Homework(#1!Posted:(January(11,(2015(Due:(January(21,(2015(at(the(start(of(class(

1.!!A!one(mole!sample!of!a!monatomic!ideal!gas!is!initially!at!100!kPa!atm!and!300K.!A!constant!external!pressure!of!500!kPa!is!suddenly!applied,!compressing!the!gas!irreversibly!to!a!final!state!in!which!P!is!5!atm,!T=!400K.!Calculate!(a)!ΔE,!(b)!W,!(c)!Q,!(d)!ΔH,!and!(e)!ΔS.!!Hint:&You&can&think&of&this&as&a&constant&pressure&process&at&5&atm.!

2.!!The!enthalpy!of!unfolding!of!cytochrome!c!is!50!kcal/mol!at!323K!and!88!kcal/mol!at!343K.!(a)!Estimate!ΔCp!for!the!unfolding!of!this!protein,!assuming!ΔCp!is!constant!over!this!temperature!range.!(b)!The!heat!capacity!of!denatured!(unfolded)!protein!is!generally!found!to!be!higher!than!for!the!same!proteins!in!their!native!structures.!Can!you!qualitatively!describe!this!observation?!!

3.!!Consider!a!coin!that!is!weighted!so!that!it!is!twice!as!likely!to!come!up!heads!as!tails.!(a)!What!is!the!most!likely!outcome!of!a!series!of!2000!coin!tosses!using!this!biased!coin?!(b)!What!is!the!relative!probability!of!getting!1500!heads!versus!1000!heads!in!a!series!of!2000!coin!tosses!using!this!coin?!Express!your!answer!as!a!power!of!10.!!

4.!A!system!with!100,000!molecules!has!two!energy!levels!(A!and!B).!At!first,!the!two!energy!levels!are!populated!equally.!After!a!reversible!process,!energy!level!A!is!populated!by!65%!of!the!molecules!and!the!system!is!at!293K.!(a)!What!is!the!difference!in!energy!between!the!two!levels?!(Hint:&this&is&the&Free&Energy)!(b)!How!much!heat!was!added!or!removed!from!the!system?!(c)!What!is!the!change!in!entropy?!!

5.!!20!particles!are!in!a!closed!system!with!equally!spaced!energy!levels.!The!system!has!a!total!energy!of!14.!In!State!A,!you!have!6!particles!at!the!lowest!energy!level!(zero!energy!level),!and!14!particles!at!energy!level!1.!In!state!B,!there!are!6,5,3,!and!1!in!energy!levels!0,1,2,!and!3!respectively.!!(a)!Calculate!W!for!states!A!and!B.!!(b)!How!much!more!likely!is!it!to!find!the!system!in!state!B!than!in!state!A?!(c)!Based!on!the!the!shape!of!the!Boltmann!distribution,!guess!the!most!probably!arrangement!of!particles!among!energy!states!if!there!were!24!particles!with!total!energy!of!28.!!(d)!For!the!distribution!you!chose!in!(c),!what!is!W?!!

6.!Assume!that!entropy!and!enthalpy!changes!are!independent!of!temperature.!A!system!in!state!A!has!an!enthalpy!of!–22!kJ!and!an!entropy!of!7!J/K.!In!state!B,!it!has!an!enthalpy!of!–12!kJ!and!an!entropy!of!15!J/K.!At!what!temperatures!will!state!B!be!favored?!!!

7.!A!chemist!wants!to!develop!a!fuel!by!converting!water!back!to!elemental!hydrogen!and!oxygen!using!coupled!ATP!hydrolysis!to!drive!the!reaction.!Given!that!the!value!of!∆!f&Go!for!water!is!–237!kJ/mol!and!that!one!mole!of!ATP!hydrolyzed!to!ADP!yields!–30!kJ/mol,!how!much!ATP!is!needed!to!yield!three!moles!of!H2!gas?!!!