Q139CP - Chemistry: Molecular Nature Of Matter And Change

Question

The seven most abundant ions in seawater make up more than 99% by mass of the dissolved compounds. They are listed in units of mg ion/kg seawater: chloride 18,980; sodium 10,560;sulfate 2650; magnesium 1270; calcium 400; potassium 380;hydrogen carbonate 140.
 (a) What is the mass % of each ion in seawater?
 (b) What percent of the total mass of ions in sodium ions?

(c) How does the total mass % of alkaline earth metal ions compare with the total mass % of alkali metal ions?
(d) Which makes up the larger mass fraction of dissolved components, anions, or cations?

Step-by-Step Solution

Answer

(a) The mass % of each ion in seawater,

       i) $\mathbf{1}\mathbf{.}\mathbf{898}\mathbf{\%}\mathit{C}{\mathit{I}}^{\mathbf{‐}}$

    $$\begin{gathered} \mathbf{ }\mathbf{ }\mathbf{ii}\mathbf{)}\mathbf{ }\mathbf{1}\mathbf{.}\mathbf{056}\mathbf{\%}{\mathbf{Na}}^{\mathbf{+}} \\ \mathbf{ }\mathbf{iii}\mathbf{)}\mathbf{ }\mathbf{0}\mathbf{.}\mathbf{265}\mathbf{\%}{\mathbf{SO}}_{\mathbf{4}}^{\mathbf{2}\mathbf{‐}} \\ \mathbf{ }\mathbf{iv}\mathbf{)}\mathbf{ }\mathbf{0}\mathbf{.}\mathbf{127}\mathbf{\%}{\mathbf{mg}}^{\mathbf{2}\mathbf{+}} \\ \mathbf{ }\mathbf{ }\mathbf{v}\mathbf{)}\mathbf{ }\mathbf{0}\mathbf{.}\mathbf{0400}\mathbf{\%}{\mathbf{Ca}}^{\mathbf{2}\mathbf{+}} \\ \mathbf{ }\mathbf{vi}\mathbf{)}\mathbf{ }\mathbf{ }\mathbf{0}\mathbf{.}\mathbf{0380}\mathbf{\%}{\mathbf{K}}^{\mathbf{+}} \\ \mathbf{ }\mathbf{vii}\mathbf{)}\mathbf{ }\mathbf{0}\mathbf{.}\mathbf{0140}\mathbf{\%}{\mathbf{HCO}}_{\mathbf{3}}^{\mathbf{‐}} \end{gathered}$$

(a) The total mass of ions in a sodium ion is 30.72 %.

(b) There are more alkali metal ions than alkaline earth metal ions in seawater.

(c) There are more anions than cations in seawater.

Step 1: Introduction to mass percent

The mass of the element or solute divided by the mass of the compound or solute equals the mass percent.

Step 2: Mass percent of each ion in seawater

The percent mass is computed as follows,

$$\begin{gathered} \mathbf{\%}{\mathbf{massCI}}^{\mathbf{‐}}\mathbf{=}\mathbf{18980}\frac{\mathbf{mg}}{\mathbf{kg}}\mathbf{\times }\frac{\mathbf{1}\mathbf{kg}}{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}\mathbf{mg}}\mathbf{\times }\mathbf{100}\mathbf{\%} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{898}\mathbf{\%}\mathbf{CI}\mathbf{‐} \\ \mathbf{ }\mathbf{\%}{\mathbf{massNa}}^{\mathbf{+}}\mathbf{=}\mathbf{10560}\frac{\mathbf{mg}}{\mathbf{kg}}\mathbf{\times }\frac{\mathbf{1}\mathbf{kg}}{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}\mathbf{mg}}\mathbf{\times }\mathbf{100}\mathbf{\%} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{0560}\mathbf{\%}{\mathbf{Na}}^{\mathbf{+}} \\ \mathbf{\%}{\mathbf{massSO}}_{\mathbf{4}\mathbf{ }}^{\mathbf{2}\mathbf{‐}}\mathbf{=}\mathbf{2650}\frac{\mathbf{mg}}{\mathbf{kg}}\mathbf{\times }\frac{\mathbf{1}\mathbf{kg}}{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}\mathbf{mg}}\mathbf{\times }\mathbf{100}\mathbf{\%} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{265}\mathbf{\%}{\mathbf{SO}}_{\mathbf{4}\mathbf{ }}^{\mathbf{2}\mathbf{‐}} \\ \mathbf{\%}{\mathbf{massMg}}^{\mathbf{2}\mathbf{+}}\mathbf{=}\mathbf{1270}\frac{\mathbf{mg}}{\mathbf{kg}}\mathbf{\times }\frac{\mathbf{1}\mathbf{kg}}{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}\mathbf{mg}}\mathbf{\times }\mathbf{100}\mathbf{\%} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{127}\mathbf{\%}{\mathbf{Mg}}^{\mathbf{2}\mathbf{+}} \\ \mathbf{ }\mathbf{\%}{\mathbf{massCa}}^{\mathbf{2}\mathbf{+}}\mathbf{=}\mathbf{400}\frac{\mathbf{mg}}{\mathbf{kg}}\mathbf{\times }\frac{\mathbf{1}\mathbf{kg}}{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}\mathbf{mg}}\mathbf{\times }\mathbf{100}\mathbf{\%} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0400}\mathbf{\%}{\mathbf{Ca}}^{\mathbf{2}\mathbf{+}} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{\%}{\mathbf{massK}}^{\mathbf{+}}\mathbf{=}\mathbf{380}\frac{\mathbf{mg}}{\mathbf{kg}}\mathbf{\times }\frac{\mathbf{1}\mathbf{kg}}{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}\mathbf{mg}}\mathbf{\times }\mathbf{100}\mathbf{\%} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0380}\mathbf{\%}{\mathbf{K}}^{\mathbf{+}} \\ \mathbf{ }\mathbf{\%}{\mathbf{massHCO}}_{\mathbf{3}}\mathbf{=}\mathbf{140}\frac{\mathbf{mg}}{\mathbf{kg}}\mathbf{\times }\frac{\mathbf{1}\mathbf{kg}}{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}\mathbf{mg}}\mathbf{\times }\mathbf{100}\mathbf{\%} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0140}\mathbf{\%}{\mathbf{HCO}}_{\mathbf{3}} \end{gathered}$$

So, the different percentage has been calculated.

Step 3:Mass percent of the total mass of ions in the sodium ion

To calculate mass percent of Na⁺ ion, compute the total mass of ions in seawater

Here, the total mass of ions

 $$\begin{gathered} \mathbf{=}\mathbf{18980}\mathbf{+}\mathbf{10560}\mathbf{+}\mathbf{2650}\mathbf{+}\mathbf{1270}\mathbf{+}\mathbf{400}\mathbf{+}\mathbf{380}\mathbf{+}\mathbf{140} \\ \mathbf{=}\mathbf{34380}\mathbf{mg}\mathbf{/}\mathbf{kg} \end{gathered}$$

The mass percent of sodium ions is then calculated,

 $$\begin{gathered} \mathbf{\%}{\mathbf{massNa}}^{\mathbf{+}}\mathbf{=}\frac{\mathbf{10560}}{\mathbf{34380}}\mathbf{\times }\mathbf{100}\mathbf{\%} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{30}\mathbf{.}\mathbf{72}\mathbf{\%} \end{gathered}$$

Step 4: Comparison of alkaline earth and alkali metals

i) Alkaline earth metal ions are Mg²⁺ and Ca²⁺ ions. 

Add the ${\mathbf{Mg}}^{\mathbf{2}\mathbf{+}}$and ${\mathbf{Ca}}^{\mathbf{2}\mathbf{+}}$percentages together.

$$\begin{gathered} \mathbf{0}\mathbf{.}\mathbf{127}\mathbf{\%}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{0400}\mathbf{\%} \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{167}\mathbf{\%} \end{gathered}$$

ii) Alkali metal ions are Na⁺ and K⁺ ions.

Add the${\mathbf{Na}}^{\mathbf{+}}$and${\mathbf{K}}^{\mathbf{+}}$ percentages together.

$$\begin{gathered} \mathbf{1}\mathbf{.}\mathbf{056}\mathbf{\%}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{0380}\mathbf{\%} \\ \mathbf{=}\mathbf{1}\mathbf{.}\mathbf{094}\mathbf{\%} \end{gathered}$$ 

In seawater, there are more alkali metal ions than alkaline earth metal ions.

Step 5:Mass fraction of dissolved components

i) Cations percentage 

Let’s determine the total percentage of cations,

$$\begin{gathered} \mathbf{0}\mathbf{.}\mathbf{167}\mathbf{\%}\mathbf{+}\mathbf{1}\mathbf{.}\mathbf{094}\mathbf{\%} \\ \mathbf{=}\mathbf{1}\mathbf{.}\mathbf{261}\mathbf{\%} \end{gathered}$$

ii) Anions percentage 

Let’s determine the total percentage of anions,

 $$\begin{gathered} \mathbf{1}\mathbf{.}\mathbf{898}\mathbf{\%}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{265}\mathbf{\%}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{0140}\mathbf{\%} \\ \mathbf{=}\mathbf{2}\mathbf{.}\mathbf{177}\mathbf{\%} \end{gathered}$$

In seawater, there are more anions than cations.