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For sea water one may take \(\mathrm{pH}=8\). Use the equilibrium constants \(K_{1}=\) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\left[\mathrm{HCO}_{3}^{-}\right] /\left[\mathrm{H}_{2} \mathrm{CO}_{3}\right]=4.3 \times 10^{-7}\) and \(K_{2}=\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\left[\mathrm{CO}_{3}^{--}\right] /\left[\mathrm{HCO}_{3}^{-}\right]=\) \(4.8 \times 10^{-11}\) to calculate the fractions in sea water of \(\left[\mathrm{CO}_{3}{ }^{2-}\right],\left[\mathrm{HCO}_{3}{ }^{-}\right]\)and \(\left[\mathrm{H}_{2} \mathrm{CO}_{3}\right]\). Students proficient with computers may plot the three fractions as a function of \(\mathrm{pH}\).

Short Answer

Expert verified
The fractions are approximately 0.0226 for \([\mathrm{H}_2\mathrm{CO}_3]\), 0.9721 for \([\mathrm{HCO}_3^-]\), and 0.0053 for \([\mathrm{CO}_3^{2-}]\).

Step by step solution

01

Express the Concentrations

Using the equilibrium constants provided, express the concentrations of the species involved. We know from the equilibrium constants that \(K_1 = \frac{[\mathrm{H}_{3}\mathrm{O}^+][\mathrm{HCO}_3^-]}{[\mathrm{H}_2\mathrm{CO}_3]} = 4.3 \times 10^{-7}\) and \(K_2 = \frac{[\mathrm{H}_{3}\mathrm{O}^+][\mathrm{CO}_3^{2-}]}{[\mathrm{HCO}_3^-]} = 4.8 \times 10^{-11}\). Both equilibria involve the hydronium concentration \([\mathrm{H}_3\mathrm{O}^+]= 10^{-\mathrm{pH}}\).
02

Calculate Hydronium Ion Concentration

Since the pH of seawater is given as 8, calculate the hydronium ion concentration: \([\mathrm{H}_3\mathrm{O}^+] = 10^{-8}\).
03

Use K1 to Determine Relationships

From \(K_1\), express the concentration ratio:\[ [\mathrm{HCO}_3^-] = \frac{K_1 [\mathrm{H}_2\mathrm{CO}_3]}{[\mathrm{H}_3\mathrm{O}^+]} = \frac{(4.3 \times 10^{-7}) [\mathrm{H}_2\mathrm{CO}_3]}{10^{-8}} \]Simplifying gives:\[[\mathrm{HCO}_3^-] = 43 [\mathrm{H}_2\mathrm{CO}_3] \].
04

Use K2 to Determine Relationships

From \(K_2\), express the concentration ratio:\[ [\mathrm{CO}_3^{2-}] = \frac{K_2 [\mathrm{HCO}_3^-]}{[\mathrm{H}_3\mathrm{O}^+]} = \frac{(4.8 \times 10^{-11}) [\mathrm{HCO}_3^-]}{10^{-8}} \]Simplifying gives:\[[\mathrm{CO}_3^{2-}] = 4.8 \times 10^{-3} [\mathrm{HCO}_3^-] \].
05

Relate All Concentrations

We now have the relationships:\[[\mathrm{HCO}_3^-] = 43 [\mathrm{H}_2\mathrm{CO}_3]\] \[[\mathrm{CO}_3^{2-}] = 4.8 \times 10^{-3} [\mathrm{HCO}_3^-] = (4.8 \times 10^{-3})(43 [\mathrm{H}_2\mathrm{CO}_3])\]Simplifying gives:\[[\mathrm{CO}_3^{2-}] = 0.2064 [\mathrm{H}_2\mathrm{CO}_3]\].
06

Calculate Fractions of Each Species

The total concentration of the carbon species is \([[\mathrm{CO}_3^{2-}] + [\mathrm{HCO}_3^-] + [\mathrm{H}_2\mathrm{CO}_3]]\). Using the relationships from previous steps, express each species as a fraction:\[\text{Fraction of } [\mathrm{H}_2\mathrm{CO}_3] = \frac{[\mathrm{H}_2\mathrm{CO}_3]}{[\mathrm{H}_2\mathrm{CO}_3](1 + 43 + 0.2064)}\] \[\text{Fraction of } [\mathrm{HCO}_3^-] = \frac{43[\mathrm{H}_2\mathrm{CO}_3]}{[\mathrm{H}_2\mathrm{CO}_3](1 + 43 + 0.2064)}\] \[\text{Fraction of } [\mathrm{CO}_3^{2-}] = \frac{0.2064[\mathrm{H}_2\mathrm{CO}_3]}{[\mathrm{H}_2\mathrm{CO}_3](1 + 43 + 0.2064)}\].The fractions calculate to:\[\text{Fraction of } [\mathrm{H}_2\mathrm{CO}_3] \approx 0.0226\] \[\text{Fraction of } [\mathrm{HCO}_3^-] \approx 0.9721\] \[\text{Fraction of } [\mathrm{CO}_3^{2-}] \approx 0.0053\].

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Key Concepts

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

pH
Understanding pH is essential when discussing chemical equilibrium, especially in seawater. The pH scale measures how acidic or basic a solution is, ranging from 0 to 14. A pH of 7 is neutral, below 7 is acidic, and above 7 is basic. In the context of seawater, which typically has a pH of around 8, it is slightly basic.
The pH of a solution is calculated using the negative logarithm of the hydronium ion concentration: \(\mathrm{pH} = -\log_{10} [\mathrm{H}_3\mathrm{O}^+]\).
For seawater with a pH of 8, the hydronium ion concentration is \([\mathrm{H}_3\mathrm{O}^+] = 10^{-8}\). This value is crucial for determining the dissociation and equilibrium of substances in seawater chemistry, such as carbonic acid and its derivatives.
seawater chemistry
Seawater chemistry involves several components that interact to maintain a delicate chemical equilibrium. This equilibrium is influenced by factors like temperature, salt content, and the pH of the sea. Seawater is a complex solution containing various salts, organic materials, and gasses.
One of the crucial interactions in seawater chemistry is between carbon dioxide (CO₂) and water (H₂O), forming carbonic acid (H₂CO₃). This carbonic acid partially dissociates into bicarbonate (HCO₃⁻) and carbonate ions (CO₃⁻²), which are vital in buffering the ocean's pH and supporting marine life.
Seawater chemistry helps understand how these species interact under different conditions, influencing marine ecosystems and the global carbon cycle.
carbonic acid dissociation
The dissociation of carbonic acid is a critical component of the carbonate buffering system in seawater. Carbonic acid (H₂CO₃), formed when carbon dioxide dissolves in water, can dissociate in two main steps: first forming bicarbonate (\[\mathrm{H}_2\mathrm{CO}_3 \rightleftharpoons \mathrm{HCO}_3^− + \mathrm{H}_3\mathrm{O}^+\]), and then carbonate (\[\mathrm{HCO}_3^− \rightleftharpoons \mathrm{CO}_3^{2-} + \mathrm{H}_3\mathrm{O}^+\]).
This dissociation process is vital because it helps regulate pH levels in seawater. For each step, there's a specific equilibrium constant that quantifies the degree to which the reaction proceeds. These are \(K_1\) and \(K_2\), known as the first and second dissociation constants.
In seawater, the equilibrium state tends to favor the formation of bicarbonate ions over carbonate ions, with bicarbonate being the dominant species. This makes bicarbonate crucial for maintaining the ocean's ability to neutralize added acids and bases, stabilizing the marine environment.
hydronium ion concentration
Hydronium ions (\(\mathrm{H}_3\mathrm{O}^+\)) are central to understanding acidic and basic behavior in aqueous solutions, including seawater. Their concentration determines the pH of a solution. The formation and concentration of hydronium ions in water arise from the self-ionization of water and the dissociation of acids, like carbonic acid.
In the context of seawater, hydronium ions play a role in chemical equilibria. The concentration of these ions is calculated from the pH, using the formula: \([\mathrm{H}_3\mathrm{O}^+] = 10^{−\mathrm{pH}}\). For example, at a pH of 8, \([\mathrm{H}_3\mathrm{O}^+] = 10^{-8}\), which indicates a relatively low concentration, as seawater is slightly basic.
Understanding hydronium ion concentration becomes crucial when calculating the distribution and fractions of different ionic species in chemical equilibria, such as those involving dissolved CO₂ in ocean chemistry. This concept helps us predict how changes in environmental conditions, like increased CO₂ levels, might affect marine chemistry.

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