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 carbonate was required for complete neutralization of the spill, and what quantity of heat was evolved? \(\left(\Delta H_{\mathrm{f}}^{\circ}\right.\) 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

Find values for enthalpy changes of formation

From the problem, we know the enthalpy change of formation for NaNO3(aq) is \(-467\,kJ/mol\). We don't have the other values provided, so we'll need to look up the enthalpy change of formation for the remaining compounds in a table. From a standard table, we find: \(\Delta H_f^\circ(HNO_3(aq))=-207\,kJ/mol\) \(\Delta H_f^\circ(H_2O(l))=-286\,kJ/mol\) \(\Delta H_f^\circ(CO_2(g))=-394\,kJ/mol\) We also know that there's no enthalpy change for Na2CO3(s) since it is a reactant in its standard state.

02

Calculate enthalpy change for the reaction

We can now calculate the enthalpy change for the reaction using the enthalpy changes of formation and the balanced stoichiometric coefficients: \[\Delta H^\circ = \sum \Delta H_f^\circ (products) - \sum \Delta H_f^\circ (reactants)\] \[\Delta H^\circ = [2 \times (-467) + (-286) + (-394)] - [2 \times (-207)]\] \[\Delta H^\circ = -1614\,kJ/mol\] Step 2: Calculate the mass of sodium carbonate needed

03

Calculate the mass of nitric acid spilled

Given the volume of the nitric acid spill (2.0 x 10^4\,gal) and its density (1.42\,g/cm^3), we can first convert it into mass: (2.0 x 10^4\,gal) x (3.78541\,L/gal) x (1000\,mL/L) x (1\,cm^3/mL) x (1.42\,g/cm^3) = 1.07 x 10^8\,g

04

Calculate the mass of pure HNO3 in the spilled solution

We know that the spilled nitric acid solution contains 70% HNO3, by mass. So, we can now calculate the mass of pure HNO3 in the spilled solution: Mass of HNO3 in solution = (1.07 x 10^8\,g) x (0.70) = 7.5 x 10^7\,g

05

Convert mass of HNO3 to moles

To find the mass of Na2CO3 required, convert the mass of HNO3 to moles first: Moles of HNO3 = Mass HNO3 / Molar mass HNO3 Moles of HNO3 = (7.5 x 10^7\,g) / (63.01\,g/mol) = 1.19 x 10^6\,mol

06

Calculate moles of Na2CO3 needed

Now, using stoichiometry and the balanced equation, we can determine the moles of Na2CO3 needed: Moles Na2CO3 = (1 mol Na2CO3 / 2 mol HNO3) x Moles of HNO3 Moles Na2CO3 = (1/2) x 1.19 x 10^6\,mol = 5.95 x 10^5\,mol

07

Calculate mass of sodium carbonate required

To calculate the mass of sodium carbonate required, we can now convert moles of Na2CO3 to mass using its molar mass: Mass of Na2CO3 = Moles Na2CO3 x Molar mass Na2CO3 Mass of Na2CO3 = (5.95 x 10^5\,mol) x (105.99\,g/mol) = 6.31 x 10^7\,g Step 3: Calculate the heat evolved

08

Calculate heat evolved

Since we know the enthalpy change for the reaction and the moles of nitric acid reacted, we can calculate the heat evolved: Q = \(\Delta H^\circ \) x Moles of HNO3 Q= (-1614\,kJ/mol) x 1.19 x 10^6\,mol = -1.92 x 10^9\,kJ a. Answer: The enthalpy change of the reaction is -1614\,kJ/mol. The mass of sodium carbonate required for complete neutralization is 6.31 x 10^7\,g, and the amount of heat evolved is -1.92 x 10^9\,kJ. b.

09

Determine major air pollution concern

The reaction releases a significant amount of heat, as indicated by the large negative value of \(\Delta H^\circ \) (-1614\,kJ/mol). This heat release can cause the temperature of the local environment to increase significantly, leading to thermal air pollution and potentially causing harm to local ecosystems and human health. b. Answer: The major air pollution concern was the significant release of heat, which could have led to thermal air pollution and negative effects on local ecosystems and human health.

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