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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

Write thermochemical equations for the formation of one mole of the following compounds from the elements in their stable states at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\). (a) acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}(g)\) (b) nitrogen dioxide \((g)\) (c) lead(II) bromide (s) (d) phosphorus pentachloride \((g)\)

A sample of sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\), is contaminated by sodium chloride. When the contaminated sample is burned in a bomb calorimeter, sodium chloride does not burn. What is the percentage of sucrose in the sample if a temperature increase of \(1.67^{\circ} \mathrm{C}\) is observed when \(3.000 \mathrm{~g}\) of the sample is burned in the calorimeter? Sucrose gives off \(5.64 \times 10^{3} \mathrm{~kJ} / \mathrm{mol}\) when burned. The heat capacity of the calorimeter is \(22.51 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}\).

How many mL of water at \(10^{\circ} \mathrm{C}\) ( 2 significant figures) must be added to \(75 \mathrm{~mL}\) of water at \(35^{\circ} \mathrm{C}\) to obtain a final temperature of \(19^{\circ} \mathrm{C} ?\) (Make the same assumptions as in Question 9.)

Strontium metal is responsible for the red color in fireworks. Fireworks manufacturers use strontium carbonate, which can be produced by combining strontium metal, graphite (C), and oxygen gas. The formation of one mole of \(\mathrm{SrCO}_{3}\) releases \(1.220 \times 10^{3} \mathrm{~kJ}\) of energy. (a) Write a balanced thermochemical equation for the reaction. (b) What is \(\Delta H\) when \(10.00 \mathrm{~L}\) of oxygen at \(25^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) is used by the reaction?

Mercury has a specific heat of \(0.140 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\). Assume that a thermometer has 20 (2 significant figures) grams of mercury. How much heat is absorbed by the mercury when the temperature in the thermometer increases from \(98.6^{\circ} \mathrm{F}\) to \(103.2^{\circ} \mathrm{F} ?\) (Assume no heat loss to the glass of the thermometer.)
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