Lecture'Notes'5:'Chemical'Equilibrium'!Chemical!equilibrium!is!an!important!concept.!!It!touches!on!what!we!will!spend!most!of!the!rest!of!the!semester!dealing!with.!!However,!the!basic!concepts!are!universal!such! that!if!you!can!grasp!the!key!ideas!you! see!how!they!will!apply!over!and!over!again!in!different!situations.!!In!many!ways,!you!already!have!seen!the!key!ideas!look!a!physical!equilbrium!but!I!will!try!to!emphasize!those!concepts!again.!!Along!with!what!is!unique!to!chemical!equilibria!(the!plural!of!equilibrium). Why should we care? At its heart, the idea of equilibria is predictive. That is because it is derived from thermodynamics which is predictive. If I mix this and that can I make this other thing? It tells us the possibilities of chemical reactions. Moreover, if we have a system at equilibrium we can easily predict how it will react to changes or “stresses” that we apply. What will happen if I add more of this? What will happen if I compress the system to increase the pressure? What will happen at a higher temperature? Finally, with the help of our knowledge that matter is composed of atoms and reactions are governed by balanced equations, equilibrium ideas lead to quantified measures of reactions.Equilibrium!happens!!Let’s!look!at!what!happens!during!a!reaction!that!is!approaching!chemical!equilibrium.!!For!my!example,!we!can!look!at!the!reaction!of!carbonmonoxide!and!water!to!make!hydrogen!and!carbondioxide.!!!!€ CO(g) + H2O(g) ↔ H2(g) + CO2(g)! !As!the!reaction!proceeds!the!concentrations!of!the!reactants!CO!and!H2O!drop!while!the!concentrations!of!the!CO2!and!H2!rise.!!While!you!may!have!in!the!past!viewed!all!reactions!as!having!“gone!to!completion”.!!This!is!not!always!the!case.!!In!fact,!with!the!except!of!some!heterogeneous!reactions,!technically!they!will!never!go!absolutely!100%!to!completion.!!In!many!cases!they!don’t!even!get!close.!!Instead,!at!somepoint!the!concentrations!level!off!and!stop!changing.!!Why!is!this?!!Has!the!chemistry!stopped?!!In!a!sense!it!has!as!the!net! concent rations!have!stopped!changing.!!However,!the!situation!is!very!dynamic.!!Rather!than!all!chemistry!stopping,!what!has!occurred!is!that!the!forward!and!backward!chemical!reactions!are!now!proceeding!at!the!same!rate.!!This!is!dynamic!equilibrium.!!This!is!seen!in!the!graph!on!the!next!page!that!shows!the!rates!as!a!function!of!time.!!!This!graph!assumes!the!previous!reaction!in!which!the!initial!concentrations!are!all!reactant!and!the!products!are!zero.!!When!the!reaction!starts!the!forward!rate!is!the!fastest.!!It!drops!with!time!as!the!reactant!concentrations!are!dropping.!!Also,!at!time!=!zero,!the!backward!reaction!is!zero!since!there!is!nothing!to!reaction.!!!However,!as!the!products!form,!some!of!them!react!backward.!!The!rate!of!the!backward!reaction!increases!until!finally!the!forward!and!backward!rates!are!equal.!!This!is!when!we!have!reach!equilibrium.!!!Key!idea:!!At!equilibrium!we!have!a!fixed!ratio!of!the!concentrations.!!We’ll!see!more!about!this!later.!!!!Free!Energy!and!Equilibrium!!!First,!what!is!happening!with!equilibrium?!!When!you!put!a!bunch!of!molecules!together!they!will!“react”!in!such!a!way!to!lower!their!free!energy.!!!One!of!the!easiest!ways!to!look!at!this!is!to!imagine!a!situations!in!which!we!have!only!two!molecules!A!and!B.!!By!chance!these!two!molecules!have!identical!free!energies.!!If!this!is!the!case!then!the!standard!free!energy!of!reaction!ΔrG°!=!0.!!On!this!basis!we!would!predict!that!A!and!B!have!identical!stabilities?!!So!what!will!happen!if!I!start!out!with!a!!system!of!pure!A?!!Will!any!B!form?!!What!if!everything!is!B?!!What!about!mixtures?!!!!Let’s!look!at!a!plot!of!free!energy!a s!a!function!of!the!reaction!!!!!!!The!case!where!ΔrG°!=!0!is!on!the!left.!!!The!lowest!free!energy!state!is!the!state!with!equal!number!of!molecules!of!A!&!B.!!This!is!the!state!with!the!highest!entropy.!!Neither!pure!state!has!any!entropy!from!mixing.!!Thus!the!even!though!A!and!B!have!identical!free!energies,!the!lowest!free!energy!is!in!the!50/50!mixture.!!Higher!entropy!leads!to!lower!free!energy!(G!=!H!–TS).!So!the!equilibrium!mixture!will!be!right!in!the!middle.!BBBBBBBBBBBBBBAAAAABAAA AAAAAAAll AAAll B50:50 mix A:BReactionGibb’s Free EnergyBBBBBBBBBBBBAAAAAAAA AAAAAAAll AAAll BMostly A“favors reactant”ReactionGibb’s Free Energy!rG° > 0AAABBBBBBBBBBBBBBAABAAA AAAAAAAll AAAll BMostly B“favors products”ReactionGibb’s Free Energy!rG° <
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