Problem 106 - Chemistry The Science in Context

Question

Some scientists have proposed adding iron(III) compounds to large expanses of the open ocean to promote the growth of phytoplankton that would in turn remove \(\mathrm{CO}_{2}\) from the atmosphere through photosynthesis. Assuming the average pH of open ocean water is \(8.13,\) what is the maximum value of \(\left[\mathrm{Fe}^{3+}\right]\) in seawater if the \(K_{\mathrm{sp}}\) value of \(\mathrm{Fe}(\mathrm{OH})_{3}\) is \(1.1 \times 10^{-36} ?\)

Step-by-Step Solution

Answer

Answer: To find the maximum concentration of \(\mathrm{Fe}^{3+}\), follow these steps: 1. Calculate the hydroxide ion concentration (\(\mathrm{[OH^{-}] = \frac{1.0 \times 10^{-14}}{10^{-8.13}}\)). 2. Write the solubility equilibrium expression for \(\mathrm{Fe}(\mathrm{OH})_{3}\): \(K_\text{sp} = [\mathrm{Fe}^{3+}][\mathrm{OH}^-]^3\). 3. Calculate the maximum \(\mathrm{Fe}^{3+}\) concentration: \(\mathrm{[Fe^{3+}]} = \frac{1.1 \times 10^{-36}}{\left(\frac{1.0 \times 10^{-14}}{10^{-8.13}}\right)^3}\). After calculating the value of \([\mathrm{Fe}^{3+}]\), we can find the maximum concentration of iron(III) in seawater.

Step 1: Calculate the hydroxide ion concentration

To find the hydroxide ion concentration (\([\mathrm{OH}^{-}]\)), we must first calculate the hydronium ion concentration (\([\mathrm{H}^{+}]\)) using the given pH. The pH of a solution is defined as: pH \(= -\log \left[\mathrm{H}^{+}\right]\) Given pH \(= 8.13\), we can find \([\mathrm{H}^{+}]\) as follows: \([\mathrm{H}^{+}] = 10^{-\text{pH}} = 10^{-8.13}\) Next, we need to calculate the hydroxide ion concentration using the ion product of water (\(K_\text{w}\)) which is \(1.0 \times 10^{-14}\) at \(25^{\circ}\text{C}\): \(K_\text{w} = [\mathrm{H}^{+}][\mathrm{OH}^{-}]\) \([\mathrm{OH}^{-}] = \dfrac{K_\text{w}}{[\mathrm{H}^{+}]} = \dfrac{1.0 \times 10^{-14}}{10^{-8.13}}\)

Step 2: Write the solubility equilibrium expression for \(\mathrm{Fe}(\mathrm{OH})_{3}\)

The solubility equilibrium expression for \(\mathrm{Fe}(\mathrm{OH})_{3}\) can be written as follows: \(\text{Fe(OH)}_3(s) \rightleftharpoons \text{Fe}^{3+}(aq) + 3\text{OH}^-(aq)\) The solubility product constant, \(K_\text{sp} = [\mathrm{Fe}^{3+}][\mathrm{OH}^-]^3\) Given \(K_\text{sp} = 1.1 \times 10^{-36}\), we can now find the concentration of \(\mathrm{Fe}^{3+}\).

Step 3: Calculate the maximum \(\mathrm{Fe}^{3+}\) concentration in seawater

Using the solubility product expression, we can solve for the maximum concentration of \(\mathrm{Fe}^{3+}\) as follows: \(K_\text{sp} = [\mathrm{Fe}^{3+}][\mathrm{OH}^-]^3\) \([\mathrm{Fe}^{3+}] = \dfrac{K_\text{sp}}{[\mathrm{OH}^-]^3} = \dfrac{1.1 \times 10^{-36}}{\left(\dfrac{1.0 \times 10^{-14}}{10^{-8.13}}\right)^3}\) Calculate the value of \([\mathrm{Fe}^{3+}]\) to find the maximum concentration of iron(III) in seawater.

Key Concepts

Phytoplankton Growth

Phytoplankton are tiny, plant-like organisms found in the ocean. They play a crucial role in supporting marine life and in global carbon cycles.
They perform photosynthesis, converting sunlight, carbon dioxide (from the atmosphere), and nutrients into energy. This process helps to reduce atmospheric \(CO_2\), which is a significant greenhouse gas.

• Growth of phytoplankton depends greatly on the availability of nutrients like iron, nitrogen, and phosphorus in seawater.
• When there's a scarcity of these essential nutrients, especially iron, their growth is limited.
  

Scientists have proposed adding iron to oceans to stimulate phytoplankton bloom. This potential solution aims to enhance carbon uptake and mitigate climate change impacts. However, it is essential to balance such interventions to avoid ecological imbalances.

Iron Solubility

Iron's solubility in ocean water is vital since it determines how readily it can be taken up by phytoplankton.
Iron in its ferrous state ( (Fe^{2+}) ) is more soluble than in its ferric state ( (Fe^{3+}) ), which tends to form complexes and precipitate out as iron hydroxide ( Fe(OH)_3 ).

• The solubility of iron in water is influenced by factors such as temperature, salinity, and pH.
• These conditions affect how iron compounds dissolve and the availability of free iron ions ( Fe^{3+} ) for phytoplankton.

Understanding iron solubility is crucial when considering how to add iron to the ocean effectively without causing harmful side effects.

Seawater pH

The pH of seawater is a measure of its acidity or basicity.
Ocean pH can alter the solubility of various compounds and the distribution of ions in the water.

• Standard open ocean water has an average pH around 8.1, making it slightly basic.
• pH levels influence the concentration of hydronium ( ( [H^+] ) ) and hydroxide ions ( ( [OH^-] ) ) in the water.
  

Changes in pH levels can significantly affect marine ecosystems, influencing everything from the calcification process in shells to the general health of marine organisms.
Careful management of ocean pH is necessary when proposing geoengineering solutions like iron fertilization.

Solubility Product

The solubility product ( (K_{sp}) ) is a fundamental principle in chemistry used to describe the solubility of a compound.
Specifically, it applies to sparingly soluble ionic compounds, determining the extent to which a solute will dissolve in solvent.

• For iron hydroxide ( (Fe(OH)_3) ), the (K_{sp}) value determines the threshold beyond which no more iron will dissolve in seawater.
  
• Knowing the (K_{sp}) of a compound can help estimate how much of it can be added to a solution before precipitation occurs.
  

This understanding is crucial in the context of ocean fertilization, as it informs how much iron can realistically be dissolved and utilized by phytoplankton in the seawater based on the (K_{sp}) and environmental factors like pH. Such insights guide the practical application of iron fertilization in marine environments.