Basis concepts of Thermochemistry

1. Multi-component systems Basis concepts of Thermochemistry Goal: Using the general concept of minimal Gibbs free energy for chemical reactions at constant T& P to derive law of mass action To apply the concept of minimal Gibbs free energy in chemical reactions we need generalization of single component systems (such as water only) and to For now restriction to single phase systems (think of chemical reaction of gases into a gaseous product such as ) The Gibbs free energy of a multi-component system with Nj particles in each component reads

2. Using homogeneity of G according to and especially for as generalization of Likewise is generalized into

3. On the way towards the law of mass action let’s derive a useful relation (Gibbs-Duham) between change of the chemical potentials as a result of particle exchange With and - Gibbs-Duhem equation - When T and P are constant telling us that the chemical potentials of the different components are related For example: in a 2 component mixture when knowing we can calculate from

4. Law of mass action Let’s consider a chemical reaction among  species (components) For example the reaction Dh=-92,5kJ/mol Let’s write this in the form - =0 Or in a general notation stoichiometric coefficient For example: - =0 with and reactant Ajis a product if > 0 Ajis a reactant if < 0 Reaction goes in both directions: where is the equilibrium

5. At constant T and P: equilibrium determined by minimum With and T,P constant =0 in equilibrium If we look, e.g., at the forward direction of the reaction we identify =0 Consequences of this relation for ideal gases The chemical potential of an ideal gas can be derived from implying

6. For each component (reactant and product) of the chemical reaction we can write (under the assumption that the components can be described by ideal gases) With =0 and concentration of component j partial pressure of component j =0 total pressure according Dalton’s law =0 Example: Law of mass action where Equilibrium constant

7. Consequences from law of mass action in equilibrium large with small with meaning product concentration large If large requires meaning reactant concentration low small with large with meaning product concentration low If small requires meaning reactant concentration large What can we say about P and T dependence of Can we use P to shift the equilibrium to the side of reactants or products If increase in P decreases Equilibrium shifts towards reactants If increase in P increases Equilibrium shifts towards products If no P dependence of

8. Can we use T to shift the equilibrium to the side of reactants or products Next we replace by a quantity closely related to the experiment such as the heat released in an exothermal reaction From A From using & B A B

9. From and where is the enthalpy of the reaction For a better understanding let’s integrate the equation heat leaves the system, the reaction is exothermic decreases with increasing T and the yield goes down If (consider the reaction of hydrogen and oxygen into water. At high temperature (about 6000K ) there is virtually no yield for water and at even higher T water dissociates into hydrogen and oxygen.) the reaction is endotherm increases with increasing T and the yield goes up If

10. The Haber-Bosch process An example to utilize the full potential of the law of mass action Industrial route to ammonia (Nobel Prize in Chemistry 1918, Fritz Haber) http://en.wikipedia.org/wiki/File:Fritz_Haber.png Fritz Haber, 1868-1934 Dh=-92,5kJ/mol Let’s recall: At room temperature the reaction is slow (note: our equilibrium considerations say nothing about kinetics ! ) Is it a good idea to increase T to increase reaction speed Equilibrium consideration from law of mass action limits this possibility Since reaction is exothermicdecreases with increasing T and the yield goes down Compromise: T not higher than needed for catalyst to work (400 C) http://en.wikipedia.org/wiki/Haber_process

11. Can pressure be utilized to favor the forward direction Law of mass action provides the answer: Yes Means here Let’s recall - =0 high-pressure reactor (1913) in the ammonia plant of the BadischeAnilin und Soda Fabrik (BASF) increases with increasing P Expenses/technical reasons of high P equipment bring limitations to this approach Compromise: 6–18 MPa (59–178 atm) Finally: we have seen from the discussion of stability conditions A perturbation away from equilibrium creates a force driving the system back (Le Chatelier’s principle) removing NH3 will increase yield of production (In the Haber-Bosch process ammonia is removed as a liquid)