General Chemistry
General Chemistry
4th Edition
ISBN: 9781891389603
Author: Donald A. McQuarrie, Peter A. Rock, Ethan B. Gallogly
Publisher: University Science Books
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Chapter 14, Problem 14.79P
Interpretation Introduction

Interpretation:

The value of standard enthalpy (ΔH°rxn) of combustion per gram of CH3CH2OH(l) and that of C8H18(l) has to be determined. Also, substance with more energy per gram has to be determined.

Concept Introduction:

Thermodynamics is a study of energy transfers that can be done by either heat or work. The energy transferred through work involves force. When work is positive then system gains energy while when work is negative then system loses energy. Since energy as heat is not state function thus it order to find change in energy produced or evolved, change in enthalpy of reaction ΔH°rxn as a state function has been introduced. The expression to calculate ΔH°rxn is as follows:

  ΔHrxn=HprodHreact

The useful property of ΔH°rxn is that it is an additive property.

Expert Solution & Answer
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Answer to Problem 14.79P

The value of standard enthalpy (ΔH°rxn) of combustion per gram for CH3CH2OH(l) and C8H18(l) are 29.67 kJ/g and 47.89 kJ/g respectively.

Explanation of Solution

The chemical equation for combustion reaction of CH3CH2OH(l) is as follows:

  CH3CH2OH(l)+3O2(g)2CO2(g)+3H2O(l)        (1)

The expression of ΔH°rxn for chemical equation (1) is as follows:

  ΔH°rxn=[(2)ΔH°f(CO2)+(3)ΔH°f(H2O)][(1)ΔH°f(CH3CH2OH)+(3)ΔH°f(O2)]        (2)

Substitute 393.5 kJ·mol–1 for ΔH°f(CO2), 285.8 kJ·mol–1 for ΔH°f(H2O), 277.6 kJ·mol–1 for ΔH°f(CH3CH2OH), and 0 kJ·mol–1 for ΔH°f(O2), and  in equation (2).

  ΔH°rxn=[(2)(393.5 kJ·mol–1)+(3)(285.8 kJ·mol–1)][(1)(277.6 kJ·mol–1)+(3)(0 kJ·mol–1)]=1366.8 kJ·mol–1

The expression to calculate standard enthalpy of combustion per gram of the fuels CH3CH2OH(l) is as follows:

  ΔH°rxn(kJ/g)=ΔH°rxn(kJ/mol)Molar mass(g/mol)        (3)

Substitute 1366.8 kJ·mol–1 for ΔH°rxn(kJ/mol) and 46.07 g/mol for molar mass in equation (3).

  ΔH°rxn(kJ/g)=1366.8 kJ·mol–146.07 g/mol=29.67 kJ/g

The chemical equation for combustion reaction of C8H18(g) is as follows:

  C8H18(g)+252O2(g)8CO2(g)+9H2O(l)        (4)

The expression of ΔH°rxn for chemical equation (4) is as follows:

  ΔH°rxn=[(8)ΔH°f(CO2)+(9)ΔH°f(H2O)][(1)ΔH°f(C8H18)+(252)ΔH°f(O2)]        (5)

Substitute 393.5 kJ·mol–1 for ΔH°f(CO2), 285.8 kJ·mol–1 for ΔH°f(H2O), 250.1 kJ·mol–1 for ΔH°f(C8H18), and 0 kJ·mol–1 for ΔH°f(O2) in equation (5).

  ΔH°rxn=[(8)(393.5 kJ·mol–1)+(9)(285.8 kJ·mol–1)][(1)(250.1 kJ·mol–1)+(252)(0 kJ·mol–1)]=5470.1 kJ·mol–1

The expression to calculate standard enthalpy of combustion for unitgram of the fuels C8H18(g) is as follows:

  ΔH°rxn(kJ/g)=ΔH°rxn(kJ/mol)Molar mass(g/mol)        (6)

Substitute 5470.1 kJ·mol–1 for ΔH°rxn(kJ/mol) and 114.23 g/mol for molar mass in equation (6).

  ΔH°rxn(kJ/g)=5470.1 kJ·mol–1114.23 g/mol=47.89 kJ/g

The substance which has more energy in unit gram of the fuel is octane.

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Chapter 14 Solutions

General Chemistry

Ch. 14 - Prob. 14.11PCh. 14 - Prob. 14.12PCh. 14 - Prob. 14.13PCh. 14 - Prob. 14.14PCh. 14 - Prob. 14.15PCh. 14 - Prob. 14.16PCh. 14 - Prob. 14.17PCh. 14 - Prob. 14.18PCh. 14 - Prob. 14.19PCh. 14 - Prob. 14.20PCh. 14 - Prob. 14.21PCh. 14 - Prob. 14.22PCh. 14 - Prob. 14.23PCh. 14 - Prob. 14.24PCh. 14 - Prob. 14.25PCh. 14 - Prob. 14.26PCh. 14 - Prob. 14.27PCh. 14 - Prob. 14.28PCh. 14 - Prob. 14.29PCh. 14 - Prob. 14.30PCh. 14 - Prob. 14.31PCh. 14 - Prob. 14.32PCh. 14 - Prob. 14.33PCh. 14 - Prob. 14.34PCh. 14 - Prob. 14.35PCh. 14 - Prob. 14.36PCh. 14 - Prob. 14.37PCh. 14 - Prob. 14.38PCh. 14 - Prob. 14.39PCh. 14 - Prob. 14.40PCh. 14 - Prob. 14.41PCh. 14 - Prob. 14.42PCh. 14 - Prob. 14.43PCh. 14 - Prob. 14.44PCh. 14 - Prob. 14.45PCh. 14 - Prob. 14.46PCh. 14 - Prob. 14.47PCh. 14 - Prob. 14.48PCh. 14 - Prob. 14.49PCh. 14 - Prob. 14.50PCh. 14 - Prob. 14.51PCh. 14 - Prob. 14.52PCh. 14 - Prob. 14.53PCh. 14 - Prob. 14.54PCh. 14 - Prob. 14.55PCh. 14 - Prob. 14.56PCh. 14 - Prob. 14.57PCh. 14 - Prob. 14.58PCh. 14 - Prob. 14.59PCh. 14 - Prob. 14.60PCh. 14 - Prob. 14.61PCh. 14 - Prob. 14.62PCh. 14 - Prob. 14.63PCh. 14 - Prob. 14.64PCh. 14 - Prob. 14.65PCh. 14 - Prob. 14.66PCh. 14 - Prob. 14.67PCh. 14 - Prob. 14.68PCh. 14 - Prob. 14.69PCh. 14 - Prob. 14.70PCh. 14 - Prob. 14.71PCh. 14 - Prob. 14.72PCh. 14 - Prob. 14.73PCh. 14 - Prob. 14.74PCh. 14 - Prob. 14.75PCh. 14 - Prob. 14.77PCh. 14 - Prob. 14.78PCh. 14 - Prob. 14.79PCh. 14 - Prob. 14.82PCh. 14 - Prob. 14.83PCh. 14 - Prob. 14.84PCh. 14 - Prob. 14.85PCh. 14 - Prob. 14.86PCh. 14 - Prob. 14.87PCh. 14 - Prob. 14.88PCh. 14 - Prob. 14.89PCh. 14 - Prob. 14.90PCh. 14 - Prob. 14.92PCh. 14 - Prob. 14.94PCh. 14 - Prob. 14.95PCh. 14 - Prob. 14.96P
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