Question

In a particular \(3000 \mathrm{~km}^{2}\) region of southern Sweden, the annual rainfall averages \(850 \mathrm{~mm}\), its mean \(\mathrm{pH}\) is \(4.27\), and \(66 \%\) of the hydrogen ion is associated with sulfuric acid; the remaining \(34 \%\) is derived from nitric acid. Calculate whether soils of this region are subject to excessive sulfate loading if the only source of sulfate is rainfall and if the recommended maximum is set at \(20 \mathrm{~kg} \mathrm{SO}_{4}^{2-} \mathrm{ha}^{-1}\).

Short answer

Yes, the soils are subject to excessive sulfate loading.

Step-by-step solution

Convert Land Area to Hectares

The area of the region is given in square kilometers, but we need it in hectares. To convert from square kilometers to hectares, note that 1 square kilometer equals 100 hectares. Therefore, \(3000 \text{ km}^2 = 3000 \times 100 = 300,000 \text{ hectares}\).

Convert Rainfall to Meters

Annual rainfall is given as 850 mm. We need to convert this to meters to calculate the volume of water. Since 1 mm is 0.001 meters, \( 850 \text{ mm} = 0.85 \text{ meters}\).

Calculate Total Volume of Rainfall

The volume of rainfall can be calculated using the formula \( ext{Volume} = ext{Area} \times ext{Height} \). The area is 300,000 hectares, and the rainfall height is 0.85 meters.\[\text{Volume} = 300,000 \times 10,000 \times 0.85 = 2.55 \times 10^{9} \text{ m}^3\]Note: Hectares converted to square meters by multiplying by 10,000.

Determine Total Moles of Hydrogen Ion

The pH value is 4.27. The hydrogen ion concentration \([H^+]\) is found using \([H^+] = 10^{- ext{pH}}\).\[[H^+] = 10^{-4.27} \approx 5.37 \times 10^{-5} \text{ mol/L}\]Convert volume from cubic meters to liters (1 m extsuperscript{3} = 1000 L):\[2.55 \times 10^{9} \text{ m}^3 = 2.55 \times 10^{12} \text{ L}\]Calculate total moles of \(H^+\):\[\text{Total moles} = 5.37 \times 10^{-5} \text{ mol/L} \times 2.55 \times 10^{12} L = 1.36935 \times 10^{8} \text{ moles}\]

Calculate Moles of Sulfuric Acid

66% of hydrogen ions are from sulfuric acid. Therefore:\[\text{Moles of } H_{2}SO_{4} = 0.66 \times 1.36935 \times 10^{8} \approx 9.0399 \times 10^{7} \text{ moles}\]Each mole of \(H_{2}SO_{4}\) dissociates into one mole of \(SO_{4}^{2-}\), yielding the same number of moles of sulfate.

Calculate Mass of Sulfate

The molar mass of \(SO_{4}^{2-}\) is approximately 96 g/mol. Therefore, the mass of sulfate is:\[\text{Mass of } SO_{4}^{2-} = 9.0399 \times 10^{7} \text{ moles} \times 96 \text{ g/mol} = 8.6783 \times 10^{9} \text{ g} = 8,678.3 \text{ tonnes}\]

Determine Sulfate Loading per Hectare

Divide the total mass of sulfate by the total area in hectares:\[\text{Sulfate loading} = \frac{8,678,300 \text{ kg}}{300,000 \text{ hectares}} \approx 28.93 \text{ kg/hectare}\]

Compare with Recommended Maximum

The calculated sulfate loading of approximately 28.93 kg/ha exceeds the recommended maximum of 20 kg/ha. Thus, soils are subject to excessive sulfate loading.

Key concepts

Sulfate Loading

Sulfate loading refers to the accumulation of sulfate ions in an area, typically from sources such as rainfall or pollution. In the context of acid rain, sulfate loading becomes a critical factor to consider when determining the health of an ecosystem. To calculate sulfate loading, the amount of sulfate deposited over an area is assessed.
Understanding sulfate loading involves a few steps:

• First, measure the total amount of sulfate ions that rainfall brings into an area. This can be calculated by understanding the chemical reactions involved when sulfur compounds in the atmosphere convert into sulfuric acid, which dissociates into sulfate ions.
• Next, translate this amount into mass per hectare, which is especially relevant in agricultural or natural landscapes. In our exercise, we calculated the annual sulfate loading as 28.93 kg per hectare.
• Lastly, compare the calculated loading to recommended levels to understand if the ecosystem could be at risk, as seen when the sulfate loading exceeds the maximum recommended value of 20 kg per hectare.

The excessive sulfate can affect soil quality and plant health, making it crucial to evaluate and manage sulfate loading effectively.

pH of Rainwater

The pH of rainwater is an important indicator of its acidity, and can provide insight into the presence of acid rain. A pH less than 7 implies acidity, with lower values indicating higher acidity.
Normal rainwater has a mildly acidic pH of about 5.6 due to the presence of carbonic acid, formed when carbon dioxide dissolves in water. However, rainwater becomes more acidic when sulfur and nitrogen oxides in the atmosphere convert into sulfuric and nitric acids. In our exercise, rainwater in southern Sweden has a pH of 4.27, due to these pollutants, indicating significant acidity and potential environmental impacts.
The calculation for hydrogen ion concentration using pH is given by: \[ [H^+] = 10^{-\text{pH}} \]For a pH of 4.27, the hydrogen ion concentration calculates to approximately \( 5.37 \times 10^{-5} \text{ mol/L} \). This further helps in determining the contribution of acid rain to sulfate and nitrate ion deposition in the region.

Environmental Impact of Acid Rain

Acid rain can severely affect the environment, leading to consequences across soil, water bodies, and biodiversity.
Key impacts include:

• **Soil Degradation:** Acid rain can leach essential nutrients from the soil, reducing its fertility. It also increases the concentration of toxic metals like aluminum, which can harm vegetation.
• **Water Pollution:** Acid rain can lower the pH of lakes and streams, affecting aquatic life by causing stress or even death.
• **Vegetation Damage:** Leaves and bark of trees and plants can be harmed by acid rain, impairing photosynthesis and increasing susceptibility to disease and harsh weather.
• **Infrastructure Decay:** Buildings, especially those constructed with calcium-containing materials like limestone, can corrode and wear away faster.
  

In the context of our exercise, the slightly acidic rain in Sweden indicates potential environmental concerns like soil and water degradation if not managed.

Soil Chemistry

The chemistry of soil is crucial when assessing the impact of acid rain as it dictates how different pollutants affect soil composition and plant growth.
Sulphate from acid rain enters the soil, altering its chemical makeup. This can lead to:

• **Depletion of Nutrients:** Excessive sulfate can leach away important ions like calcium and magnesium necessary for plant growth.
• **Soil Acidity Increase:** Acid rain causes soil pH to decrease, resulting in further nutrient loss and potential aluminum toxicity.
• **Microbial Effects:** Soil acidity affects microbial communities, reducing the rates of organic matter decomposition and nutrient cycling.

In our calculation, sulfate loading exceeds recommended levels, indicating a high potential for adverse soil chemistry changes. Adequate management can mitigate these risks, preserving soil quality and ecosystem health.

Chemical Calculations in Environmental Science

Chemical calculations are essential tools in environmental science to quantify the interactions of chemicals like acids in the environment. These calculations help scientists evaluate the magnitude of environmental challenges and guide decision-making processes.
Key aspects include:

• **Concentration to Mass Calculations:** Converting hydrogen ion concentration into total pollutant mass in a region, as seen in the calculation of sulfate loadings.
• **Area-Based Metrics:** Understanding how much of a substance is deposited per area unit helps in comparing actual values against regulatory limits.
• **Mass Balance and Conversion Factors:** Frequently used to translate the volumetric rainfall data into meaningful mass of substances contributing to pollution.
  

In our exercise, we calculated the moles of hydrogen ions using the given pH, translated that into moles of sulfuric acid and subsequently quantified sulfate loading. This systematic approach highlights the significance of chemical calculations in assessing environmental impacts.