Question

The organic anion is found in most detergents. Assume that the anion undergoes aerobic decomposition in the following manner: $$\begin{aligned} 2 \mathrm{C}_{18} \mathrm{H}_{29} \mathrm{SO}_{3}^{-}(a q)+51 \mathrm{O}_{2}(a q) & \longrightarrow \\ & 36 \mathrm{CO}_{2}(a q)+28 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{H}^{+}(a q)+2 \mathrm{SO}_{4}^{2-}(a q) \end{aligned}$$ What is the total mass of \(\mathrm{O}_{2}\) required to biodegrade 10.0 \(\mathrm{g}\) of this substance?

Short answer

The total mass of O₂ required to biodegrade 10.0 g of the organic anion is approximately 25.08 g.

Step-by-step solution

Calculate the molar mass of the organic anion and O₂

First, we have to find the molar mass of the organic anion (C₁₈H₂₉SO₃⁻) and oxygen (O₂). Molar mass of C₁₈H₂₉SO₃⁻: - C: 18 * 12.01 g/mol = 216.18 g/mol - H: 29 * 1.008 g/mol = 29.232 g/mol - S: 1 * 32.07 g/mol = 32.07 g/mol - O: 3 * 16.00 g/mol = 48.00 g/mol Total molar mass of C₁₈H₂₉SO₃⁻ = 216.18 + 29.232 + 32.07 + 48.00 = 325.482 g/mol Molar mass of O₂: 2 * 16.00 g/mol = 32.00 g/mol The molar masses are 325.482 g/mol for C₁₈H₂₉SO₃⁻ and 32.00 g/mol for O₂.

Convert the given mass of the organic anion to moles

Now convert the given mass of the organic anion (10.0 g) to moles using its molar mass. Moles of C₁₈H₂₉SO₃⁻ = (10.0 g) / (325.482 g/mol) = 0.03073 mol

Use stoichiometry to find the moles of O₂ needed

The balanced equation tells us that 2 moles of C₁₈H₂₉SO₃⁻ react with 51 moles of O₂. So, we will use the mole ratio (51:2) to find the moles of O₂ needed for the reaction: Moles of O₂ = (0.03073 mol C₁₈H₂₉SO₃⁻)(51 mol O₂ / 2 mol C₁₈H₂₉SO₃⁻) = 0.7836 mol O₂

Convert moles of O₂ to mass

Finally, we will convert the moles of O₂ to mass using the molar mass of O₂ (32.00 g/mol): Mass of O₂ = (0.7836 mol O₂) * (32.00 g/mol) = 25.0768 g Therefore, the total mass of O₂ required to biodegrade 10.0 g of the organic anion is approximately 25.08 g.

Key concepts

Molar Mass Calculation

Understanding the molar mass calculation is crucial for a variety of scientific disciplines, including chemistry, biology, and environmental science. The term 'molar mass' refers to the weight of one mole of a given substance and is measured in grams per mole (g/mol). To calculate the molar mass of a compound, one must sum the masses of all atoms in a single molecule of that compound. For the organic anion found in detergents, C₈₁₈H₂₉SO₃⁻, its molar mass is calculated by multiplying the amount of each atom by its standard atomic mass and adding these quantities together. Each element from the periodic table has a standard atomic mass.

For example, carbon (C) has an atomic mass of 12.01 g/mol, and the anion contains 18 carbon atoms, so the total mass contributed by carbon is 18 x 12.01 g/mol. Once we have computed the individual contributions from carbon, hydrogen, sulfur, and oxygen, we sum them to determine the molar mass of the compound. This step is fundamental as it allows us to convert from mass to moles, which is the bridge between the tangible weight of a substance and the reactions it undergoes on a molecular level.

Stoichiometric Calculations

Stoichiometric calculations are a cornerstone of understanding chemical reactions. They involve using the balanced chemical equation to determine the relationships between the quantities of reactants and products. When tackling stoichiometry problems, we focus on the mole ratio derived from the balanced equation. For instance, in our exercise, the mole ratio between the organic anion and oxygen is 2:51, which means it takes 51 moles of oxygen to completely react with 2 moles of the organic anion.

With the mole ratio, we can convert moles of one substance to moles of another. In the case of our organic anion, knowing the amount present in grams, we first converted it to moles, then used the mole ratio to find out how many moles of oxygen are needed for complete biodegradation. This part of the calculation is critical because it tells us precisely how much of each reactant we need and allows us to predict the amount of each product formed.

Chemical Reactions in Environmental Chemistry

The chemical reactions in environmental chemistry usually involve processes that are vital for the ecosystem's health, such as biodegradation. Biodegradation is the chemical breakdown of materials by living organisms, and it's an essential concept in environmental sustainability for reducing waste. Our exercise explores the aerobic decomposition of an organic anion, a process by which organic substances are converted into simpler compounds by microorganisms in the presence of oxygen.

The balanced chemical equation for this reaction provides insight into the stoichiometry and the environment's capacity to handle pollutants. From a broader perspective, understanding the specifics of such chemical reactions helps in waste management and pollution mitigation. By calculating the amount of oxygen needed to degrade a given mass of a pollutant, we can gauge the pollutant's environmental impact and the natural biodegradation potential of the ecosystem involved. This information informs how we approach environmental conservation and the development of eco-friendly products.