Question

"Acid rain" forms when rain falls through air polluted by oxides of sulfur and nitrogen. Trees and plants are affected if the acid rain has a pH of 3.5 or lower. What is the hydrogen ion concentration in acid rain that has a \(\mathrm{pH}\) of 3.16 ? What is the \(\mathrm{pH}\) of a solution having twice your calculated hydrogen ion concentration?

Short answer

The hydrogen ion concentration in acid rain with a pH of 3.16 is approximately \(6.92 \times 10^{-4} M\). The pH of a solution with twice this hydrogen ion concentration is approximately 2.86.

Step-by-step solution

Calculate the hydrogen ion concentration

To find the hydrogen ion concentration from the pH, use the formula \(\mathrm{[H^+]} = 10^{-\mathrm{pH}}\). For a pH of 3.16, the hydrogen ion concentration is \(\mathrm{[H^+]} = 10^{-3.16}\) moles per liter (M).

Determine the new hydrogen ion concentration

If the hydrogen ion concentration is doubled, the new concentration \(\mathrm{[H^+]_{new}}\) would be \(2 \times \mathrm{[H^+]}\). Thus, \(\mathrm{[H^+]_{new}} = 2 \times 10^{-3.16}\).

Calculate the new pH

To find the new pH, use the inverse of the formula from Step 1: \(\mathrm{pH} = -\log(\mathrm{[H^+]})\). Hence, the new pH is \(\mathrm{pH} = -\log(2 \times 10^{-3.16})\).

Calculate the numerical values and simplify

First, calculate the initial hydrogen ion concentration \(\mathrm{[H^+]} = 10^{-3.16} = 6.92 \times 10^{-4} M\). Then the new hydrogen ion concentration is \(\mathrm{[H^+]_{new}} = 2 \times 6.92 \times 10^{-4} = 1.384 \times 10^{-3} M\). Lastly, find the new pH: \(-\log(1.384 \times 10^{-3}) \approx -\log(1.38 \times 10^{-3}) + \log(1.38) \approx 3 - 0.14 = 2.86\).

Key concepts

Hydrogen Ion Concentration

Understanding the hydrogen ion concentration, denoted as \( [H^+] \) in chemistry, is pivotal when investigating the nature of acidic or basic solutions. Such concentration refers to the amount of hydrogen ions present in a solution. Measured in moles per liter (M), it determines the acidity or basicity of a substance. For instance, when focusing on acid rain, the exercise provided illustrates that a rain with a pH of 3.16 has a hydrogen ion concentration calculated by the formula \( [H^+] = 10^{-\text{pH}} \).

For a given pH of 3.16, one can compute this concentration as \( 10^{-3.16} \), which translates into \( 6.92 \times 10^{-4} \) M. To further grasp the concept, if the concentration doubles, it directly affects the pH value, highlighting the delicate balance between \( [H^+] \) and pH levels in environmental chemistry.

pH Scale

The pH scale is an essential tool used by chemists to measure the acidity or basicity of a solution. It is a logarithmic scale ranging from 0 to 14, with 7 being neutral. pH values less than 7 indicate acidity, while values greater than 7 denote basicity. The pH is inversely related to the hydrogen ion concentration, exemplified by the formula \( \text{pH} = -\log([H^+]) \).

This means that as \( [H^+] \) increases, the pH decreases, making the solution more acidic. In the context of the acid rain problem, knowing that the pH of 3.16 corresponds to a rather acidic solution, we can infer that environmental measures targeting a reduction in acid rain should aim for higher pH values. The calculation to find the new pH after doubling \( [H^+] \) is a direct application of the fundamental relationship governing the pH scale.

Environmental Chemistry

Environmental chemistry revolves around chemical processes occurring in nature and the impact of human activities on natural systems. The study of acid rain and its effects on ecosystems is a critical area within this field. Acid rain arises when sulfur and nitrogen oxides react in the atmosphere and dissolve in rainwater, lowering its pH. Trees and plants, as shown in the exercise, become vulnerable when exposed to pH levels of 3.5 or lower.

By understanding how the pH reflects the hydrogen ion concentration, environmental chemists can better assess the extent of acidification and its potential damages. This knowledge enables them to propose strategies for reducing pollution emissions, improving air quality, and ameliorating the impacts of acid rain on vegetation and water bodies—fundamental actions for maintaining a balanced ecosystem.