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On Easter Sunday, April \(3,1983,\) nitric acid spilled from a tank car near downtown Denver, Colorado. The spill was neutralized with sodium carbonate: $$ 2 \mathrm{HNO}_{3}(a q)+\mathrm{Na}_{2} \mathrm{CO}_{3}(s) \longrightarrow 2 \mathrm{NaNO}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g) $$ a. Calculate \(\Delta H^{\circ}\) for this reaction. Approximately \(2.0 \times\) \(10^{4}\) gal nitric acid was spilled. Assume that the acid was an aqueous solution containing 70.0\(\% \mathrm{HNO}_{3}\) by mass with a density of 1.42 \(\mathrm{g} / \mathrm{cm}^{3} .\) What mass of sodium car- bonate was required for complete neutralization of the spill, and what quantity of heat was evolved? ( \(\Delta H_{\mathrm{f}}^{\circ}\) for \(\mathrm{NaNO}_{3}(a q)=-467 \mathrm{kJ} / \mathrm{mol} )\) b. According to The Denver Post for April \(4,1983,\) authorities feared that dangerous air pollution might occur during the neutralization. Considering the magnitude of \(\Delta H^{\circ},\) what was their major concern?

Step by step solution

01

Calculate ΔH° for the reaction

To calculate the ΔH° for the given reaction, we can use the formula: ΔH° = Σ ΔH° products - Σ ΔH° reactants We are given the ΔHf° for NaNO3(aq) as -467 kJ/mol. We also know the standard enthalpies of formation for other substances in the reaction: ΔHf° for H2O(l) = -285.8 kJ/mol ΔHf° for CO2(g) = -393.5 kJ/mol ΔHf° for HNO3(aq) = -207 kJ/mol ΔHf° for Na2CO3(s) = -1131 kJ/mol Plugging the values into the formula, we have: ΔH° = [(2 × -467) + (-285.8) + (-393.5)] - [(2 × -207) + (-1131)] = -787 kJ/mol

02

Calculate the mass of HNO3 spilled

Given the volume of spilled nitric acid: 2.0 × 10^4 gal, and the density as 1.42 g/cm³. First, let's convert the volume to liters, and then to cubic centimeters: 1 gal = 3.78541 L 2.0 × 10^4 gal × 3.78541 L/gal = 75709 L 1 L = 1000 cm³ 75709 L × 1000 cm³/L = 75709000 cm³ Now, we can find the mass of the spilled nitric acid: Mass = Volume × Density Mass = 75709000 cm³ × 1.42 g/cm³ = 107606980 g Since the nitric acid solution is 70% HNO3 by mass, the mass of HNO3 is: Mass_HNO3 = 0.7 × 107606980 g = 75324786 g

03

Calculate moles of HNO3 spilled

To calculate the moles of HNO3, we can use its molecular weight, which is (1 + 14 + 16*3) = 63 g/mol: Moles_HNO3 = Mass_HNO3 / Molecular_weight Moles_HNO3 = 75324786 g / 63 g/mol = 1195713.42 mol

04

Calculate the moles and mass of sodium carbonate required for complete neutralization

From the balanced equation, we can see that 2 moles of HNO3 react with 1 mole of Na2CO3. Using stoichiometry, we can calculate the moles of sodium carbonate needed: Moles_Na2CO3 = Moles_HNO3 / 2 Moles_Na2CO3 = 1195713.42 mol / 2 = 597856.71 mol Now, we can find the mass of sodium carbonate needed using its molecular weight (23*2 + 12 + 16*3) = 106 g/mol: Mass_Na2CO3 = Moles_Na2CO3 × Molecular_weight Mass_Na2CO3 = 597856.71 mol × 106 g/mol = 63374711.46 g

05

Calculate the heat evolved during the process

Using the calculated ΔH° and the moles of HNO3, we can calculate the heat evolved: Heat_evolved = Moles_HNO3 × ΔH° Heat_evolved = 1195713.42 mol × -787 kJ/mol = -941418168 kJ

06

Analyze the dangerous air pollution concern

The major concern was the release of CO2 gas during the neutralization process, which could have caused air pollution. The magnitude of ΔH° being negative (-787 kJ/mol) indicates that the reaction is exothermic, meaning heat is being released into the surroundings. This release of heat could worsen the situation with air pollution, as it could cause an increase in temperature and expansion of the gas, leading to more potential danger to the environment and people living nearby.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Neutralization Reactions

A neutralization reaction occurs when an acid reacts with a base to form a salt and water. In the context of the nitric acid spill in Denver, this type of reaction is crucial for mitigating the spill's impact. Here, nitric acid (\(\mathrm{HNO}_3\)) is neutralized by sodium carbonate (\(\mathrm{Na}_2\mathrm{CO}_3\)), a basic compound. The balanced chemical equation for this reaction is:

• \(2 \mathrm{HNO}_{3}(aq) + \mathrm{Na}_{2} \mathrm{CO}_{3}(s) \rightarrow 2 \mathrm{NaNO}_{3}(aq) + \mathrm{H}_{2} \mathrm{O}(l) + \mathrm{CO}_{2}(g)\)

It's important to note that this process not only neutralizes the harmful acid but also generates carbon dioxide gas (\(\mathrm{CO}_2\)). This reaction helps prevent environmental damage by stabilizing the acidic components formed during the spill.

The Role of Stoichiometry in Chemical Reactions

Stoichiometry is a powerful tool in chemistry that allows us to calculate the exact amounts of reactants and products involved in a chemical reaction. For the spill scenario, stoichiometry is used to determine the mass of sodium carbonate needed for complete neutralization. The balanced equation shows a 2:1 ratio of nitric acid to sodium carbonate. This means:

• Two moles of \(\mathrm{HNO}_3\) react with one mole of \(\mathrm{Na}_2\mathrm{CO}_3\).
• If you know the moles of one, you can determine the moles of the other.

By applying stoichiometry, one can ensure that no excess harmful chemicals remain and that the correct amount of base is used to neutralize the acid fully, preventing unnecessary resource waste.

The Nature of Exothermic Reactions

Exothermic reactions release heat during the chemical process. Our reaction, which neutralizes nitric acid with sodium carbonate, is a classic example. The calculated enthalpy change (\(\Delta H^{\circ} = -787\, \mathrm{kJ/mol}\)) indicates that the reaction is exothermic. This means:

• Heat is released into the surroundings.
• The reaction can lead to an increase in local temperature.

An exothermic reaction can be beneficial as it means energy is not required to drive the reaction forward. However, it can also pose safety risks, especially in large-scale scenarios like chemical spills, where the heat release can accelerate processes that might be dangerous in an uncontrolled environment.

Air Pollution Concerns During the Neutralization Process

The major concern during the neutralization of the nitric acid spill was air pollution due to the release of carbon dioxide (\(\mathrm{CO}_2\)) gas. This gas is a byproduct of the reaction and can lead to several environmental concerns:

• Accumulation of \(\mathrm{CO}_2\) in the atmosphere can contribute to air pollution.
• Increased local temperatures due to the exothermic nature of the reaction could enhance the expansion and dispersion of the gas.

Authorities were rightfully concerned that the rapid release and expansion of \(\mathrm{CO}_2\) could pose a health hazard to residents and the environment. In such situations, managing the release of gases and associated heat is vital to minimize the impact on air quality and public safety.