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Chapter 5: Problem 96

It is interesting to compare the "fuel value" of a hydro- carbon in a hypothetical world where oxygen is not the combustion agent. The enthalpy of formation of \(\mathrm{CF}_{4}(g)\) is \(-679.9 \mathrm{kJ} / \mathrm{mol} .\) Which of the following two reactions is the more exothermic? $$\begin{array}{l}{\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)} \\ {\mathrm{CH}_{4}(g)+4 \mathrm{F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)}\end{array}$$

Short Answer

Expert verified
The combustion of methane with fluorine (CH4(g) + 4F2(g) -> CF4(g) + 4HF(g)) is more exothermic than the combustion with oxygen, as it has a more negative change in enthalpy (鈭咹 = -1698.5 kJ/mol) compared to the combustion with oxygen (CH4(g) + 2O2(g) -> CO2(g) + 2H2O(g)) with a 鈭咹 value of -802.5 kJ/mol.

Step by step solution

01

Find 鈭咹 for reaction 1

For this step, we will need the standard enthalpies of formation for each of the products and reactants in reaction 1. The following values are needed: - Methane (CH4): -74.6 kJ/mol - Oxygen (O2): 0 kJ/mol (by definition, since it's a diatomic element) - Carbon dioxide (CO2): -393.5 kJ/mol - Water (H2O, gas): -241.8 kJ/mol The change in enthalpy for the reaction (鈭咹_reaction1) can be calculated as follows: \[\Delta H_{\text{reaction1}} = \sum H_{\text{products}} - \sum H_{\text{reactants}} \] \[\Delta H_{\text{reaction1}} = [1 (-393.5) + 2 (-241.8)] - [1 (-74.6) + 2 (0)]\]
02

Calculate 鈭咹 for reaction 1

Now, let's plug in the known values and calculate 鈭咹 for reaction 1: \[\Delta H_{\text{reaction1}} = [-393.5 - 2(241.8)] - (-74.6)\] \[\Delta H_{\text{reaction1}} = [-393.5 - 483.6 + 74.6 ]\] \[\Delta H_{\text{reaction1}} = -802.5 \, \text{kJ/mol}\]
03

Find 鈭咹 for reaction 2

For this step, we will need the standard enthalpies of formation for each of the products and reactants in reaction 2. The following values are needed: - Methane (CH4): -74.6 kJ/mol - Carbon tetrafluoride (CF4): -679.9 kJ/mol - Hydrogen fluoride (HF): -273.3 kJ/mol - Fluorine (F2): 0 kJ/mol (by definition, since it's a diatomic element) The change in enthalpy for the reaction (鈭咹_reaction2) can be calculated as follows: \[\Delta H_{\text{reaction2}} = \sum H_{\text{products}} - \sum H_{\text{reactants}} \] \[\Delta H_{\text{reaction2}} = [1 (-679.9) + 4 (-273.3)] - [1 (-74.6) + 4 (0)]\]
04

Calculate 鈭咹 for reaction 2

Now, let's plug in the known values and calculate 鈭咹 for reaction 2: \[\Delta H_{\text{reaction2}} = [-679.9 - 4(273.3)] - (-74.6)\] \[\Delta H_{\text{reaction2}} = [-679.9 - 1093.2 + 74.6]\] \[\Delta H_{\text{reaction2}} = -1698.5 \, \text{kJ/mol}\]
05

Compare 鈭咹 values for both reactions

Now we have the 鈭咹 values for both reactions: - Reaction 1: 鈭咹 = -802.5 kJ/mol - Reaction 2: 鈭咹 = -1698.5 kJ/mol As the 鈭咹 value for reaction 2 is more negative than that for reaction 1, reaction 2 is more exothermic. So, the combustion of methane with fluorine is more exothermic than combustion with oxygen.

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Key Concepts

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

Exothermic Reaction
Exothermic reactions are chemical processes where energy is released to the surroundings, usually in the form of heat. In these reactions, the enthalpy change (\( \Delta H \) is negative, indicating that the products possess less energy than the reactants. This release of energy is what typically makes exothermic reactions feel hot.
Exothermic reactions are prevalent in various everyday phenomena:
  • Combustion reactions, like burning wood or gasoline, release heat, keeping homes warm or engines running.
  • Chemical hand warmers use exothermic reactions to provide warmth in cold environments.
In the exercise, two reactions were compared for their exothermicity. Reaction 2, involving methane and fluorine, was more exothermic owing to its larger negative \( \Delta H \) value, demonstrating a larger energy release to the surroundings.
Standard Enthalpy of Formation
The standard enthalpy of formation is a key concept in calculating the enthalpy changes of reactions. It refers to the change in enthalpy when one mole of a compound is formed from its elements under standard conditions (usually 1 atm pressure and 25掳C).
For any element in its standard state (like \( O_2 \) gas or \( F_2 \) gas), the standard enthalpy of formation is zero. This serves as a baseline for calculating the energy released or absorbed during chemical reactions.
In the problem, this data was used to calculate the total enthalpy change in both reactions. By utilizing standard enthalpies of formation for each compound, it is possible to determine which reaction releases more energy and is more exothermic.
Combustion
Combustion is a class of exothermic reactions where a substance reacts with an oxidant, often releasing energy as heat and light. It's a crucial reaction in both daily life and industrial applications.
Conventionally, combustion involves hydrocarbon fuels like methane (\( CH_4 \)), with oxygen as the oxidant, producing carbon dioxide and water. This process powers engines, heats buildings, and facilitates cooking.
In the given exercise, a comparison is made between the traditional combustion of methane with oxygen and an atypical combustion using fluorine. While both are exothermic, the use of fluorine resulted in a greater release of energy, reflecting in a more negative \( \Delta H \).
The differing heat outputs in such reactions can be utilized to optimize energy efficiency in various applications, from creative industrial uses to novel technological designs.

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Most popular questions from this chapter

A sodium ion, \(\mathrm{Na}^{+},\) with a charge of \(1.6 \times 10^{-19} \mathrm{Cand}\) a chloride ion, \(\mathrm{Cl}^{-},\) with charge of \(-1.6 \times 10^{-19} \mathrm{C}\) , are separated by a distance of 0.50 \(\mathrm{nm}\) . How much work would be required to increase the separation of the two ions to an infinite distance?

(a) Which releases the most energy when metabolized, 1 \(\mathrm{g}\) of carbohydrates or 1 \(\mathrm{g}\) of fat? (b) A particular chip snack food is composed of 12\(\%\) protein, 14\(\%\) fat, and the rest carbohydrate. What percentage of the calorie content of this food is fat? (c) How many grams of protein provide the same fuel value as 25 of fat?

A coffee-cup calorimeter of the type shown in Figure 5.18 contains 150.0 g of water at \(25.1^{\circ} \mathrm{C} .\) A \(121.0-\mathrm{g}\) block of copper metal is heated to \(100.4^{\circ} \mathrm{C}\) by putting it in a beaker of boiling water. The specific heat of \(\mathrm{Cu}(s)\) is \(0.385 \mathrm{J} / \mathrm{g}-\mathrm{K}\) . The Cu is added to the calorimeter, and after a time the contents of the cup reach a constant temperature of \(30.1^{\circ} \mathrm{C}\) (a) Determine the amount of heat, in J, lost by the copper block. (b) Determine the amount of heat gained by the water. The specific heat of water is \(4.18 \mathrm{J} / \mathrm{g}-\mathrm{K}\) . (c) The difference between your answers for (a) and (b) is due to heat loss through the Styrofoam cups and the heat necessary to raise the temperature of the inner wall of the apparatus. The heat capacity of the calorimeter is the amount of heat necessary to raise the temperature of the apparatus (the cups and the stopper) by 1 K. Calculate the heat capacity of the calorimeter in J/K. (d)What would be the final temperature of the system if all the heat lost by the copper block were absorbed by the water in the calorimeter?

Burning methane in oxygen can produce three different carbon-containing products: soot (very fine particles of graphite), CO(g), and \(\mathrm{CO}_{2}(g) .\) (a) Write three balanced equations for the reaction of methane gas with oxygen to produce these three products. In each case assume that \(\mathrm{H}_{2} \mathrm{O}(l)\) is the only other product. (b) Determine the standard enthalpies for the reactions in part (a).(c) Why, when the oxygen supply is adequate, is \(\mathrm{CO}_{2}(g)\) the predominant carbon-containing product of the combustion of methane?

Ammonia \(\left(\mathrm{NH}_{3}\right)\) boils at \(-33^{\circ} \mathrm{C} ;\) at this temperature it has a density of 0.81 \(\mathrm{g} / \mathrm{cm}^{3} .\) The enthalpy of formation of \(\mathrm{NH}_{3}(g)\) is \(-46.2 \mathrm{kJ} / \mathrm{mol},\) and the enthalpy of vaporization of \(\mathrm{NH}_{3}(l)\) is 23.2 \(\mathrm{kJ} / \mathrm{mol} .\) Calculate the enthalpy change when 1 \(\mathrm{L}\) of liquid \(\mathrm{NH}_{3}\) is burned in air to give \(\mathrm{N}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g) .\) How does this compare with \(\Delta H\) for the complete combustion of 1 Lof liquid methanol, \(\mathrm{CH}_{3} \mathrm{OH}(l) ?\) For \(\mathrm{CH}_{3} \mathrm{OH}(l),\) the density at \(25^{\circ} \mathrm{C}\) is \(0.792 \mathrm{g} / \mathrm{cm}^{3},\) and \(\Delta \mathrm{H}_{f}^{\circ}=-239 \mathrm{kJ} / \mathrm{mol}\)
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