Question

Natural or "unpolluted" rain has a pH of \(5.6 .\) By what factor has the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) increased in acid rain with a \(\mathrm{pH}\) of \(3.6 ?\) (b) In southeastern Canada the average \(\mathrm{pH}\) of lakes is \(5.1\), well below the \(\mathrm{pH}\) of \(6.5\) required for a healthy aquatic ecosystem. Calculate \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) in a lake with \(\mathrm{pH}=5.10 .\)

Short answer

The concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) increases by a factor of 100. For pH 5.1, \([\mathrm{H}_3 \mathrm{O}^+] = 7.94 \times 10^{-6} \text{ M}\) and \([\mathrm{OH}^-] = 1.26 \times 10^{-9} \text{ M}\).

Step-by-step solution

Understand pH Scale and Formula

The pH scale measures the acidity of a solution, calculated using the formula: \[ \text{pH} = -\log_{10} [\mathrm{H}_3\mathrm{O}^+] \] where \([\mathrm{H}_3\mathrm{O}^+]\) is the hydrogen ion concentration.

Calculate Increase in \([\mathrm{H}_3\mathrm{O}^+]\) Factor

For natural rain with pH 5.6, calculate \([\mathrm{H}_3\mathrm{O}^+]\): \[ [\mathrm{H}_3\mathrm{O}^+] = 10^{-5.6} \] For acid rain with pH 3.6, \([\mathrm{H}_3\mathrm{O}^+]\) is \[ 10^{-3.6} \]. The increase factor is \(\frac{10^{-3.6}}{10^{-5.6}} = 10^2 = 100\).

Calculate \([\mathrm{H}_3\mathrm{O}^+]\) for pH 5.1

Using the formula \([\mathrm{H}_3\mathrm{O}^+] = 10^{-\text{pH}}\), calculate for \(\text{pH} = 5.1\): \[ [\mathrm{H}_3\mathrm{O}^+] = 10^{-5.1} = 7.94 \times 10^{-6} \text{ M} \].

Calculate \([\mathrm{OH}^-]\) for pH 5.1

Using the relation \([\mathrm{H}_3\mathrm{O}^+] \times [\mathrm{OH}^-] = 10^{-14}\) (at 25°C), calculate \([\mathrm{OH}^-]\): \[ [\mathrm{OH}^-] = \frac{10^{-14}}{7.94 \times 10^{-6}} = 1.26 \times 10^{-9} \text{ M} \].

Key concepts

Acid Rain

Acid rain is a form of precipitation with high levels of hydrogen ions, making it more acidic than usual rainwater. Regular rain is slightly acidic with a pH of around 5.6, mainly due to the dissolution of carbon dioxide forming carbonic acid. However, acid rain has a much lower pH, typically around 4.0 or less.

This increased acidity is primarily due to human activities releasing sulfur dioxide (SO₂) and nitrogen oxides (NOₓ) into the atmosphere. These gases react with water vapor to produce sulfuric and nitric acids. These acids then fall as acid rain, which can have harmful effects on the environment. It leads to the deterioration of forests, buildings, and aquatic environments by changing the soil and water chemistry.

Acid rain directly impacts the hydronium ion concentration of water bodies, as it raises the amount of \(\mathrm{H}_3\mathrm{O}^+\) ions present. This increase in acidity can severely affect aquatic life by making the water uninhabitable for many organisms.

Hydronium Ion Concentration

The hydronium ion \([\mathrm{H}_3\mathrm{O}^+]\) is a measure of the concentration of positive hydrogen ions in a solution, indicating its acidity. The concentration is crucial in determining the pH of a solution. It is calculated using the formula: \[ [\mathrm{H}_3\mathrm{O}^+] = 10^{-\text{pH}} \]The higher the concentration, the lower the pH, making the solution more acidic.

For example, natural rain with a pH of 5.6 has a hydronium ion concentration of \(10^{-5.6}\). In contrast, acid rain with a pH of 3.6 has a significantly higher concentration of \(10^{-3.6}\). This means acid rain is about 100 times more acidic than natural rain.

• Higher \([\mathrm{H}_3\mathrm{O}^+]\) results in a lower pH.
• A pH change of one unit represents a tenfold change in hydronium ion concentration.

The concept of hydronium ion concentration is vital in understanding how industrial emissions affect rainwater and its capability to damage natural ecosystems.

Hydroxide Ion Concentration

Hydroxide ions \([\mathrm{OH}^-]\) represent the basicity of a solution. Just as \(\mathrm{H}_3\mathrm{O}^+\) ions are measures of acidity, \(\mathrm{OH}^-\) ions help understand the basic character of the solution. The relationship between hydronium ions and hydroxide ions in aqueous solutions is connected by the ion product of water:\[ [\mathrm{H}_3\mathrm{O}^+] \times [\mathrm{OH}^-] = 10^{-14} \] \(\text{(at 25°C)}\)

This means an increase in \(\mathrm{H}_3\mathrm{O}^+\) ions results in a decrease in \(\mathrm{OH}^-\) ions to maintain balance. In a lake with a pH of 5.1, the hydroxide ion concentration is much lower, calculated as \(\frac{10^{-14}}{7.94 \times 10^{-6}}\) resulting in \(1.26 \times 10^{-9} \text{ M}\).

The fundamental takeaway is that both ions are interdependent:

• When one increases, the other decreases.
• A balance between them maintains the neutrality of solutions.

Understanding this balance is important for chemical reactions and environmental assessments involving water ecosystems.

pH Scale

The pH scale is a measure of how acidic or basic a solution is, ranging from 0 to 14. Neutral solutions, like pure water, have a pH of around 7. Solutions with a pH less than 7 are acidic, while those with a pH greater than 7 are basic or alkaline. The pH scale is logarithmic, meaning each whole number change represents a tenfold change in hydrogen ion concentration.

For example, when rain has a pH of 5.6, it is slightly acidic, while acid rain might have a pH of 3.6, indicating a drastic increase in acidity. The formula relating pH to hydronium ion concentration is given by:\[ \text{pH} = -\log_{10} [\mathrm{H}_3\mathrm{O}^+] \]

This mathematical relationship helps scientists and environmentalists evaluate the acidity of different solutions. Understanding the pH scale is essential in many scientific fields such as chemistry, biology, environmental science, and even medicine, as it helps predict how chemicals will behave in a solution.