{of}\text{potassium ion}}{\text{Total}\text{mass}\text{of}\text{sea}\text{water}}\right)\left(100\right)\%$

Mass of ium ion is $400\text{mg}$ .

Total mass of seawater is ${10}^6\text{mg}$ .

Substitute the values in the above formula.

  $\begin{array}{c}\text{Mass}\%\text{of}\text{potassium ion}\text{in}\text{seawater}=\left(\frac{\text{Mass}\text{of}\text{potassium ion}}{\text{Total}\text{mass}\text{of}\text{sea}\text{water}}\right)\left(100\right)\%\\ =\left(\frac{380\text{mg}}{{10}^6\text{mg}}\right)\left(100\right)\%\\ =0.038\%\end{array}$

Formula to calculate the mass $\%$ of hydrogen carbonate ion is as follows:

  $\text{Mass}\%\text{of}\text{hydrogen}\text{carbonate ion}=\left(\frac{\text{Mass}\text{of}\text{hydrogen carbonate ion}}{\text{Total}\text{mass}\text{of}\text{sea}\text{water}}\right)\left(100\right)\%$

Mass of hydrogen carbonate ion is $\text{140}\text{mg}$ .

Total mass of seawater is ${10}^6\text{mg}$ .

Substitute the values in the above formula.

  $\begin{array}{c}\text{Mass}\%\text{of}\text{hydrogen}\text{carbonate ion}=\left(\frac{\text{Mass}\text{of}\text{hydrogen}\text{carbonate ion}}{\text{Total}\text{mass}\text{of}\text{sea}\text{water}}\right)\left(100\right)\%\\ =\left(\frac{140\text{mg}}{{10}^6\text{mg}}\right)\left(100\right)\%\\ =0.014\%\end{array}$

Interpretation Introduction

Interpretation: Mass $\%$ of sodium among total mass of ion is to be calculated.

Concept introduction: Mass $\%$ is a method of representation of concentration of an element in a compound or a component mixture.

Formula to calculate mass $\%$ is done as follows:

  $\text{Mass}\%\text{of}\text{a}\text{component}=\left(\frac{\text{Mass}\text{of}\text{that}\text{component}\text{in}\text{mixture}}{\text{Total}\text{mass}\text{of}\text{mixture}}\right)\left(100\right)\%$

Answer to Problem 2.91P

Mass $\%$ of sodium ion among total mass of ion $30.715\%$

Explanation of Solution

Given Information: In $1\text{kg}$ seawater mass of chloride ion is $18980\text{mg}$ , mass of sodium ion is $10560\text{mg}$ , mass of sulfate ion is $2650\text{mg}$ , mass of magnesium ion is $1270\text{mg}$ , mass of calcium ion is $400\text{mg}$ , mass of potassium $380\text{mg}$ , and mass of hydrogen carbonate is $140\text{mg}$ .

Mass $\%$ is a method of representation of concentration of an element in a compound or a component mixture.

Formula to calculate the mass $\%$ is as follows:

  $\text{Mass}\%\text{of}\text{a}\text{component}\text{in}\text{a}\text{mixture}=\left(\frac{\text{Mass}\text{of}\text{that}\text{component}\text{in}\text{mixture}}{\text{Total}\text{mass}\text{of}\text{mixture}}\right)\left(100\right)\%$

Total mass of ionsin $1\text{kg}$ or ${10}^6\text{mg}$ seawater is calculated as follows:

  $\begin{array}{c}\text{Total}\text{mass}\text{of}\text{ion}=\left(\begin{array}{l}18980\text{mg}+10560\text{mg}+2650\text{mg}+\\ 1270\text{mg}+400\text{mg}+380\text{mg}+140\text{mg}\end{array}\right)\\ =34380\text{mg}\end{array}$

Formula to calculate the mass $\%$ of sodium ion, among total mass of ion is as follows:

  $\text{Mass}\%\text{of}\text{sodium}\text{ion}\text{among}\text{total}\text{mass}\text{of}\text{ion}=\left(\frac{\text{Mass}\text{of}\text{sodium}\text{ion}}{\text{Total}\text{mass}\text{of}\text{ions}}\right)\left(100\right)\%$

Mass of sodium ion is $10560\text{mg}$ .

Total mass of ion is $34380\text{mg}$ .

Substitute the values in above formula.

  $\begin{array}{c}\text{Mass}\%\text{of}\text{sodium}\text{ion}\text{among}\text{total}\text{mass}\text{of}\text{ion}=\left(\frac{\text{Mass}\text{of}\text{sodium}\text{ion}}{\text{Total}\text{mass}\text{of}\text{ions}}\right)\left(100\right)\%\\ =\left(\frac{10560\text{mg}}{34380\text{mg}}\right)\left(100\right)\%\\ =30.715\%\end{array}$

Interpretation Introduction

Interpretation: Mass $\%$ of alkaline earth metals among total mass of ion is to be calculated.

Concept introduction: Mass $\%$ is a method of representation of concentration of an element in a compound or a component mixture.

Formula to calculate mass $\%$ is as follows:

  $\text{Mass}\%\text{of}\text{a}\text{component}=\left(\frac{\text{Mass}\text{of}\text{that}\text{component}\text{in}\text{mixture}}{\text{Total}\text{mass}\text{of}\text{mixture}}\right)\left(100\right)\%$

Answer to Problem 2.91P

Total mass percent for alkali metal ions is $6.6$ times greater than mass percent for alkaline earth metal ions.

Explanation of Solution

Given Information: In $1\text{kg}$ seawater mass of chloride ion is $18980\text{mg}$ , mass of sodium ion is $10560\text{mg}$ , mass of sulfate ion is $2650\text{mg}$ , mass of magnesium ion is $1270\text{mg}$ , mass of calcium ion is $400\text{mg}$ , mass of potassium $380\text{mg}$ , and mass of hydrogen carbonate is $140\text{mg}$ .

${\text{Mg}}^{2+}$ and ${\text{Ca}}^{2+}$ ions are alkaline earth metal ions. Percentage of total mass of alkaline earth metal ions is equal to sum of mass percentage of ${\text{Mg}}^{2+}$ and ${\text{Ca}}^{2+}$ and is calculated as follows:

  $\begin{array}{c}\text{Mass \% of alkaline earth metal ions}={\text{Mg}}^{2+}+{\text{Ca}}^{2+}\\ =0.127\text{ \%}+0.04\text{ \%}\\ =0.167\text{ \%}\end{array}$

  ${\text{Na}}^{+}$ and ${\text{K}}^{+}$ ions are found in alkali metal ions. Percentage of total mass of alkali metal ions is equal to sum of the mass percentage of ${\text{Na}}^{+}$ and ${\text{K}}^{+}$ and is calculated as follows:

  $\begin{array}{c}\text{Mass \% of alkali metal ions}={\text{Na}}^{+}+{\text{K}}^{+}\\ =1.056\text{ \%}+0.038\text{ \%}\\ =1.094\text{ \%}\end{array}$

Expression to calculate ratio of mass $\%$ of alkali ions to mass $\%$ of alkaline earth metal ions is as follows:

  $\left(\begin{array}{l}\text{Ratio of mass \% of alkali }\\ \text{ions to mass \% of }\\ \text{alkaline earth metal ions}\end{array}\right)=\frac{\text{Mass \% of alkali ions}}{\text{Mass \% of alkaline earth metal ions}}$

Mass $\%$ of alkali ions is $1.094\text{ \%}$ .

Mass $\%$ of alkaline earth metal ions is $0.167\text{ \%}$ .

Substitute the values in above formula.

  $\begin{array}{c}\left(\begin{array}{l}\text{Ratio of mass \% of alkali }\\ \text{ions to mass \% of }\\ \text{alkaline earth metal ions}\end{array}\right)=\frac{\text{Mass \% of alkali ions}}{\text{Mass \% of alkaline earth metal ions}}\\ =\frac{1.094\text{ \%}}{0.167\text{ \%}}\\ =\mathrm{6.6.}\end{array}$

Therefore, total mass percent for alkali metal ions is $6.6$ times greater than mass percent for alkaline earth metal ions.

Interpretation Introduction

Interpretation:Cation or anion that has larger mass fraction of dissolved component is to be identified.

Concept introduction: Mass fraction is a method of representation of concentration of an element in a compound or a component mixture.

Calculation of mass fraction is done as follows:

  $\text{Mass}\text{fraction}\text{of}\text{a}\text{component}\text{in}\text{a}\text{mixture}=\left(\frac{\text{Mass}\text{of}\text{that}\text{component}\text{in}\text{mixture}}{\text{Total}\text{mass}\text{of}\text{mixture}}\right)$

Explanation of Solution

Given Information: In $1\text{kg}$ seawater mass of chloride ion is $18980\text{mg}$ , mass of sodium ion is $10560\text{mg}$ , mass of sulfate ion is $2650\text{mg}$ , mass of magnesium ion is $1270\text{mg}$ , mass of calcium ion is $400\text{mg}$ , mass of potassium $380\text{mg}$ , and mass of hydrogen carbonate is $140\text{mg}$ .

Mass fraction is a method of representation of concentration of an element in a compound or a component mixture.

Formula to calculate mass fraction is as follows:

  $\text{Mass}\text{fraction}\text{of}\text{a}\text{component}=\left(\frac{\text{Mass}\text{of}\text{that}\text{component}\text{in}\text{mixture}}{\text{Total}\text{mass}\text{of}\text{mixture}}\right)$

Total mass of ions in $1\text{kg}$ or ${10}^6\text{mg}$ seawater is calculated as follows:

  $\begin{array}{c}\text{Total}\text{mass}\text{of}\text{ion}=\left(\begin{array}{l}18980\text{mg}+10560\text{mg}+2650\text{mg}+\\ 1270\text{mg}+400\text{mg}+380\text{mg}+140\text{mg}\end{array}\right)\\ =34380\text{mg}\end{array}$

Total mass of cation is calculated follows:

  $\begin{array}{c}\text{Total}\text{mass}\text{of}\text{cation}=\left(\text{10560}\text{mg +1270}\text{mg}\text{+400}\text{mg +380}\text{mg}\right)\\ =\text{12610}\text{mg}\end{array}$

Formula to calculate the mass fraction of cation, among total mass of ion is as follows:

  $\text{Mass}\text{fraction}\text{of}\text{cation}=\left(\frac{\text{Mass}\text{of}\text{cation}}{\text{Total}\text{mass}\text{of}\text{ions}}\right)$

Mass of cation is $12610\text{mg}$ .

Total mass of ion is $34380\text{mg}$ .

Substitute the values in the above formula.

  $\begin{array}{c}\text{Mass}\text{fraction}\text{of}\text{cation}=\left(\frac{\text{Mass}\text{of}\text{cation}}{\text{Total}\text{mass}\text{of}\text{ions}}\right)\\ =\left(\frac{12610\text{mg}}{34380\text{mg}}\right)\\ =0.3668\end{array}$

Total mass of anion is calculated follows:

  $\begin{array}{c}\text{Total}\text{mass}\text{of}\text{anion}=\left(\text{18980}\text{mg +2650}\text{mg}\text{+100}\text{mg}\right)\\ =2173\text{0}\text{mg}\end{array}$

Formula to calculate the mass fraction of anion, among total mass of ion is as follows:

  $\text{Mass}\text{fraction}\text{of}\text{anion}=\left(\frac{\text{Mass}\text{of}\text{anion}}{\text{Total}\text{mass}\text{of}\text{ions}}\right)$

Mass of anion is $21730\text{mg}$ .

Total mass of ion is $34380\text{mg}$ .

Substitute the values in the above formula.

  $\begin{array}{c}\text{Mass}\text{fraction}\text{of}\text{anion}=\left(\frac{\text{Mass}\text{of}\text{anion}}{\text{Total}\text{mass}\text{of}\text{ions}}\right)\\ =\left(\frac{21730\text{mg}}{34380\text{mg}}\right)\\ =0.6332\end{array}$

Hence, mass fraction of anion in seawater is greater than that of mass fraction of cation.