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Chapter 8: Problem 50

Nitroglycerine, \(\mathrm{C}_{3} \mathrm{H}_{5}\left(\mathrm{NO}_{3}\right)_{3}(l)\), is a powerful explosive used in rock blasting when roads are created. When ignited, it produces water, nitrogen, carbon dioxide, and oxygen. Detonation of one mole of nitroglycerine liberates \(5725 \mathrm{~kJ}\) of heat. (a) Write a balanced thermochemical equation for the reaction for the detonation of four moles of nitroglycerine. (b) What is \(\Delta H_{\mathrm{f}}^{\circ}\) for \(\mathrm{C}_{3} \mathrm{H}_{5}\left(\mathrm{NO}_{3}\right)_{3}(l) ?\)

Short Answer

Expert verified
a) The balanced thermochemical equation for the detonation of nitroglycerin is: $$4\,\text{C}_{3}\text{H}_{5}\text{N}_{3}\text{O}_{9}(l) \rightarrow 6\,\text{CO}_{2}(g) + 10\,\text{H}_{2}\text{O}(l) + \frac{1}{2}\,\text{O}_{2}(g) + 6\,\text{N}_{2}(g) \hspace{.5cm} \Delta H=-22900\,\text{kJ}$$ b) The standard enthalpy of formation (\(\Delta H_{\mathrm{f}}^{\circ}\)) for nitroglycerine is \(-5725\,\text{kJ/mol}\).

Step by step solution

01

Writing the Unbalanced Equation

First, let's write the unbalanced equation for the reaction of nitroglycerine: $$\text{C}_{3}\text{H}_{5}\text{N}_{3}\text{O}_{9}(l) \rightarrow \text{CO}_{2}(g) + \text{H}_{2}\text{O}(l) + \text{O}_{2}(g) + \text{N}_{2}(g)$$
02

Balancing the Equation

Now let's balance the equation. The balanced chemical equation is: $$4\,\text{C}_{3}\text{H}_{5}\text{N}_{3}\text{O}_{9}(l) \rightarrow 6\,\text{CO}_{2}(g) + 10\,\text{H}_{2}\text{O}(l) + \frac{1}{2}\,\text{O}_{2}(g) + 6\,\text{N}_{2}(g)$$ Here we have balanced the number of carbon, hydrogen, nitrogen, and oxygen atoms on both sides of the equation.
03

from a) Balanced Thermochemical Equation for the Detonation with 4 moles of nitroglycerine

Now, as we're asked to write a balanced thermochemical equation for the reaction, let's include the heat liberated for the 4 moles of nitroglycerine detonation. $$4\,\text{C}_{3}\text{H}_{5}\text{N}_{3}\text{O}_{9}(l) \rightarrow 6\,\text{CO}_{2}(g) + 10\,\text{H}_{2}\text{O}(l) + \frac{1}{2}\,\text{O}_{2}(g) + 6\,\text{N}_{2}(g) \hspace{.5cm} \Delta H=-4\cdot5725\,\text{kJ}$$ So that the answer for part (a) will be: $$4\,\text{C}_{3}\text{H}_{5}\text{N}_{3}\text{O}_{9}(l) \rightarrow 6\,\text{CO}_{2}(g) + 10\,\text{H}_{2}\text{O}(l) + \frac{1}{2}\,\text{O}_{2}(g) + 6\,\text{N}_{2}(g) \hspace{.5cm} \Delta H=-22900\,\text{kJ}$$
04

Calculating the \(\Delta H_{\mathrm{f}}^{\circ}\) for nitroglycerine

Now let's calculate \(\Delta H_{\mathrm{f}}^{\circ}\) for 1 mole of nitroglycerine, given the released heat for 4 moles of nitroglycerin detonation as \(-22900\,\text{kJ}\). $$\Delta H_{\mathrm{f}}^{\circ} (\text{C}_{3}\text{H}_{5}\text{N}_{3}\text{O}_{9}) = \frac{-22900\,\text{kJ}}{4\,\text{moles}} = -5725\,\text{kJ/mol}$$ The answer for part (b) is \(\Delta H_{\mathrm{f}}^{\circ}(\text{C}_{3}\text{H}_{5}\text{N}_{3}\text{O}_{9})=-5725\,\text{kJ/mol}\).

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Most popular questions from this chapter

Copper is used in building the integrated circuits, chips, and printed circuit boards for computers. When \(228 \mathrm{~J}\) of heat are absorbed by \(125 \mathrm{~g}\) of copper at \(22.38^{\circ} \mathrm{C}\), the temperature increases to \(27.12^{\circ} \mathrm{C}\). What is the specific heat of copper?

Nitroglycerine, \(\mathrm{C}_{3} \mathrm{H}_{5}\left(\mathrm{NO}_{3}\right)_{3}(l)\), is an explosive most often used in mine or quarry blasting. It is a powerful explosive because four gases \(\left(\mathrm{N}_{2}\right)\) \(\mathrm{O}_{2}, \mathrm{CO}_{2}\), and steam) are formed when nitroglycerine is detonated. In addition, \(6.26 \mathrm{~kJ}\) of heat is given off per gram of nitroglycerine detonated. (a) Write a balanced thermochemical equation for the reaction. (b) What is \(\Delta H\) when \(4.65\) mol of products is formed?

Glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s),\left(\Delta H_{\mathrm{f}}^{\circ}=-1275.2 \mathrm{~kJ} / \mathrm{mol}\right)\) is converted to ethyl alcohol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\), and carbon dioxide in the fermentation of grape juice. What quantity of heat is liberated when \(750.0 \mathrm{~mL}\) of wine containing \(12.0 \%\) ethyl alcohol by volume \(\left(d=0.789 \mathrm{~g} / \mathrm{cm}^{3}\right)\) is produced by the fermentation of grape juice?

When ammonia reacts with dinitrogen oxide gas ( \(\Delta H_{\mathrm{f}}^{\circ}=82.05 \mathrm{~kJ} / \mathrm{mol}\) ), liquid water and nitrogen gas are formed. How much heat is liberated or absorbed by the reaction that produces \(345 \mathrm{~mL}\) of nitrogen gas at \(25^{\circ} \mathrm{C}\) and \(717 \mathrm{~mm} \mathrm{Hg}\) ?

Natural gas companies in the United States use the "therm" as a unit of energy. One therm is \(1 \times 10^{5} \mathrm{BTU}\). (a) How many joules are in one therm? \(\left(1 \mathrm{~J}=9.48 \times 10^{-4} \mathrm{BTU}\right)\) (b) When propane gas, \(\mathrm{C}_{3} \mathrm{H}_{8}\), is burned in oxygen, \(\mathrm{CO}_{2}\) and steam are produced. How many therms of energy are given off by \(1.00 \mathrm{~mol}\) of propane gas?
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