Question

The major ions and their concentration (mmol L -1) in sea water are: \(\begin{array}{lrlr}\mathrm{Na}^{+} & 470 & \mathrm{~K}^{+} & 10 \\\ \mathrm{Mg}^{2+} & 53 & \mathrm{Ca}^{2+} & 10 \\ \mathrm{Cl}^{-} & 547 & \mathrm{SO}_{4}^{2-} & 28 \\ \mathrm{Br}^{-} & 1 & \mathrm{HCO}_{3}^{-}+\mathrm{CO}_{3}^{2-} & x\end{array}\) Assume that charges of these species balance and calculate the total concentration of negative charge associated with the two carbonate species. With a pH of 8.2, calculate the concentrations of the two individual carbonate species.

Short answer

[HCO₃⁻] ≈ 1.98 mmol/L, [CO₃²⁻] ≈ 0.016 mmol/L.

Step-by-step solution

Calculate Total Positive Charge

To balance the charges, we first calculate the total positive charge in mmol/L from cations. - Sodium (Na⁺) contributes: 470 mmol/L - Potassium (K⁺) contributes: 10 mmol/L - Magnesium (Mg²⁺) contributes: 53 × 2 = 106 mmol/L - Calcium (Ca²⁺) contributes: 10 × 2 = 20 mmol/L Total Positive Charge = 470 + 10 + 106 + 20 = 606 mmol/L.

Calculate Total Negative Charge

Now calculate the total known negative charge in mmol/L from anions without HCO₃⁻ and CO₃²⁻. - Chloride (Cl⁻) contributes: 547 mmol/L - Sulfate (SO₄²⁻) contributes: 28 × 2 = 56 mmol/L - Bromide (Br⁻) contributes: 1 mmol/L Total Known Negative Charge = 547 + 56 + 1 = 604 mmol/L.

Determine Additional Negative Charge

The additional negative charge needed to balance total charges comes from bicarbonate and carbonate ions (HCO₃⁻ + CO₃²⁻). The positive charge totals 606 mmol/L, so the additional negative charge needed is: 606 - 604 = 2 mmol/L. Thus, HCO₃⁻ + CO₃²⁻ contributes 2 mmol/L of negative charge.

Relate pH to Carbonate System

Given that the pH is 8.2, in the carbonate system CO₂, HCO₃⁻, and CO₃²⁻ coexist. The pH helps determine concentrations of these species. The following equilibrium reactions are involved: 1. H₂CO₃ ⇌ H⁺ + HCO₃⁻ (with pKa₁ ≈ 6.3) 2. HCO₃⁻ ⇌ H⁺ + CO₃²⁻ (with pKa₂ ≈ 10.3) At pH 8.2, HCO₃⁻ is the predominant species.

Calculate Individual Concentrations

Using the Henderson–Hasselbalch equation for the bicarbonate-disolved carbon dioxide system:\[pH = pK_a + \log\left( \frac{[CO_3^{2-}]}{[HCO_3^-]} \right)\]Given:- pH = 8.2- pKa₂ = 10.3\[8.2 = 10.3 + \log\left( \frac{[CO_3^{2-}]}{[HCO_3^-]} \right)\]Rearrange to find the ratio:\[\log\left( \frac{[CO_3^{2-}]}{[HCO_3^-]} \right) = 8.2 - 10.3 = -2.1\]This gives:\[\frac{[CO_3^{2-}]}{[HCO_3^-]} = 10^{-2.1} \approx 0.0079\]Let [HCO₃⁻] = x and [CO₃²⁻] = 0.0079x. Then,x + 0.0079x = 2\[1.0079x = 2\]x = \frac{2}{1.0079} \approx 1.98 \text{ mmol/L}So, [HCO₃⁻] ≈ 1.98 mmol/L and [CO₃²⁻] ≈ 0.0079 × 1.98 mmol/L ≈ 0.016 mmol/L.

Key concepts

Ions in Sea Water

Sea water is a complex solution filled with various ions. These ions come from the natural weathering of rocks and are washed into the oceans. The major ions found in sea water include sodium (Na⁺), chloride (Cl⁻), magnesium (Mg²⁺), calcium (Ca²⁺), potassium (K⁺), and more. Among these, sodium and chloride ions are the most abundant, and they contribute to the salty taste of the ocean.

• Sodium (Na⁺): essential for nerve and muscle function in organisms.
• Chloride (Cl⁻): crucial for maintaining the body's electrolyte balance.
• Magnesium (Mg²⁺) and calcium (Ca²⁺): important for marine life, influencing biological processes like shell formation.
• Potassium (K⁺): plays a key role in cellular functions in marine life.

Understanding the composition of sea water is crucial, not just for biology, but also for chemistry as it impacts the reactivity and availability of different elements.

Charge Balance

Charge balance is a key concept in aqueous chemistry and refers to the state where the total positive charge from cations equals the total negative charge from anions in a solution. In sea water, maintaining charge balance ensures electrical neutrality. This principle can be used to determine unknown concentrations of ions if the charge contributions from known ions are known.

In the exercise provided, charge balance is achieved by ensuring that the total positive charge from sodium, potassium, magnesium, and calcium ions equals the total negative charge from chloride, sulfate, bromide, and the carbonate species.
This involves:

• Calculating the total positive charge from Na⁺, K⁺, Mg²⁺, and Ca²⁺.
• Calculating the total known negative charge from Cl⁻, SO₄²⁻, and Br⁻.
• Identifying any additional negative charge needed to achieve charge balance.

Charge balance helps in calculating additional ions like bicarbonate (HCO₃⁻) and carbonate (CO₃²⁻) through mathematical analysis.

Henderson–Hasselbalch Equation

The Henderson–Hasselbalch equation is a key tool in chemistry for relating pH and the concentrations of an acid and its conjugate base. It is particularly useful for buffer systems.
The equation is given by:\[ pH = pK_a + \log \left( \frac{[A^-]}{[HA]} \right) \]
Where:

• \( pK_a \) is the acid dissociation constant
• \([A^-] \) is the concentration of the base (deprotonated form)
• \([HA] \) is the concentration of the acid (protonated form)

In the context of the exercise, this equation helps to calculate the ratio of carbonate to bicarbonate at the given pH of 8.2. By knowing the \( pK_a \) values for the carbonic acid system, which are around 6.3 and 10.3, we can determine the distribution of the carbonate species. This relationship allows us to precisely gauge the buffering capacity of sea water in response to changes in ion concentration.

pH Impact on Carbonate Species

The pH of water significantly influences the distribution of carbonate species, which are critical for ocean chemistry. At different pH levels, carbon dioxide (CO₂), bicarbonate (HCO₃⁻), and carbonate (CO₃²⁻) shift in equilibrium. This interplay is crucial for marine organisms that rely on stable carbonate levels to maintain their shells and structures.

• At lower pH (acidic), more CO₂ is dissolved.
• At mid-range pH (around 8.2), bicarbonate (HCO₃⁻) is predominant.
• At higher pH (basic), carbonate (CO₃²⁻) becomes more prevalent.

In the exercise scenario with a pH of 8.2, bicarbonate dominates, partially displacing carbonate. This affects the ocean's buffering system and changes how marine life interacts with its environment. Understanding how pH affects these species is fundamental for predicting and mitigating the impacts of ocean acidification, an ongoing consequence of increased atmospheric CO₂ levels.