Question

The ionic composition (in units of \(\mathrm{ng} \mathrm{m}^{-3}\) ) of an atmospheric aerosol in a tropical rain forest is \(\mathrm{SO}_{4}^{2-}, 207 ; \mathrm{NO}_{3}^{-}, 18 ; \mathrm{NH}_{4}^{+}, 385 ; \mathrm{K}^{+}, 180 ; \mathrm{Na}^{+}, 247\). The \(\mathrm{pH}\) of the aerosol is \(5.22\). Use these data to calculate the total positive and negative charge 'concentration' \(\left(\mathrm{mol} \mathrm{m}^{-3}\right)\) in the aerosol and suggest reasons which might account for any discrepancy in anionic and cationic charge.

Short answer

Total positive charge is significantly greater. Discrepancy may be due to undetected anions or measurement errors.

Step-by-step solution

Convert Mass to Moles

To find the moles, use the molar mass of each ion: - \(\mathrm{SO}_4^{2-}\) has a molar mass of approximately 96.06 g/mol.- \(\mathrm{NO}_3^{-}\) has a molar mass of about 62 g/mol.- \(\mathrm{NH}_4^{+}\) has a molar mass of nearly 18 g/mol.- \(\mathrm{K}^{+}\) has a molar mass around 39.1 g/mol.- \(\mathrm{Na}^{+}\) has a molar mass close to 23 g/mol.Use the formula: \ \[ \text{Moles of ion} = \frac{\text{Concentration in ng/m}^3}{\text{Molar mass in g/mol} \times 10^6} \]

Calculate Moles of Each Ion

Calculate moles using the formula for each ion: - For \(\mathrm{SO}_4^{2-}\): \[ \frac{207 \text{ ng/m}^3}{96.06 \text{ g/mol} \times 10^6} \approx 2.16 \times 10^{-9} \text{ mol/m}^3 \]- For \(\mathrm{NO}_3^{-}\): \[ \frac{18 \text{ ng/m}^3}{62 \text{ g/mol} \times 10^6} \approx 2.90 \times 10^{-10} \text{ mol/m}^3 \]- For \(\mathrm{NH}_4^{+}\): \[ \frac{385 \text{ ng/m}^3}{18 \text{ g/mol} \times 10^6} \approx 2.14 \times 10^{-8} \text{ mol/m}^3 \]- For \(\mathrm{K}^{+}\): \[ \frac{180 \text{ ng/m}^3}{39.1 \text{ g/mol} \times 10^6} \approx 4.60 \times 10^{-9} \text{ mol/m}^3 \]- For \(\mathrm{Na}^{+}\): \[ \frac{247 \text{ ng/m}^3}{23 \text{ g/mol} \times 10^6} \approx 1.07 \times 10^{-8} \text{ mol/m}^3 \]

Calculate Total Charge Concentration

Multiply the moles of each ion by the charge of the ion to find the total charge: - Total negative charge = \(2(2.16 \times 10^{-9}) + 1(2.90 \times 10^{-10}) \approx 4.61 \times 10^{-9} \text{ mol/m}^3 \) (from \(\mathrm{SO}_4^{2-}\) and \(\mathrm{NO}_3^{-}\))- Total positive charge = \(1(2.14 \times 10^{-8}) + 1(4.60 \times 10^{-9}) + 1(1.07 \times 10^{-8}) \approx 3.66 \times 10^{-8} \text{ mol/m}^3 \) (from \(\mathrm{NH}_4^{+}\), \(\mathrm{K}^{+}\), and \(\mathrm{Na}^{+}\))

Evaluate Discrepancy in Charge

The total positive charge \((3.66 \times 10^{-8} \text{ mol/m}^3)\) is much greater than the total negative charge \((4.61 \times 10^{-9} \text{ mol/m}^3)\). This discrepancy could arise from other undetected anions that balance the charge, or potential errors in measurements or assumptions, such as non-inclusion of organic acids or other ions like chloride.

Key concepts

Ionic Composition

Understanding the ionic composition of atmospheric aerosols is crucial in atmospheric chemistry. Ions are atoms or molecules that have gained or lost electrons, giving them a charge. In the context of aerosols, these ions originate from various natural and anthropogenic sources.
For the given aerosol in a tropical rainforest, the significant ions include

• Sulfate (\(\mathrm{SO}_4^{2-}\), which is often derived from natural processes such as weathering of rocks, volcanic activity, or from human activities like burning fossil fuels)
• Nitrate (\(\mathrm{NO}_3^{-}\), typically formed from nitrogen oxides emitted by vehicles and industrial processes)
• Ammonium (\(\mathrm{NH}_4^{+}\), which originates from agricultural activities, such as the application of fertilizers)
• Potassium (\(\mathrm{K}^{+}\)) and Sodium (\(\mathrm{Na}^{+}\)), which can come from sea salt or soil dust.

These ions play a significant role in determining aerosol properties like solubility, reactivity, and ability to influence cloud formation.

Charge Balance

Charge balance is vital for understanding the chemistry of aerosols in the atmosphere. In a neutral system, the total positive charge should equal the total negative charge.
When calculating the charge balance, we look at the total numbers of positive charges from cations and negative charges from anions. This is done to ensure that there is no net electrical imbalance in the aerosol.
In our scenario, we calculated the moles of each ion and then accounted for their respective charges:

• Negative charges mainly come from sulfate (\(\mathrm{SO}_4^{2-}\)) and nitrate (\(\mathrm{NO}_3^{-}\)).
• Positive charges are contributed by ammonium (\(\mathrm{NH}_4^{+}\)), potassium (\(\mathrm{K}^{+}\)), and sodium (\(\mathrm{Na}^{+}\)).

However, a discrepancy in charge could indicate missing ions or measurement inaccuracies, highlighting the complexity of achieving perfect charge balance in real-world scenarios.

Aerosol pH

The pH of an aerosol is a measure of its acidity or basicity, which can significantly affect atmospheric chemical reactions. The pH value is determined by the concentration of hydrogen ions (\(\mathrm{H}^+\)) in the solution. In the context of aerosols, the pH can influence:

• The solubility of gases present in the atmosphere.
• The formation and phase transition of secondary pollutants.
• The bioavailability of nutrients in airborne particles.

In our exercise, an aerosol pH of 5.22 indicates a slightly acidic environment. This pH level can result from the presence of acidic ions like sulfate and nitrate, affecting the aerosol's ability to interact with other atmospheric components. Maintaining a proper understanding of aerosol pH is crucial for predicting atmospheric transformations and devising strategies for air quality control.

Charge Discrepancy

A discrepancy in the charge balance, as identified in our exercise, suggests potential gaps in ion detection or measurement errors. When the total measured positive charge vastly exceeds the negative charge, several possibilities should be considered:

• Undetected ions: Some ions may not have been measured or included in the initial analysis, such as chloride (\(\mathrm{Cl}^-\)) or organic acids.
• Measurement errors: Analytical challenges or equipment calibration issues could lead to inaccuracies in ion concentration readings.
• Ion pairing: Certain ions might be forming neutral pairs or complexes that were not accounted for.
• Air mass origins: Different sources and paths such as marine or terrestrial routes can preprocess ion compositions differently before reaching the sampling site.

Addressing these issues involves meticulous sample collection and advanced analytical techniques to refine charge calculations. This helps ensure more precise characterizations of aerosol compositions and interactions.