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Chapter 5: Problem 39

The complete combustion of methane, \(\mathrm{CH}_{4}(g)\), to form \(\mathrm{H}_{2} \mathrm{O}(l)\) and \(\mathrm{CO}_{2}(g)\) at constant pressure releases \(890 \mathrm{~kJ}\) of heat per mole of \(\mathrm{CH}_{4}\). (a) Write a balanced thermochemical equation for this reaction. (b) Draw an enthalpy diagram for the reaction.

Short Answer

Expert verified
(a) The balanced thermochemical equation for the complete combustion of methane is: \( \mathrm{CH}_{4}(g) + 2\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) + 2\mathrm{H}_{2}\mathrm{O}(l) \hspace{10mm} \Delta H = -890 \mathrm{~kJ} \). (b) To draw the enthalpy diagram, follow these steps: 1. Label the y-axis as "Enthalpy, H". 2. Draw a horizontal line representing the reactants, and label it "Reactants: \(\mathrm{CH}_4(g) + 2\mathrm{O}_2(g)\)". 3. Draw a lower horizontal line representing the products, and label it "Products: \(\mathrm{CO}_2(g) + 2\mathrm{H}_2\mathrm{O}(l)\)". 4. Connect the reactants and products lines with an arrow pointing downwards to illustrate that heat is released during the reaction. 5. Label the arrow with the heat released: "\(\Delta H = -890 \mathrm{~kJ}\)".

Step by step solution

01

(a) Balanced Thermochemical Equation

The complete combustion of methane involves the reaction of methane with oxygen to produce carbon dioxide and water. We start by writing the unbalanced equation: \( \mathrm{CH}_{4}(g) + \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) + \mathrm{H}_{2}\mathrm{O}(l) \) In order to balance the equation, we need to make sure that the number of atoms of each element on the reactant and product sides matches. We have 1 carbon atom, 4 hydrogen atoms, and 2 oxygen atoms on the reactant side, and 1 carbon atom, 2 hydrogen atoms, and 3 oxygen atoms on the product side. To balance the equation, we will perform the following steps: 1. Balance the hydrogen atoms by placing a coefficient of 2 in front of \(\mathrm{H}_{2}\mathrm{O}(l)\): \( \mathrm{CH}_{4}(g) + \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) + 2\mathrm{H}_{2}\mathrm{O}(l) \) 2. Balance the oxygen atoms by placing a coefficient of 2 in front of \(\mathrm{O}_{2}(g)\): \( \mathrm{CH}_{4}(g) + 2\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) + 2\mathrm{H}_{2}\mathrm{O}(l) \) Now that the chemical equation is balanced, we can include the enthalpy change information: \( \mathrm{CH}_{4}(g) + 2\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) + 2\mathrm{H}_{2}\mathrm{O}(l) \hspace{10mm} \Delta H = -890 \mathrm{~kJ} \)
02

(b) Enthalpy Diagram

To draw the enthalpy diagram, we will represent the reactants and products with horizontal lines, where the heights of the lines represent their respective enthalpy levels. The difference between the heights of the reactants and products lines reflects the amount of heat released during the reaction. 1. Label the y-axis as "Enthalpy, H". 2. Draw a horizontal line representing the reactants, and label it "Reactants: \(\mathrm{CH}_4(g) + 2\mathrm{O}_2(g)\)". 3. Draw a lower horizontal line representing the products, and label it "Products: \(\mathrm{CO}_2(g) + 2\mathrm{H}_2\mathrm{O}(l)\)". 4. Connect the reactants and products lines with an arrow pointing downwards to illustrate that heat is released during the reaction. 5. Label the arrow with the heat released: "\(\Delta H = -890 \mathrm{~kJ}\)". The enthalpy diagram should look like: [![Enthalpy Diagram][1]][1] [1]: https://i.stack.imgur.com/k5SRk.png

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Key Concepts

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

Combustion Reaction
A combustion reaction is a type of chemical reaction where a substance combines with oxygen to produce heat and usually light. The combustion of methane (\( \mathrm{CH}_4(g) \)) is a classic example of this process. Here, methane burns in oxygen \( \mathrm{O}_2(g) \) to form carbon dioxide \( \mathrm{CO}_2(g) \) and water \( \mathrm{H}_2O(l) \).
In combustion, the substance that burns is called the fuel. The products of complete combustion of hydrocarbons like methane are carbon dioxide and water. Incomplete combustion might produce carbon monoxide or carbon (soot) when there isn't enough oxygen.
Understanding this concept helps in multiple applications, from energy production to transportation. For thermochemical calculations, the key feature is the heat released, which can be measured as part of the energy output of the reaction.
Enthalpy Change
Enthalpy change, denoted by \( \Delta H \), represents the heat absorbed or released during a chemical reaction at constant pressure. In thermochemistry, it is crucial to know whether a reaction releases or absorbs heat.
For the complete combustion of methane, the reaction is exothermic, meaning it releases heat. The enthalpy change is negative: \( \Delta H = -890 \, \mathrm{kJ/mol} \). This indicates the reaction releases 890 kJ of energy per mole of methane combusted, showcasing its energy output.

Enthalpy change is essential for understanding energy management in chemical processes. For instance, power plants rely on burning fuels like methane, and knowing the \( \Delta H \) helps calculate efficiency and optimize energy production.
Balanced Chemical Equation
A balanced chemical equation provides a clear representation of the chemical reaction, ensuring that the number of atoms for each element are equal on both sides of the equation. This follows the law of conservation of mass where matter is neither created nor destroyed.

To balance the combustion reaction of methane:
  • Write the initial equation: \( \mathrm{CH}_4(g) + \mathrm{O}_2(g) \longrightarrow \mathrm{CO}_2(g) + \mathrm{H}_2O(l) \).
  • Balance the hydrogen atoms by adding a coefficient of 2 before \( \mathrm{H}_2O \), matching the 4 hydrogen atoms from methane: \( \mathrm{CH}_4(g) + \mathrm{O}_2(g) \longrightarrow \mathrm{CO}_2(g) + 2\mathrm{H}_2O(l) \).
  • Balance the oxygen by placing a coefficient of 2 in front of \( \mathrm{O}_2 \), aligning with the total 4 oxygen atoms needed for carbon dioxide and water: \( \mathrm{CH}_4(g) + 2\mathrm{O}_2(g) \longrightarrow \mathrm{CO}_2(g) + 2\mathrm{H}_2O(l) \).
Including the enthalpy change in the balanced equation helps provide a complete picture of the reaction:\( \Delta H = -890 \, \mathrm{kJ/mol} \) reflects the energy dynamics involved.

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Most popular questions from this chapter

Calculate \(\Delta E\) and determine whether the process is endothermic or exothermic for the following cases: \((\mathbf{a}) q=0.763 \mathrm{~kJ}\) and \(w=-840 \mathrm{~J}\). (b) A system releases \(66.1 \mathrm{~kJ}\) of heat to its surroundings while the surroundings do \(44.0 \mathrm{~kJ}\) of work on the system.

(a) Under what condition will the enthalpy change of a process equal the amount of heat transferred into or out of the system? (b) During a constant-pressure process, the system releases heat to the surroundings. Does the enthalpy of the system increase or decrease during the process? (c) In a constant-pressure process, \(\Delta H=0\). What can you conclude about \(\Delta E, q,\) and \(w ?\)

(a) What is the electrostatic potential energy (in joules) between two electrons that are separated by \(460 \mathrm{pm} ?\) (b) What is the change in potential energy if the distance separating the two electrons is increased to \(1.0 \mathrm{nm}\) ? (c) Does the potential energy of the two particles increase or decrease when the distance is increased to \(1.0 \mathrm{nm}\) ?

Consider two solutions, the first being \(50.0 \mathrm{~mL}\) of \(1.00 \mathrm{M} \mathrm{CuSO}_{4}\) and the second \(50.0 \mathrm{~mL}\) of \(2.00 \mathrm{M} \mathrm{KOH} .\) When the two solutions are mixed in a constant-pressure calorimeter, a precipitate forms and the temperature of the mixture rises from 21.5 to \(27.7^{\circ} \mathrm{C} .(\mathbf{a})\) Before mixing, how many grams of Cu are present in the solution of \(\mathrm{CuSO}_{4}\) ? (b) Predict the identity of the precipitate in the reaction. (c) Write complete and net ionic equations for the reaction that occurs when the two solutions are mixed. \((\mathbf{d})\) From the calorimetric data, calculate \(\Delta H\) for the reaction that occurs on mixing. Assume that the calorimeter absorbs only a negligible quantity of heat, that the total volume of the solution is \(100.0 \mathrm{~mL},\) and that the specific heat and density of the solution after mixing are the same as those of pure water.

A 2.20-g sample of phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\) was burned in a bomb calorimeter whose total heat capacity is \(11.90 \mathrm{~kJ} /{ }^{\circ} \mathrm{C} .\) The temperature of the calorimeter plus contents increased from 21.50 to \(27.50^{\circ} \mathrm{C} .(\mathbf{a})\) Write a balanced chemical equation for the bomb calorimeter reaction. (b) What is the heat of combustion per gram of phenol and per mole of phenol?
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