Question

The seven most abundant ions in seawater make up more than \(99 \%\) by mass of the dissolved compounds. Here are their abundances in units of \(\mathrm{mg}\) 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 is represented by sodium ions? (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 components, anions or cations?

Short answer

a) Cl-: 55.14%, Na+: 30.68%, SO4^{2-}: 7.7%, Mg^{2+}: 3.69%, Ca^{2+}: 1.16%, K+: 1.10%, HCO3-: 0.41%. b) 30.68%. c) Alkaline: 4.85%, Alkali: 31.78%. d) Anions: 63.25%, Cations: 36.63%.

Step-by-step solution

- Determine the total ion mass

Add the masses of all ions to find the total mass:\[ 18980 + 10560 + 2650 + 1270 + 400 + 380 + 140 = 34430 \mathrm{mg/kg}\]

- Calculate the mass percentage of each ion (Part a)

Use the formula for mass percentage: \( \text{Mass \%} = \left( \frac{\text{mass of ion}}{\text{total mass}} \right) \times 100 \).For Chloride (\[ \text{Cl}^- \]):\[ \left( \frac{18980}{34430} \right) \times 100 = 55.14\% \]For Sodium (\[ \text{Na}^+ \]):\[ \left( \frac{10560}{34430} \right) \times 100 = 30.68\% \]Continue similarly for all other ions.

- Calculate the mass percentage for Sodium ion (Part b)

We already calculated the mass percentage of \( \text{Na}^+ \) in the previous step: \[ 30.68\% \]

- Compare Alkaline Earth Metal Ions and Alkali Metal Ions (Part c)

Sum the percentages of Alkaline Earth Metal Ions (\( \text{Mg}^{2+} \) and \( \text{Ca}^{2+} \)):\[ ( \text{Mg}^{2+}) \left( \frac{1270}{34430} \right) \times 100 + ( \text{Ca}^{2+} ) \left( \frac{400}{34430} \right) \times 100 = 3.69 + 1.16 = 4.85\% \]Sum the percentages of Alkali Metal Ions (\( \text{Na}^+ \) and \( \text{K}^+ \)):\[ ( \text{Na}^+ ) \left( \frac{10560}{34430} \right) \times 100 + ( \text{K}^+ ) \left( \frac{380}{34430} \right) \times 100 = 30.68 + 1.10 = 31.78\% \]

- Compare Anions and Cations (Part d)

Sum the percentages of Anions (\( \text{Cl}^- \), \( \text{SO}_4^{2-} \), \( \text{HCO}_3^- \)):\[ ( \text{Cl}^- ) \left( \frac{18980}{34430} \right) \times 100 + ( \text{SO}_4^{2-} ) \left( \frac{2650}{34430} \right) \times 100 + ( \text{HCO}_3^- ) \left( \frac{140}{34430} \right) \times 100 = 55.14 + 7.7 + 0.41 = 63.25\% \]Sum the percentages of Cations (\( \text{Na}^+ \), \( \text{Mg}^{2+} \), \( \text{Ca}^{2+} \), \( \text{K}^+ \)):\[ 30.68 + 3.69 + 1.16 + 1.10 = 36.63\% \]

Key concepts

mass percentage calculation

To find the mass percentage of an ion in a solution, we use the formula: \( \text{Mass \%} = \left( \frac{\text{mass of ion}}{\text{total mass}} \right) \times 100 \). This helps us understand the proportion of each ion present in a given total mass of the solution.
For example, to calculate the mass percentage of chloride ions (\( \text{Cl}^-\)) in seawater, we use the given mass of chloride (18,980 mg/kg) and the total mass of all ions (34,430 mg/kg). The calculation looks like this: \( \left( \frac{18980}{34430} \right) \times 100 = 55.14\% \). This means that 55.14% of the ions in seawater by mass are chloride ions.
Repeat these steps for each ion to understand their contributions to the total mass.

alkali metals

Alkali metals are a group of elements in the first column of the periodic table. These metals include lithium (\(\text{Li}\)), sodium (\(\text{Na}\)), potassium (\(\text{K}\)), rubidium (\(\text{Rb}\)), cesium (\(\text{Cs}\)), and francium (\(\text{Fr}\)). They are known for having one electron in their outermost shell, which makes them highly reactive.
In the context of seawater, sodium (\(\text{Na}^+\)) and potassium (\(\text{K}^+\)) are the primary alkali metals present. Sodium ions contribute significantly to the mass percentage, representing about 30.68% of the total ions. Potassium ions contribute a smaller though significant portion at approximately 1.10%.
Alkali metal ions are crucial for various physiological and geological processes, playing essential roles in the chemical dynamics of seawater.

alkaline earth metals

Alkaline earth metals belong to the second group of the periodic table. This includes beryllium (\(\text{Be}\)), magnesium (\(\text{Mg}\)), calcium (\(\text{Ca}\)), strontium (\(\text{Sr}\)), barium (\(\text{Ba}\)), and radium (\(\text{Ra}\)). These metals have two electrons in their outermost shell, making them reactive, although less so than alkali metals.
In seawater, the primary alkaline earth metal ions are magnesium (\(\text{Mg}^{2+}\)) and calcium (\(\text{Ca}^{2+}\)). Magnesium ions make up about 3.69% of the total mass of ions in seawater, while calcium ions contribute around 1.16%.
These ions are important for marine life and play significant roles in biological functions and biogeochemical cycles. They are also vital in processes like the formation of shells and skeletons in marine organisms.

anions and cations

Anions and cations are types of ions, differentiated by their electrical charges. Anions are negatively charged ions, while cations carry a positive charge.
In the seawater context, common anions include chloride (\(\text{Cl}^-\)), sulfate (\(\text{SO}_4^{2-}\)), and hydrogen carbonate (\(\text{HCO}_3^-\)). The total mass percentage of anions in seawater is found by summing the contributions of each: 55.14% from chloride, 7.7% from sulfate, and 0.41% from hydrogen carbonate, giving us a combined 63.25% mass.
Common cations in seawater are sodium (\(\text{Na}^{+} \)), magnesium (\( \text{Mg}^{2+} \)), calcium (\( \text{Ca}^{2+} \)), and potassium ( \( \text{K}^{+} \)). Their combined mass percentage is 36.63%.
This balance of anions and cations is crucial for maintaining the ionic equilibrium in seawater, affecting its overall chemistry and various biological processes.