(a) Explanation Write the stoichiometric equation for dissociation of 1 kmol of Oxygen ( O 2 ) . O 2 → x O 2 + 2 ( 1 − x ) O (I) Write the acual equation for dissociation of 1 kmol of Oxygen ( O 2 ) . O 2 → 2 O Write the formula to calculate the equilibrium constant ( K P ) for the reaction. K P = N O v O N O 2 v O 2 ( P N total ) ( v O + v O 2 ) (II) Here, number of moles of O 2 is N O 2 , number of moles of O is N O , pressure is P , total number of moles of the mixture is N total , stoichiometric coefficient of CO 2 is v CO 2 , stoichiometric coefficient of CO is v CO , and stoichiometric coefficient of O 2 is v O 2 . Write the energy balance equation to determine the heat transfer ( Q out ) for the dissociation process. − Q out = ∑ N P ( h ¯ f o + h ¯ − h ¯ o ) P − N R ( h ¯ f o + h ¯ − h ¯ o ) R (III) Here, number of moles of products is N P , number of moles of reactants is N R , enthalpy of vaporization is h ¯ f o , and the enthalpy of formation is h ¯ . Write the expression to calculate the molar flow rate of Oxygen ( N ˙ ) . N ˙ = m ˙ M (IV) Here, mass flowrate of Oxygen is m ˙ and the molar mass of Oxygen is M . Write the expression to calculate the rate of heat transfer ( Q ˙ out ) . Q ˙ out = N ˙ Q out (V) Conclusion: The stoichiometric coefficients from the Equation (II), v O = 2 v O 2 = 1 Calculate the total number of moles of products ( N total ) . N total = x + 2 ( 1 − x ) = 2 − x From the Table A-28 of “Natural logarithms of the equilibrium constant K P ”, the value of equilibrium constant K P at the temperature of 3000 K is ln K P = − 4.357 K P = 0.01282 Substitute 0.01282 for K P , 2 for v O , 1 for v O 2 , 1 atm for P , and ( 2 − x ) for N total in Equation (III). 0.01282 = ( 2 − 2 x ) 2 x ( 2 2 − x ) ( 2 − 1 ) x ≃ 0.943 Substitute 0.943 for x in Equation (I). O 2 → 0.943 O 2 + 2 ( 1 − 0.943 ) O O 2 → 0.943 O 2 + 0.114 O Rewrite the Equation (V) for the dissociation of Oxygen. Q ˙ i n = { [ N O 2 ( h ¯ f o + h ¯ 3000 K − h ¯ 298 K ) O 2 ] P − [ N O ( h ¯ f o + h ¯ 300 K − h ¯ 298 K ) O ] R } (VI) Here, enthalpy of formation at 3000 K is h ¯ 3000 K , enthalpy of formation at 298 K is h ¯ 298 K , number of moles of monoatomic oxygen is N O , and number of moles of O 2 is N O 2 (b) To determine The amount of heat transfer for the absence of dissociation of Oxygen.

8th Edition

ISBN: 9780073398174

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

Publisher: McGraw-Hill Education

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Chapter 16.6, Problem 37P

(a)

To determine

The amount of heat transfer for the dissociation of Oxygen is 5066 kJ/min.

(b)

To determine

The amount of heat transfer for the absence of dissociation of Oxygen.

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Chapter 16.6, Problem 35P

Chapter 16.6, Problem 38P

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The amount of heat transfer for the dissociation of Oxygen is 5066 kJ / min .

Solution Summary: The author calculates the equilibrium constant (K_P) for the reaction.