Chemical Reaction Equilibria Part IV

Liquid-phase reactions For a liquid phase, fio is the fugacity of pure component i at T of the system and Po = 1 bar fi is the fugacity of i at T and P, and fi0 is the fugacity of i at T and Po

K for liquids at low to moderate pressures if the equilibrium mixture This expression holds at high pressures, i.e., When P >> Po at low to moderate pressures if the equilibrium mixture is an ideal solution

Homogeneous reactions only one phase Read and work examples 13.5, 13.6, 13.7; 13.8; 13.9

Heterogeneous reactions more than one phase two criteria: phase equilibrium and chemical equilibrium Question: where the reaction takes place? example: A(g) + B (l)  C (l) liquid rxn takes place in the gas phase rxn takes place in the liquid phase rxn takes place in both phases gas

If the rxn takes place in both phases The value of K depends on the chosen standard states however, all methods lead to the same equilibrium composition

1st example Ethylene reacts with water to form ethanol at 200oC and 34.5 bar; there are two phases: liquid and vapor. The pressure is kept constant. Estimate the compositions of the liquid and vapor phases. F = 2-p + N = 2 -2 +2 = 2 If we specify T and P the intensive variables are fixed.

assume the rxn takes place in the gas phase C2H4(g)+H2O(g)  C2H5OH (g) standard pressure P0 is 1 bar calculate K at 200oC yields K =0.031 Next we need to add the VLE equations:

where the liquid-phase fugacities can be written as:

Unknowns: xH2O, xEtOH, yC2H4 Use this eqn Because ethylene much more volatile than H2O and C2H5OH Unknowns: xH2O, xEtOH, yC2H4 Virial EOS for fi Activity coeff. model or exp. Data for gi

2nd example Limestone (CaCo3) decomposes upon heating to yield quicklime (CaO) and carbon dioxide. At what temperature is the decomposition pressure of limestone =1 atm? CaCO3 (s)  CaO (s) + CO2 (g) Each species exists pure as an individual phase For the solid phases, the ratio f/fo =1 (pure) For CO2, f/fo = P/Po =1.033 So, K = P = 1.0133, we need to find T

From the data in appendix C DGo (298K) = 130401 J/mol DHo (298K) = 178321 J/mol Calculate DA, DB, DC, DD And get the integral to calculate DG(T), such that K = 1.0133 = exp (- DG(T)/RT) Solve for T, T=1151.83 K

3rd example Ammonium chloride NH4Cl(s) decomposes upon heating to yield a mixture of ammonia and hydrochloric acid. At what temperature does ammonium chloride exert a decomposition pressure of 1.5 bar? For NH4Cl(s), DHf(298 K)=-314,430 J and DGf(298 K)=-202,870 J. NH4Cl(s) pure phase, f/fo =1 (pure) The gas mixture NH3 and HCl at 1.5 bar, ideal gas mixture, for each gas the fugacity is the partial pressure yiP

yiP = 0.5x1.5 =0.75 for each gas K = 0.75x0.75 = 0.5625, we must find T that gives that value of K From Appendix C DGo (298K) = 91121 J/mol DHo (298K) = 176013 J/mol Calculate DA, DB, DC, DD And get the integral to calculate DG(T), such that K = 0.5625 = exp (- DG(T)/RT) Solve for T, T=623.97 K

example 4 The following isomerization reaction occurs in the liquid phase: AB, where A and B are miscible liquids for which GE/RT =0.1xAxB. If DGo (298 K)=-1,000 J, what is the equilibrium composition of the mixture at 25oC? How much error is introduced if one assumes that A and B form and ideal solution? Solve for xA = 0.3955

For the ideal solution: How much error is introduced if one assumes that A and B form and ideal solution? For the ideal solution: Solve for xA = 0.4005