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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 (∆H = -1698.5 kJ/mol) compared to the combustion with oxygen (CH4(g) + 2O2(g) -> CO2(g) + 2H2O(g)) with a ∆H value of -802.5 kJ/mol.

Step by step solution

01

Find ∆H 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 (∆H_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 ∆H for reaction 1

Now, let's plug in the known values and calculate ∆H 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 ∆H 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 (∆H_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 ∆H for reaction 2

Now, let's plug in the known values and calculate ∆H 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 ∆H values for both reactions

Now we have the ∆H values for both reactions: - Reaction 1: ∆H = -802.5 kJ/mol - Reaction 2: ∆H = -1698.5 kJ/mol As the ∆H 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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Most popular questions from this chapter

Without doing any calculations, predict the sign of \(\Delta H\) for each of the following reactions: $$\begin{array}{l}{\text { (a) } \mathrm{NaCl}(s) \longrightarrow \mathrm{Na}^{+}(g)+\mathrm{Cl}^{-}(\mathrm{g})} \\ {\text { (b) } 2 \mathrm{H}(g) \longrightarrow \mathrm{H}_{2}(g)} \\ {\text { (c) } \mathrm{Na}(g) \longrightarrow \mathrm{Na}^{+}(g)+\mathrm{e}^{-}} \\ {\text { (d) } \mathrm{I}_{2}(s) \longrightarrow \mathrm{I}_{2}(l)}\end{array}$$

A 1.800 -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 11.66 \(\mathrm{kJ} /^{\circ} \mathrm{C}\) The temperature of the calorimeter plus contents increased from 21.36 to \(26.37^{\circ} \mathrm{C}\) (a) Write a balanced chemical equation for the bomb calorimeter reaction. (b) What is the heat of combustion per gram of phenol? Per mole of phenol?

For the following processes, calculate the change in internal energy of the system and determine whether the process is endothermic or exothermic: (a) A balloon is cooled by removing 0.655 \(\mathrm{kJ}\) of heat. It shrinks on cooling, and the atmosphere does 382 J of work on the balloon. (b) A 100.0 -g bar of gold is heated from \(25^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\) during which it absorbs 322 \(\mathrm{J}\) of heat. Assume the volume of the gold bar remains constant.

The heat of combustion of fructose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) is \(-2812 \mathrm{kJ} / \mathrm{mol} .\) If a fresh golden delicious apple weighing 4.23 oz \((120 \mathrm{g})\) contains 16.0 \(\mathrm{g}\) of fructose, what caloric content does the fructose contribute to the apple?

(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?
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