6. Coal and natural gas are two very common fossil fuels used for electricity productionthrough combustion. Although the composition of both (especially coal) varies dramat-ically, we will treat them as pure graphite and methane, respectively.(a) Compute the heat of combustion of 1 kg 1 of coal and natural gas at 298 K usingthe following standard heats of formation at 298 K: AƒH°(H₂O, g) = -241.8 kJ mol¯¹,AfH (CO₂, g) = −393.5 kJ mol−¹, AƒHª(CH4, g) = −74.5 kJ mol−¹.(b) Compute AU of combustion by taking into account only the volumes of gases inthese reactions.(c) In practice combustion products are exhausted at temperatures higher than 298 K.Find the amount of heat produced by burning 1 kg of coal and natural gas at 298 K ifthe temperature of combustion products is 800 K (hint: combust at 298K, then heatup the products). You will need the following heat capacity expressions valid over thetemperature range:

Answered: 6. Coal and natural gas are two very…

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

Section: Chapter Questions

Problem 1.1P

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Question

6. Coal and natural gas are two very common fossil fuels used for electricity production
through combustion. Although the composition of both (especially coal) varies dramat-
ically, we will treat them as pure graphite and methane, respectively.
(a) Compute the heat of combustion of 1 kg 1 of coal and natural gas at 298 K using
the following standard heats of formation at 298 K: AƒH°(H₂O, g) = -241.8 kJ mol¯¹,
AfH (CO₂, g) = −393.5 kJ mol−¹, AƒHª(CH4, g) = −74.5 kJ mol−¹.
(b) Compute AU of combustion by taking into account only the volumes of gases in
these reactions.
(c) In practice combustion products are exhausted at temperatures higher than 298 K.
Find the amount of heat produced by burning 1 kg of coal and natural gas at 298 K if
the temperature of combustion products is 800 K (hint: combust at 298K, then heat
up the products). You will need the following heat capacity expressions valid over the
temperature range:

Expert Solution

Step 1: (a) Heat of combustion of graphite & methane

To compute the heat of combustion, we will write combustion reaction for coal and natural gas

$c o m b u s t i o n space r e a c t i o n space f o r space c o a l space left parenthesis g r a p h i t e right parenthesis C left parenthesis g r a p h i t e right parenthesis space plus space O ₂ left parenthesis g right parenthesis space rightwards arrow space C O ₂ left parenthesis g right parenthesis C o m b u s t i o n space r e a c t i o n space f o r space N a t u r a l space g a s space left parenthesis M e t h a n e right parenthesis C H ₄ left parenthesis g right parenthesis space plus space 2 O ₂ left parenthesis g right parenthesis space rightwards arrow space C O ₂ left parenthesis g right parenthesis space plus space 2 H ₂ O left parenthesis g right parenthesis$

As we know heat of formation of elements in their standard state is zero. Therefore heat of formation of C and O₂ is zero.

Thus, heat of combustion of coal is

$capital delta H to the power of o subscript c o m b u s t i o n end subscript space equals space capital sigma capital delta subscript f H to the power of 0 subscript left parenthesis p r o d u c t s right parenthesis end subscript space minus space capital sigma capital delta subscript f H to the power of o subscript left parenthesis r e a c tan t s right parenthesis end subscript increment subscript c H to the power of o subscript c o a l end subscript space equals increment subscript f H to the power of o subscript C O 2 end subscript minus space increment subscript f H to the power of o subscript C minus increment subscript f H to the power of o subscript O 2 end subscript increment subscript c H to the power of o subscript c o a l end subscript space equals negative 393.5 space minus space 0 space minus space 0 space equals space minus 393.5 space fraction numerator k J over denominator m o l end fraction$

Heat of combustion of natural gas is

$increment subscript c H to the power of o subscript N G end subscript equals space increment subscript f H to the power of o subscript C O 2 end subscript space plus space 2 asterisk times increment subscript f H to the power of o subscript H 2 O end subscript minus increment subscript f H to the power of o subscript C H 4 end subscript minus 2 asterisk times increment subscript f H to the power of o subscript O 2 end subscript increment subscript c H to the power of o subscript N G end subscript space equals space minus 393.5 space minus 2 space asterisk times space 241.8 space minus space left parenthesis negative 74.5 right parenthesis space minus space 2 asterisk times 0 increment subscript c H to the power of o subscript N G end subscript space equals space minus 802.6 space fraction numerator k J over denominator m o l end fraction$