Solved: Nitroglycerin, one of the most commonly used

Chapter 9, Problem 138P

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Nitroglycerin, one of the most commonly used explosives, has the following structure

                   \(\mathrm{CH}_{2} \mathrm{ONO}_{2}\)

                    │

                    \(\mathrm{CHONO}_{2}\)

                    │

                    \(\mathrm{CH}_{2} \mathrm{ONO}_{2}\)

The decomposition reaction is

\(4\mathrm{C}_3\mathrm{H}_5\mathrm{N}_3\mathrm{O}_9(l)\longrightarrow12\mathrm{CO}_2(g)+10\mathrm{H}_2\mathrm{O}(g)+6\mathrm{N}_2(g)+\mathrm{O}_2(g)\)

The explosive action is the result of the heat released and the large increase in gaseous volume. (a) Calculate the \(\Delta H^{\circ}\) for the decomposition of one mole of nitroglycerin using both standard enthalpy of formation values and bond enthalpies. Assume that the two \(\mathrm {O}\) atoms in the \(\mathrm {NO}_2\) groups are attached to \(\mathrm {N}\) with one single bond and one double bond. (b) Calculate the combined volume of the gases at \(\mathrm {STP}\). (c) Assuming an initial explosion temperature of 3000 K, estimate the pressure exerted by the gases using the result from (b). (The standard enthalpy of formation of nitroglycerin is -371.1 kJ/mol.)