Course summary English

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Fundamentals of Chemical Processes summary L. Spinelli 1 Chemical equilibrium In order to study chemical reactions, we must first introduce some fundamental quantities. The centrepiece of chemistry is the stoichiometry of reaction, which we can express as follows: 4NH3 + 4NO + O2 → 4N2 + 6H2O (1.1) representing the standard SCR reaction, utilised in NOx abatement. In general we can write νAA +νBB⇌νP P +νQQ (1.2) where stoichiometric coefficients νi represent how many moles of a given species are consumed/produced per unit extent of reactionε = dnA/νA = dnB/νB = dnP/νP = dnQ/νQ = dni/νi. By convention, we consider positiveνi for products, and negative for reactants. We can also introduce some important quantities such as: • conversion of species A χA = nA,converted nA,fed = n◦ A −nA n◦ A (1.3) • selectivity of A to product P SP,A = nP,produced/|νP| nA,converted/|νA| = nP −n◦ P n◦ A −nA |νA| |νP | (1.4) • yield of P from A ηP,A = nP,produced/|νP| nA,fed/|νA| = nP −n◦ P n◦ A |νA| |νP | =χA ·SP,A (1.5) 1.1 Equilibrium criteria Let’s now consider a closed system containing an arbitrary number of species, which is in equilibrium with its surroundings, that is T =Tsurr andp =psurr. The II law of thermodynamics states that dS +dSsurr ≥ 0 (1.6) where the equality holds for reversible transformations between equilibrium states: in such an instance, we havedSsurr = δQsurr Tsurr = −δQ T ⇒dS ≥ δQ T : we can plug this result into the I law of thermodynamics to write dU =δQ −pdV ⇒dU −TdS +pdV ≤ 0 (1.7) which we can further elaborate to get d (U +PV −TS )p,T =dU +pdV +Vdp −TdS −SdT ≤ 0 dG|p,T ≤ 0 (1.8) we can interpret this result as follows: any spontaneous transformation will decrease its Gibbs free energy until equilibrium is reached when dG|p,T = 0. 1 ConsideringG =G (T,p,n i)…