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Upon complete combustion, the indicated substances evolve the given quantities of heat. Write a balanced equation for the combustion of \(1.00 \mathrm{mol}\) of each substance, including the enthalpy change, \(\Delta H\), for the reaction.Upon complete combustion, the indicated substances evolve the given quantities of heat. Write a balanced equation for the combustion of \(1.00 \mathrm{mol}\) of each substance, including the enthalpy change, \(\Delta H\), for the reaction. (a) \(0.584 \mathrm{g}\) of propane, \(\mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{g}),\) yields \(29.4 \mathrm{kJ}\) (b) \(0.136 \mathrm{g}\) of camphor, \(\mathrm{C}_{10} \mathrm{H}_{16} \mathrm{O}(\mathrm{s}),\) yields \(5.27 \mathrm{kJ}\) (c) \(2.35 \mathrm{mL}\) of acetone, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO}(\mathrm{l})(d=0.791\) \(\mathrm{g} / \mathrm{mL}),\) yields \(58.3 \mathrm{kJ}\)

Short Answer

Expert verified
\[ \mathrm{C}_{3} \mathrm{H}_{8}(g) + 5O_{2}(g) \rightarrow 3CO_{2}(g) + 4H_{2}O(l), \Delta H = -29.4 \mathrm{kJ}\] \[ \mathrm{C}_{10} \mathrm{H}_{16} \mathrm{O}(s) + 15O_{2}(g) \rightarrow 10CO_{2}(g) + 8H_{2}O(l) , \Delta H = -5.27 \mathrm{kJ}\] \[ \left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO}(l) + 4O_{2}(g) \rightarrow 3CO_{2}(g) + 3H_{2}O(l) , \Delta H = -58.3 \mathrm{kJ}\]

Step by step solution

01

Combustion of propane

Balance the following equation: \(\mathrm{C}_{3} \mathrm{H}_{8}(g) + 5O_{2}(g) \rightarrow 3CO_{2}(g) + 4H_{2}O(l)\) and append the enthalpy change: \(\mathrm{C}_{3} \mathrm{H}_{8}(g) + 5O_{2}(g) \rightarrow 3CO_{2}(g) + 4H_{2}O(l) \quad \Delta H = -29.4 \mathrm{kJ}\)
02

Combustion of camphor

Balance the equation: \(\mathrm{C}_{10} \mathrm{H}_{16} \mathrm{O}(s) + 15O_{2}(g) \rightarrow 10CO_{2}(g) + 8H_{2}O(l)\) and append the enthalpy change: \(\mathrm{C}_{10} \mathrm{H}_{16} \mathrm{O}(s) + 15O_{2}(g) \rightarrow 10CO_{2}(g) + 8H_{2}O(l) \quad \Delta H = -5.27 \mathrm{kJ}\)
03

Combustion of acetone

Balance the equation: \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO}(l) + 4O_{2}(g) \rightarrow 3CO_{2}(g) + 3H_{2}O(l)\) and append the enthalpy change: \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO}(l) + 4O_{2}(g) \rightarrow 3CO_{2}(g) + 3H_{2}O(l) \quad \Delta H = -58.3 \mathrm{kJ}\)

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Key Concepts

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

Enthalpy Change
In chemical reactions, the enthalpy change (\( \Delta H \)) plays a crucial role in understanding the energy dynamics involved. Enthalpy is a measure of total energy within a system and is observed during reactions when a change occurs. If the system releases heat, the reaction is exothermic, and \( \Delta H \) is negative. Conversely, if the system absorbs heat, the reaction is endothermic, and \( \Delta H \) is positive.
This concept is essential in combustion reactions, where substances react with oxygen, producing energy—usually in the form of heat—and other byproducts like carbon dioxide and water. When analyzing reactions like those of propane, camphor, or acetone, the measure of \( \Delta H \) provides insight into the energy transfer within the system.
The listed enthalpy changes for each are negative, indicating that these combustion reactions release heat. Understanding this not only tells us about the energy produced but also helps in comparing the efficiency of different fuels.
Balanced Chemical Equations
A balanced chemical equation is a fundamental aspect of chemistry that ensures mass conservation in reactions. This means the number of atoms for each element on the reactant side should equal the number on the product side.
The combustion equations for substances like propane (\( \mathrm{C}_3\mathrm{H}_8 \)), camphor (\( \mathrm{C}_{10}\mathrm{H}_{16}\mathrm{O} \)), or acetone (\( \left(\mathrm{CH}_3\right)_2 \mathrm{CO} \)) all demonstrate this principle.
  • Propane combustion: \( \mathrm{C}_3\mathrm{H}_8 + 5\mathrm{O}_2 \rightarrow 3\mathrm{CO}_2 + 4\mathrm{H}_2\mathrm{O} \)
  • Camphor combustion: \( \mathrm{C}_{10}\mathrm{H}_{16}\mathrm{O} + 15\mathrm{O}_2 \rightarrow 10\mathrm{CO}_2 + 8\mathrm{H}_2\mathrm{O} \)
  • Acetone combustion: \( \left(\mathrm{CH}_3\right)_2 \mathrm{CO} + 4\mathrm{O}_2 \rightarrow 3\mathrm{CO}_2 + 3\mathrm{H}_2\mathrm{O} \)

Balancing involves proper counting and adjustment of the coefficients (numbers placed before formulas) to maintain equal quantities of elements. This not only respects the laws of chemistry but also provides a foundation for calculating other important measures, such as the enthalpy change.
Thermochemistry
Thermochemistry is a branch of chemistry that focuses on the energy and heat associated with chemical reactions. Understanding thermochemical principles is pivotal when examining the energy changes in reactions like combustion.
  • In combustion reactions, a fuel reacts with oxygen to produce energy, often in the form of heat and light. This is where thermochemistry overlaps with real-world applications, such as energy production and fuel efficiency.
  • Using concepts like enthalpy (\( \Delta H \)), thermochemistry enables us to quantify the energy released or absorbed during reactions.

Thermochemistry is invaluable in everyday life, influencing how we choose fuels, predict the outcomes of mixing substances, and design energy solutions for industries. It helps predict product stability and understand reactions at both theoretical and practical levels. By examining exercises that involve combustion and enthalpy changes, learners can gain insights into these practical applications and the broader impact of chemical reactions on energy use and efficiency.

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Most popular questions from this chapter

A 1.22 kg piece of iron at \(126.5^{\circ} \mathrm{C}\) is dropped into \(981 \mathrm{g}\) water at \(22.1^{\circ} \mathrm{C} .\) The temperature rises to \(34.4^{\circ} \mathrm{C} .\) What will be the final temperature if this same piece of iron at \(99.8^{\circ} \mathrm{C}\) is dropped into \(325 \mathrm{mL}\) of glycerol, \(\mathrm{HOCH}_{2} \mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{2} \mathrm{OH}(1)\) at \(26.2^{\circ} \mathrm{C} ?\) For glycerol, \(d=1.26 \mathrm{g} / \mathrm{mL} ; C_{n}=219 \mathrm{JK}^{-1} \mathrm{mol}^{-1}\).

Look up the specific heat of several elements, and plot the products of the specific heats and atomic masses as a function of the atomic masses. Based on the plot, develop a hypothesis to explain the data. How could you test your hypothesis?

A \(1.00 \mathrm{g}\) sample of \(\mathrm{Ne}(\mathrm{g})\) at 1 atm pressure and \(27^{\circ} \mathrm{C}\) is allowed to expand into an evacuated vessel of \(2.50 \mathrm{L}\) volume. Does the gas do work? Explain.

Calculate the quantity of work associated with a \(3.5 \mathrm{L}\) expansion of a gas \((\Delta V)\) against a pressure of \(748 \space\mathrm{mmHg}\) in the units (a) atm \(\mathrm{L} ;\) (b) joules (J); (c) calories (cal).

How much heat, in kilojoules, is evolved in the complete combustion of (a) \(1.325 \mathrm{g} \mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g})\) at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{atm} ;\) (b) \(28.4 \mathrm{L} \mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g})\) at \(\mathrm{STP} ;(\mathrm{c})\) \(12.6 \mathrm{LC}_{4} \mathrm{H}_{10}(\mathrm{g})\) at \(23.6^{\circ} \mathrm{C}\) and \(738 \mathrm{mmHg} ?\) Assume that the enthalpy change for the reaction does not change significantly with temperature or pressure. The complete combustion of butane, \(\mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g}),\) is represented by the equation $$\begin{array}{r} \mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g})+\frac{13}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 4 \mathrm{CO}_{2}(\mathrm{g})+5 \mathrm{H}_{2} \mathrm{O}(1) \\ \Delta H^{\circ}=-2877 \mathrm{kJ} \end{array}$$

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