To determine The partial pressure of the carbon dioxide. Explanation Write the stoichiometric equation for methane dissociation process. CH 4 ⇌ C + 2 H 2 (I) Write the natural logarithmic value for methane dissociation process. ln K P = − 9.685 K P = e − 9.685 Write the stoichiometric equation for carbon dioxide dissociation process. C + O 2 ⇌ CO 2 (II) Write the natural logarithmic value for carbon dioxide dissociation process. ln K P = 15.869 K P = e 15.869 Add Equations (I) and (II) and cancel the common terms from the stoichiometric equation. CH 4 + C + O 2 ⇌ C + 2 H 2 + CO 2 CH 4 + O 2 ⇌ 2 H 2 + CO 2 (III) Add the values of equilibrium constants of methane and carbon dioxide dissociation process to calculate the new equilibrium constant. K P = e − 9.685 + e 15.869 = e 6.184 Write the stoichiometric equation for water dissociation reaction. 2H 2 + O 2 ⇌ 2 H 2 O (IV) Refer table A-28, “Natural logarithms of equilibrium constants”, obtain the ln K p value for water dissociation process as − ( − 3.086 ) at 3000 K. Write the natural logarithmic value for water dissociation process. ln K P = 2 ( 3.086 ) K P = e 6.172 Add Equations (3) and (4). CH 4 +O 2 + O 2 + 2H 2 ⇌ 2 H 2 + CO 2 + 2 H 2 O CH 4 +2O 2 ⇌ CO 2 + 2 H 2 O (V) From Equation (V), infer that the stoichiometric coefficient for CH 4 ( v CH 4 ) and H 2 O ( v H 2 O ) is 1, and for oxygen ( v O 2 ) and CO 2 ( v CO 2 ) is 2. Add the values of equilibrium constants to calculate the new equilibrium constant. K P = e 6.172 + e 6.184 = e 12.356 = 232 , 350 Write the actual reaction for the dissociation process. CH 4 +2O 2 → x CH 4 + y O 2 + z CO 2 + w H 2 O (VI) From the actual reaction, infer that the equilibrium composition contains x kmol of CH 4 ( N CH 4 ) , y kmol of O 2 ( N O 2 ) , z kmol of CO 2 ( N CO 2 ) , w kmol of H 2 O . Write the formula for total number of moles ( N t o t a l ) . N t o t a l = N CH 4 + N O 2 + N CO 2 + N H 2 O (VII) Here, number of moles of CH 4 is N CH 4 , number of moles of O 2 is N O 2 , number of moles of CO 2 is N CO 2 , and N O 2 , and number of moles of H 2 O is N H 2 O . Write the equilibrium constant ( k p ) for the reported process. k p = N CO 2 v CO 2 N H 2 O v H 2 O N CH 4 v CH 4 N O 2 v O 2 ( P N t o t a l ) ( v CO 2 + v H 2 O − v CH 4 − v O 2 ) (VIII) Here, pressure is P . Write the mole fraction of carbon dioxide ( y CO 2 ) . y CO 2 = N CO 2 N t o t a l (IX) Write the partial pressure of the carbon dioxide ( P CO 2 )

Loose Leaf for Thermodynamics: An Engineering Approach

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ISBN: 9780077624835

Author: Cengel Dr., Yunus A.; Boles, Michael A.

Publisher: McGraw-Hill Education

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Chapter 16.6, Problem 90RP

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Loose Leaf for Thermodynamics: An Engineering Approach

Ch. 16.6 - Write three different KPrelations for reacting...Ch. 16.6 - A reaction chamber contains a mixture of CO2, CO,...Ch. 16.6 - A reaction chamber contains a mixture of N2and N...Ch. 16.6 - A reaction chamber contains a mixture of CO2, CO,...Ch. 16.6 - Which element is more likely to dissociate into...Ch. 16.6 - Prob. 6P Ch. 16.6 - Prob. 7P Ch. 16.6 - Prob. 8P Ch. 16.6 - Prob. 9P Ch. 16.6 - Prob. 10P

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