Problem 103 - Chemistry The Molecular Science

Question

Carbon dioxide released from burning of fossil fuels contributes to the acidity of the oceans' surface water, whose current average \(\mathrm{pH}\) is \(8.1 .\) It has been estimated that if \(\mathrm{CO}_{2}\) emissions are not curbed, the oceans' surface water pH could drop to 7.8 by the end of this century. Calculate the percent change in acidity if that were to happen.

Step-by-Step Solution

Answer

Acidity could increase by approximately 98.9%.

Step 1: Understand pH and Acidity

The pH scale is logarithmic, meaning each whole number change represents a tenfold change in hydrogen ion concentration. A lower pH means higher acidity.

Step 2: Determine Initial Conditions

The initial pH of the ocean's surface water is given as 8.1. Convert this to hydrogen ion concentration using the formula: \[ \text{[H}^+] = 10^{-\text{pH}} \] So, \[ \text{[H}^+]_{\text{initial}} = 10^{-8.1} \]

Step 3: Calculate Initial Hydrogen Ion Concentration

Plugging in the initial pH: \[ \text{[H}^+]_{\text{initial}} = 10^{-8.1} \approx 7.94 \times 10^{-9} \text{ M} \]

Step 4: Determine Final Conditions

The expected future pH of the ocean is 7.8. Again, convert this to hydrogen ion concentration: \[ \text{[H}^+]_{\text{final}} = 10^{-7.8} \]

Step 5: Calculate Final Hydrogen Ion Concentration

Plugging in the future pH: \[ \text{[H}^+]_{\text{final}} = 10^{-7.8} \approx 1.58 \times 10^{-8} \text{ M} \]

Step 6: Calculate the Change in Hydrogen Ion Concentration

Find the difference in hydrogen ion concentration: \[ \Delta \text{[H}^+] = \text{[H}^+]_{\text{final}} - \text{[H}^+]_{\text{initial}} \approx 1.58 \times 10^{-8} - 7.94 \times 10^{-9} \approx 7.85 \times 10^{-9} \text{ M} \]

Step 7: Compute the Percentage Change in Acidity

The percent change in acidity is calculated by dividing the change by the initial concentration and then multiplying by 100:\[ \text{Percent Change} = \left(\frac{\Delta \text{[H}^+]}{\text{[H}^+]_{\text{initial}}}\right) \times 100 \] Substituting the values, we get:\[ \text{Percent Change} \approx \left(\frac{7.85 \times 10^{-9}}{7.94 \times 10^{-9}}\right) \times 100 \approx 98.9\% \]

Key Concepts

pH Scale

The pH scale is a fundamental concept for measuring acidity and alkalinity in solutions. Ranging from 0 to 14, it classifies substances as highly acidic, neutral, or highly alkaline. A pH of 7 is considered neutral, like pure water.
These measurements are crucial in various fields, especially in understanding processes like ocean acidification. The scale is logarithmic, meaning each step represents a tenfold change in hydrogen ion concentration. So, when the pH drops from 8.1 to 7.8, the acidity increases significantly.

• A lower pH value indicates higher acidity and a greater presence of hydrogen ions.
• A higher pH value implies alkalinity, where fewer hydrogen ions are present.

This scientific understanding underscores the importance of monitoring changes in ocean acidity, as even a small shift in pH can drastically affect marine ecosystems.

Hydrogen Ion Concentration

Hydrogen ion concentration is central to determining a solution's pH level and its associated acidity or alkalinity. It's often expressed in terms of molarity (M), which is a measure of the number of moles of hydrogen ions per liter of solution. As the pH level changes, so does the hydrogen ion concentration.
The relation between pH and hydrogen ion concentration is expressed by the formula: \[ \text{[H}^+\text{]} = 10^{-\text{pH}} \]This formula shows that when the ocean's pH changes from 8.1 to 7.8:

• The initial concentration at pH 8.1 is approximately \(7.94 \times 10^{-9}\text{ M}\).
• At pH 7.8, it increases to approximately \(1.58 \times 10^{-8}\text{ M}\).

Understanding these changes is essential because even slight variations in hydrogen ion concentration can lead to significant ecological impacts, affecting marine life and ocean chemistry.

Fossil Fuels

Fossil fuels, like coal, oil, and natural gas, are crucial energy sources, but their combustion contributes significantly to environmental issues such as ocean acidity. When fossil fuels are burned, they release carbon dioxide (\(\text{CO}_2\)) into the atmosphere. This \(\text{CO}_2\) eventually gets absorbed by ocean water, forming carbonic acid and increasing the ocean's acidity.
This process, known as ocean acidification, can harm marine organisms and ecosystems. As \(\text{CO}_2\) levels rise, the pH of ocean water decreases, posing threats to coral reefs, shellfish, and other marine forms of life.

• Burning fossil fuels is a major source of \(\text{CO}_2\) emissions.
• More \(\text{CO}_2\) in the ocean leads to lower pH values and increased acidity.

Reduction of fossil fuel reliance is crucial for mitigating ocean acidification, which requires international cooperation and innovative approaches to clean energy solutions.