Question

Unpolluted rain water has a pH of about 5.5. Acid rain has been shown to have a \(\mathrm{pH}\) as low as \(3.0\). Calculate the \(\left[\mathrm{H}^{+}\right]\) ratio of acid rain to unpolluted rain.

Short answer

Answer: The ratio of hydrogen ion concentration in acid rain to that in unpolluted rain is approximately 316.23.

Step-by-step solution

Calculate \(\left[\mathrm{H}^{+}\right]\) for acid rain and unpolluted rain

Since we are given the pH values of both types of rain, we can use the formula: \(\mathrm{pH} = -\log_{10}\left(\left[\mathrm{H}^{+}\right]\right)\) to find the \(\left[\mathrm{H}^{+}\right]\) for each type. For acid rain, the given pH is \(3.0\). Plugging this value into the formula, we get: \(\left[\mathrm{H}^{+}\right]_\text{acid} = 10^{-\mathrm{pH}} = 10^{-3.0} = 1 \times 10^{-3} \thinspace \mathrm{mol/L}\) For unpolluted rain, the given pH is \(5.5\). Plugging this value into the formula, we get: \(\left[\mathrm{H}^{+}\right]_\text{unpolluted} = 10^{-\mathrm{pH}} = 10^{-5.5} = 3.16 \times 10^{-6} \thinspace \mathrm{mol/L}\)

Calculate the ratio of acid rain \(\left[\mathrm{H}^{+}\right]\) to unpolluted rain \(\left[\mathrm{H}^{+}\right]\)

Now that we have the \(\left[\mathrm{H}^{+}\right]\) for both types of rain, we can divide the acid rain value by the unpolluted rain value to find the ratio: \(\text{Ratio} = \frac{\left[\mathrm{H}^{+}\right]_\text{acid}}{\left[\mathrm{H}^{+}\right]_\text{unpolluted}} = \frac{1 \times 10^{-3} \thinspace \mathrm{mol/L}}{3.16 \times 10^{-6} \thinspace \mathrm{mol/L}} \approx 316.23\) Hence, the ratio of hydrogen ion concentration in acid rain to that in unpolluted rain is approximately 316.23.

Key concepts

Hydrogen Ion Concentration Explained

The concentration of hydrogen ions, often represented by \( [H^+] \), is a fundamental measure in chemistry, particularly in the study of acid-base reactions. It refers to the amount of hydrogen ions present in a solution, and it's crucial for determining the solution's acidity or alkalinity. In our example, the hydrogen ion concentration is derived from the pH value of rainwater. This is done by using the formula \( pH = -\log_{10}([H^+]) \).

By calculating the \( [H^+] \) for both acid and unpolluted rain, we can understand the impact of acid rain on the environment. Unpolluted rain has a natural acidity due to the presence of carbon dioxide in the atmosphere, which forms carbonic acid when it dissolves in rainwater. However, acid rain has a higher \( [H^+] \) due to the presence of stronger acids like sulfuric and nitric acid, which come from industrial emissions.

The pH Scale Decoded

The pH scale is a log scale used in chemistry to specify the acidity or basicity of an aqueous solution. It typically ranges from 0 to 14, where 7 represents a neutral pH. Values below 7 indicate acidity, and values above 7 indicate alkalinity. Each unit of change represents a tenfold change in \( [H^+] \).

Understanding the Math Behind pH

Using the equation \( pH = -\log_{10}([H^+]) \), we can invert the relationship to find the hydrogen ion concentration from a given pH value: \( [H^+] = 10^{-pH} \). This tells us that the lower the pH, the higher the \( [H^+] \) and vice versa. When comparing the pH of acid rain to unpolluted rain, it is evident that even a small decrease in pH means a significant increase in acidity.

Environmental Chemistry of Acid Rain

Environmental chemistry delves into chemical processes occurring in the environment and their effects on human health and ecosystems. Acid rain is a significant topic within this field, resulting from emissions of sulfur dioxide and nitrogen oxides which react with water vapor to form acids.

These reactions lead to an increase in the \( [H^+] \) in rainwater, lowering the pH and causing the rain to become more acidic. Acid rain's implications are vast, affecting soil chemistry, plant life, aquatic ecosystems, and building materials. Understanding the chemistry of acid rain and its consequences allows for better management and mitigation strategies to protect the environment.