Question

Unpolluted rain water has a pH of about \(5.5 .\) Acid rain has been shown to have a 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 the concentration of hydrogen ions in acid rain to that in unpolluted rain is approximately 316.23.

Step-by-step solution

Calculate \([\mathrm{H}^{+}]\) from the pH values

Recall that the relationship between the hydrogen ion concentration \([\mathrm{H}^{+}]\) and the pH of a solution is given by the formula: $$ \mathrm{pH} = -\log_{10} [\mathrm{H}^{+}] $$ Reversing this equation, we can find the \([\mathrm{H}^{+}]\) in both the acid rain and unpolluted rain: $$ [\mathrm{H}^{+}] = 10^{-\mathrm{pH}} $$ Calculating \([\mathrm{H}^{+}]\) for both acid rain and unpolluted rain: $$ [\mathrm{H}^{+}]_{\text{Acid rain}} = 10^{-3.0} $$ $$ [\mathrm{H}^{+}]_{\text{Unpolluted rain}} = 10^{-5.5} $$

Calculate the ratio of \([\mathrm{H}^{+}]\) values

Now that we have the \([\mathrm{H}^{+}]\) for both acid rain and unpolluted rain, we can calculate the ratio: $$ \text{Ratio} = \frac{[\mathrm{H}^{+}]_{\text{Acid rain}}}{[\mathrm{H}^{+}]_{\text{Unpolluted rain}}} $$ Plugging in the values we calculated earlier: $$ \text{Ratio} = \frac{10^{-3.0}}{10^{-5.5}} $$ Simplifying the expression, we get: $$ \text{Ratio} = 10^{-3.0 + 5.5} = 10^{2.5} $$ Finally, we evaluate this expression to find the ratio of the \([\mathrm{H}^{+}]\) values in acid rain to unpolluted rain: $$ \text{Ratio} = 10^{2.5} \approx 316.23 $$

Key concepts

pH Scale

The pH scale is a measure of how acidic or basic a solution is. It runs from 0 to 14, with 7 being neutral. Solutions with a pH less than 7 are considered acidic, while those with a pH greater than 7 are basic. The scale is logarithmic, meaning each whole pH value below 7 is ten times more acidic than the next higher value. For example, a solution with a pH of 3 is ten times more acidic than one with a pH of 4.

It is particularly useful in environmental chemistry to track acidification of rain and bodies of water caused by industrial pollution. This measure can indicate the presence of acid rain, which is significantly more acidic than unpolluted rain. The pH of unpolluted rain water is typically around 5.5, due to the natural presence of carbon dioxide in the atmosphere, which forms carbonic acid when dissolved in rain. However, pollutants such as sulfur dioxide and nitrogen oxides can lower the pH of rainwater to 3.0 or even lower, indicating the presence of acid rain.

Hydrogen Ion Concentration

Hydrogen ion concentration, denoted as \( [\mathrm{H}^{+}] \), represents the number of hydrogen ions present in a solution. It is directly related to the acidity of a solution: the greater the \( [\mathrm{H}^{+}] \), the more acidic the solution is. In chemistry, the concentration of hydrogen ions in a solution is used to calculate the pH through the negative logarithm to the base 10: \( \mathrm{pH} = -\log_{10} [\mathrm{H}^{+}] \).

Understanding this relationship is crucial in environmental chemistry. For example, the difference in \( [\mathrm{H}^{+}] \) between acid rain and unpolluted rain can be quite large. This concept clarifies how a seemingly small change in pH value can indicate a significant change in chemical composition, thus having vast environmental effects.

Environmental Chemistry

Environmental chemistry focuses on chemical processes occurring in the environment and the effects of human activities on these processes. It plays an essential role in understanding issues like acid rain, ozone depletion, and water and soil contamination. Analyzing the changes in \( [\mathrm{H}^{+}] \) and pH of rain water helps scientists evaluate the health of ecosystems affected by acid rain.

Incalculating the ratio of \( [\mathrm{H}^{+}] \) in acid rain to that in unpolluted rain, we can assess the impact of acid rain. A high ratio indicates a significant increase in the hydrogen ion concentration and a potential risk for aquatic life and vegetation, which can have wider implications for the ecosystem. Dedicated studies and monitoring are essential in mitigating the effects of these environmental hazards.