Question 14.8: Minimization of Gibbs Function 0.5 kmol of hydrogen and 0.5 ...
Minimization of Gibbs Function
0.5 kmol of hydrogen and 0.5 kmol of oxygen are kept in a container maintained at 1 atm and 2500 K. Which of the following component sets is more likely to be the equilibrium composition? (a) Set A: H _{2}, O _{2}, H _{2} O ; \text { (b) Set } B : H _{2}, O _{2}, H _{2} O , OH ; \text { (c) Set } C : H _{2}, O _{2}, H _{2} O , OH , O ; (d) Set D: H _{2}, O _{2}, H _{2} O , OH , O , H . Use the IGE system-state TESTcalc.
Evaluate the Gibbs function of each mixture. The one with the minimum value of the function is the most likely candidate for the equilibrium mixture.
Assumptions
The Ideal gas mixture model is applicable.
TEST Analysis
Launch the IGE system-state TESTcalc. In the composition panel, enter the moles of the reactants (select the checkbox, type in the value in a yellow field, and click on a blank cell to register the input). Then select the desired set of products components. In the state panel, select State-1, mark the products’ radio-button, enter p1=100 kPa and T1=2500 K, and calculate the state. The mixture composition can now be found in the composition panel and the Gibbs function g1 in the state panel.
Composition A: The products mixture is found to have g1 = -34149 kJ/kg and the composition is calculated as 0.0050 H _{2}+0.2525 O _{2}+0.4949 H _{2} O .
Composition B: The products mixture is found to have g1 = -34190 kJ/kg and the composition is calculated as 0.0050 H _{2}+0.2441 O _{2}+0.4781 H _{2} O +0.0337 OH .
Composition C: The products mixture is found to have g1 = -34199 kJ/kg and the composition is calculated as 0.0050 H _{2}+0.2410 O _{2}+0.4781 H _{2} O +0.0337 OH +0.0062 O .
Composition D: The products mixture is found to have g1 = -34200 kJ/kg and the composition is calculated as 0.0050 H _{2}+0.2414 O _{2}+0.4774 H _{2} O +0.0337 OH + 0.0062 O +0.0015 H .
Discussion
Composition D, with its lowest value of Gibbs function, is the most likely candidate for equilibrium composition. In reality, there are many more components, some in trace amounts, that are present at equilibrium. The Gibbs function of the mixture will continue to decline as more components are included. Note that the TESTcalc produces Gibbs function per unit mass of the mixture, while \bar{g}_{P} , in our terminology, is the Gibbs function of the products mixture per unit mole of the principal reactant (generally, a fuel).