2015 Homework 1 Answers
10
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 ΔC p for the unfolding of this protein, assuming ΔC p 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?
description
2015 Homework 1 Answers
Transcript of 2015 Homework 1 Answers
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?!!!
