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TD_Review_notes

TD_Review_notes - Thermodynamics Review A Introduction...

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Unformatted text preview: Thermodynamics Review A. Introduction Chemical TD gives us tools to: Determine the composition of a system at equilibrium (What form do the chemicals of interest take? Important!) Find direction of spontaneous change (What reactions will happen involving our chemical of interest?) B. Gibbs free energy, G G expresses relative “free” energy content of the components of a system. Free energy is that part of the total energy that is available to do useful chemical work Thermodynamic expression for free energy: G = H — TS H = enthalpy, kcal total energy content S = entropy, heal/K TS = that part of total energy not available for useful work due to its disordered and uncertain nature - AG : AH — TAS (at constant T and P) C. Equilibrium A system at equilibrium is at a state of minimum free energy A system moving toward equilibrium will decrease G to that AG is negative. (May release heat so AH is negative, or increase S, or some combination) So, for a particular reaction under a particular set of conditions, the sign of AG will tell us whether the reaction is favorable or not. If AG <- 0, the reaction will go as written! In order to understand how G changes for a reaction, let’s look in more detail at what contributes to G. Consider a system containing A, B, C, and D Each moi of each of these components will contribute additively to the total G in the system. Total free energy in system: GT : RAMA + HBMB + nCMC + HDPLD Or Gr = >3 niHi Where: ni is the number of moles of i n; is the per moi contribution of i to the free energy of the system. Free energy contributed by each species, ui, has two components in an ideal system: Mi : the + RT1n{I} 1) in" is the energy corresponding to the chemical nature of the species. Represents the energy of'formation from a reference state (Ca2+ from Ca). This information is available in tables. It is not specific to our particular system. 2) RTin{i} is the energy corresponding to the concentration of the species in the system R = 1.987 cal/(K moi) : 8.314 J/(K moi) T = absolute T in K (273 + °C) 298 K = 25 °C But we are interested in relative changes in G! How does G change with progression of the reaction? For a reaction: 8A + bB 2 CC + dD where A, B, C, and D represent the components, and a, b, c, and d represent the number of moles reacting. As reaction progesses, a moles of A is lost 1) moles of B are lost c moies of C are gained d moles of D are gained We lose pm (the per mol contribution of A) for every mol lost, etc. AG = -aMA ~be + cue + dud Let’s expand this equation based on what we learned about MA AG : —auA° ~ aRTln{A} —buB° — bRTln{B} + cuc° + cRTln{C} + duD" Jr dRTln{D} Let’s just rearrange the terms here, and group terms whether they are based on tabulated information about the chemical nature of the species, or information about our specific system E E E E E E i E E g AG : —auA°ebuB° + cuc" + dpLD" — aRTln{A} H bRTln{B} + cRTln{C} + dRTIn{D} AG = -aMA°-bMB° + Cue” + cw - RTIn({A}“{B}")/{C}“{D}d) We can simplify this into a very important equation - AG 3 AG" + RT an Where: ' ! AG0 : —auA°—buB° + cuc" + duD° and Q = {mama/{arms This is called the reaction quotient At equilibrium, AG : 0, so AGo — — RT an, or Q 2 exp [- AG°/RT] only at equilibrium We can see that the reaction quotient at equilibrium would be a very special parameter—so Q at equil has its own variablern We define K = [{A}€‘{B}b)/{C}°{D}Cl ] at equilibrium K: exp [- AG°IRT] D. Local equilibrium Even if an entire system is not at equilibrium, we may be able to assume equilibrium at certain places in our system. For example, consider a solution dissolving limestone in one area, then flowing to another location where it loses some carbon dioxide, and precipitates calcite. The entire system is clearly not at equilibrium, but'at each step along the way, equilibrium calculations can be used. Example calculation: Is it possible to oxidize sulfide in natural waters with nitrate? (You can work with pH 8 and all other concentrations 10'4 M) Compound AGfO (kcal/mol) H20 66.69 HS‘ ‘ +3.01 N03' -26.4l PF 0 3042' -177 34 urn+ —19 Free energy _ Products” (C. '1- D) Progress of the reaction ...
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