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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

Expert verified
[HCO鈧冣伝] 鈮 1.98 mmol/L, [CO鈧兟测伝] 鈮 0.016 mmol/L.

Step by step solution

01

Calculate Total Positive Charge

To balance the charges, we first calculate the total positive charge in mmol/L from cations. - Sodium (Na鈦) contributes: 470 mmol/L - Potassium (K鈦) contributes: 10 mmol/L - Magnesium (Mg虏鈦) contributes: 53 脳 2 = 106 mmol/L - Calcium (Ca虏鈦) contributes: 10 脳 2 = 20 mmol/L Total Positive Charge = 470 + 10 + 106 + 20 = 606 mmol/L.
02

Calculate Total Negative Charge

Now calculate the total known negative charge in mmol/L from anions without HCO鈧冣伝 and CO鈧兟测伝. - Chloride (Cl鈦) contributes: 547 mmol/L - Sulfate (SO鈧劼测伝) contributes: 28 脳 2 = 56 mmol/L - Bromide (Br鈦) contributes: 1 mmol/L Total Known Negative Charge = 547 + 56 + 1 = 604 mmol/L.
03

Determine Additional Negative Charge

The additional negative charge needed to balance total charges comes from bicarbonate and carbonate ions (HCO鈧冣伝 + CO鈧兟测伝). The positive charge totals 606 mmol/L, so the additional negative charge needed is: 606 - 604 = 2 mmol/L. Thus, HCO鈧冣伝 + CO鈧兟测伝 contributes 2 mmol/L of negative charge.
04

Relate pH to Carbonate System

Given that the pH is 8.2, in the carbonate system CO鈧, HCO鈧冣伝, and CO鈧兟测伝 coexist. The pH helps determine concentrations of these species. The following equilibrium reactions are involved: 1. H鈧侰O鈧 鈬 H鈦 + HCO鈧冣伝 (with pKa鈧 鈮 6.3) 2. HCO鈧冣伝 鈬 H鈦 + CO鈧兟测伝 (with pKa鈧 鈮 10.3) At pH 8.2, HCO鈧冣伝 is the predominant species.
05

Calculate Individual Concentrations

Using the Henderson鈥揌asselbalch equation for the bicarbonate-disolved carbon dioxide system:\[pH = pK_a + \log\left( \frac{[CO_3^{2-}]}{[HCO_3^-]} \right)\]Given:- pH = 8.2- pKa鈧 = 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 [HCO鈧冣伝] = x and [CO鈧兟测伝] = 0.0079x. Then,x + 0.0079x = 2\[1.0079x = 2\]x = \frac{2}{1.0079} \approx 1.98 \text{ mmol/L}So, [HCO鈧冣伝] 鈮 1.98 mmol/L and [CO鈧兟测伝] 鈮 0.0079 脳 1.98 mmol/L 鈮 0.016 mmol/L.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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鈦), chloride (Cl鈦), magnesium (Mg虏鈦), calcium (Ca虏鈦), potassium (K鈦), and more. Among these, sodium and chloride ions are the most abundant, and they contribute to the salty taste of the ocean.
  • Sodium (Na鈦): essential for nerve and muscle function in organisms.
  • Chloride (Cl鈦): crucial for maintaining the body's electrolyte balance.
  • Magnesium (Mg虏鈦) and calcium (Ca虏鈦): important for marine life, influencing biological processes like shell formation.
  • Potassium (K鈦): 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鈦, K鈦, Mg虏鈦, and Ca虏鈦.
  • Calculating the total known negative charge from Cl鈦, SO鈧劼测伝, and Br鈦.
  • Identifying any additional negative charge needed to achieve charge balance.
Charge balance helps in calculating additional ions like bicarbonate (HCO鈧冣伝) and carbonate (CO鈧兟测伝) through mathematical analysis.
Henderson鈥揌asselbalch Equation
The Henderson鈥揌asselbalch 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 (CO鈧), bicarbonate (HCO鈧冣伝), and carbonate (CO鈧兟测伝) 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 CO鈧 is dissolved.
  • At mid-range pH (around 8.2), bicarbonate (HCO鈧冣伝) is predominant.
  • At higher pH (basic), carbonate (CO鈧兟测伝) 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 CO鈧 levels.

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