Thermodynamics

Chapter 16 | 805EXAMPLE 16–5Equilibrium Compositionfor Simultaneous ReactionsA mixture of 1 kmol of H 2 O and 2 kmol of O 2 is heated to 4000 K at a pressureof 1 atm. Determine the equilibrium composition of this mixture,assuming that only H 2 O, OH, O 2 , and H 2 are present (Fig. 16–15).Solution A gas mixture is heated to a specified temperature at a specifiedpressure. The equilibrium composition is to be determined.Assumptions 1 The equilibrium composition consists of H 2 O, OH, O 2 , andH 2 . 2 The constituents of the mixture are ideal gases.Analysis The chemical reaction during this process can be expressed asH 2 O 2O 2 ¡ xH 2 O yH 2 zO 2 wOHMass balances for hydrogen and oxygen yieldH balance: 2 2x 2y w(1)O balance: 5 x 2z w(2)The mass balances provide us with only two equations with four unknowns,and thus we need to have two more equations (to be obtained from the K Prelations) to determine the equilibrium composition of the mixture. Itappears that part of the H 2 O in the products is dissociated into H 2 and OHduring this process, according to the stoichiometric reactionsH 2 O ∆ H 2 1 2 O 2 1reaction 12H 2 O ∆ 1 2 H 2 OH1reaction 22The equilibrium constants for these two reactions at 4000 K are determinedfrom Table A–28 to beln K P10.542 ¡ K P1 0.5816ln K P20.044 ¡ K P2 0.9570The K P relations for these two simultaneous reactions areK P1 N n H2nH 2NO2O2nN H2Oa P n H2n O2n H2ObH2 O N totalEquilibriumInitialcomposition atcomposition4000 K, 1 atm1 kmol H 2 Ox H 2 O2 kmol O 2y H 2z O 2w OHFIGURE 16–15Schematic for Example 16–5.whereSubstituting yieldsK P2 N n H2nH 2N OHOHnN H2Oa P n H2n OH n H2ObH2 O N totalN total N H2 O N H2 N O2 N OH x y z w0.5816 0.9570 1y2 1z21>2x1w2 1y21>2x1>21ax y z w b1>21ax y z w b(3)(4)