2 - Chapter 6

2 - Chapter 6 -...

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Unformatted text preview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hat is thermodynamics? Relationships between Thermodynamics: \ H"&(+%J/M(1D(%"&('&7#%,1.+",$(6&%3&&. d ifferent forms of energy.#',1J+(D1'2+(1D(&.&'-M(P+JF"(#+(31'4( How they are transformed. 1'("&#%U^((+%J/M(1D(%"&(%'#.+D1'2#%,1. 1D(&.&'-MC what is thermodynamics? The condition and of a system defined by certain properties P V=nRT State function? Only tha value of the p roperty matters, not the method by which it got there Thermochemistry: \ L.&'-M(6114\4&&$,.-C 0&#%(#6+1'6&/( 1'(&]17]&/(,.(#(F"&2,F#7('&#F%,1.C Thermodynamic (Equilibrium) State: \ H"&(F1./,%,1.(1D(#( +J6+%#.F&(1'(+M+%&2:(/&D,.,.-(,%+($'1$&'%,&+:(+$&F,D,&/(6M(#( D&3(,.%&.+,]&(2#F'1+F1$,F(]#',#67&+(P+JF"(#+(H:(5:(&%FCUC Thermochemistry? How likely that reaction takes place. Whether or n ot it takes in energy or releases State FunctionG((\ #($"M+,F#7($'1$&'%M(7,4&(_:(0:(H:(`:(5(%"#%( "#+(#(+$&F,D,F(]#7J&(1.F&(%"&(+%#%&(,+(/&D,.&/^(,%(/&$&./+( 1.7M(1.(%"&(+%#%&(1D(%"&(+M+%&2(#./(.1%(%"&($#%"3#M(P"13( 3&(-1%(%"&'&UC X#F'1+F1$,F(`#',#67&+ X#F'1+F1$,F(`#',#67&+(a&+F',6&+(%"&(5'1$&'%,&+(1D(YJ74( WM+%&2+(P]&'+J+(+,.-7&(217&FJ7&+UC Extensive Macroscopic Variables: \ $'1$&'%,&+(%"#%( /&$&./(J$1.(%"&(#21J.%(P2#++U(1'(b&c%&.%d 1D(%"&( +#2$7&:($'1$&'%,&+(7,4&(2#++(M:(217&(.J26&'+(ni:(17J2&(V:("&#%(F#$#F,%M(C:(,.%&'.#7(&.&'-M(U:(&.%'1$M(S:( e,66[+(D'&&(&.&'-M(G:(&%FC Extensive vs intensive macroscopic? Extensive depends on the amount or value of a certain variable Intensive describes the ratio * Intensive Macroscopic Variables: \ $'1$&'%,&+(%"#%( /&$&./(1.(%"&(.#%J'&(1D(%"&(2#%&',#7(6J%(.1%(%"&(#21J.%:( +JF"(#+(%&2$&'#%J'&(T:($'&++J'&(P:(],+F1+,%M( :(#./(#.M( '#%,1(1D(&c%&.+,]&($'1$&'%,&+(+JF"(#+(/&.+,%M( = M/V:( 217&(D'#F%,1.((( i = ni/n:(1'(#.M(217#'(fJ#.%,%,&+(+JF"(#+( 217#'(]17J2& V = V/n, U = U/n, S = S/n, H = H/n, or G = G/n. 1234(56((7 12"?'39(5 * !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- H"&(_.,]&'+&G(H"&(WM+%&2(#./(WJ''1J./,.-+ *(%"&'21/M.#2,F(+M+%&2(,+( %"#%($#'%(1D(%"&($"M+,F#7( J.,]&'+&(3",F"(,+(J./&'( F1.+,/&'#%,1.:(&C-C(%"&( +J6+%#.F&:(]&++&7:(1'('&#F%,1.( 2,c%J'&(,.(3",F"(3&(#'&( D1FJ+&/C((H"&(+J''1J./,.-+(,+( &]&'M%",.-(&7+&:(3,%"(%"&( 61J./#'M(6&%3&&.(%"&(+M+%&2( #./(+J''1J./,.-+(/,F%#%,.-( "13(%"&M(,.%&'#F%C((H"&( 61J./#'M(2#M(#7713(2#%%&'( #./g1'(&.&'-M(%1(D713C((H"&( +M+%&2($7J+(+J''1J./,.-+(,+( '&D&''&/(%1(#+(%"&(J.,]&'+&C !7#++,D,F#%,1.(1D(H"&'21/M.#2,F(WM+%&2+ K.(%"&'21/M.#2,F+:(#(+M+%&2 ,+(F7#++,D,&/(6M("13(,%( ,.%&'#F%+(3,%"(,%+(+J''1J./,.-+ G System and surrounding? System is what is being a ffected Surrounding describes what interacts with the system but is not the system System + Surrounding = Universe Surrounding and S ystem in a reaction -> P utting solvent can act a s surroudnings solute acts as system Open v. closed v. Isolated System? Open System means that energy=heat and matter=vapor pressure can escape. P#U((*.(1$&.(+M+%&2 F#.( &cF"#.-&(61%"(2#%%&'(N(&.&'-M 3,%"(,%+(+J''1J./,.-+C( P6U((*(F71+&/(+M+%&2 F#.( &cF"#.-&(&.&'-M 3,%"(%"&( +J''1J./,.-+(6J%(.1%(2#%%&'C( PFU((*.(,+17#%&/(+M+%&2 F#..1%( &cF"#.-&(&.&'-M(1'(2#%%&'C( 1234(56((7 12"?'39(5 Closed System Matter (vapor pressure) cannot escape but h eat is still able to e scape Isolated System Neither matter nor e nergy escapes @ !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- a,#%"&'2,F ]+C(*/,#6#%,F(5'1F&++&+ a,#%"&'2,F Q#77+ #7713(&.&'-M(%1(D713( #+("&#%(,D(%"&'&(,+(#(H&2$&'#%J'&( /,DD&'&.F&(6&%3&&.(%"&(+M+%&2(N( +J''1J./,.-+:(3"&'&#+(*/,#6#%,F( Q#77+ /1(.1%(#7713("&#%(%1(D713(&]&.( ,D(%"&'&(,+(#(H(/,DD&'&.F&C Diathermic vs. A diabatic? Diathermic Walls means that heat is a ble to flow through system Adiabatic means that the heat is isolated on one side. The heat comes from the system itself as o pposed to coming from the surroundings. L./1%"&'2,F(#./(Lc1%"&'2,F(5'1F&++&+( J./&'(*/,#6#%,F(]+C(a,#%"&'2,F !1./,%,1.+ */,#6#%,F a,#%"&'2,F L./1 Lc1 */,#6#%,F(!1.%#,.&'G(( H(/&F'&#+&+(/J',.-(#.( &./1%"&'2,F($'1F&++(P#U( 6J%(H(,.F'&#+&+(/J',.-(#.( &c1%"&'2,F($'1F&++(P6UC 1234(56((7 12"?'39(5 L./1 Lc1 a,#%"&'2,F !1.%#,.&'G((H('&2#,.+( F1.+%#.%(#+("&#%(&.%&'+(D'12(%"&( +J''1J./,.-+(/J',.-(#.(&./1\ %"&'2,F $'1F&++(PFU(6J%("&#%(7&#]&+( /J',.-(#.(&c1%"&'2,F($'1F&++(P/UC Adiabatic vs Diathermic Adiabatic = having insulation Endo will decrease b ecause heat cannot escape Expo will raise the h eat because it's stuck inside Diathermic =not h aving insulation Both endo and e xpo will cause no change in heat of the system because h eat is able to flow in and out of the system A !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- H"&(H1%#7(L.&'-M(1D(#(Y#77(,.(X1%,1. H1%#7(L.&'-M(h(i,.&%,F(L.&'-M(j(51%&.%,#7(L.&'-M L(h(iL(j(5L(h(Li j(L5 K.(%"&(#6+&.F&(1D( &c%&'.#7(,.D7J&.F&+( +JF"(#+(#,'( '&+,+%#.F&:(#(6#77(,.( 21%,1.("#+(F1.+%#.%( %1%#7(&.&'-MC((*(6#77( %"'13.(,.(%"&(#,':( 71+&+(4,.&%,F(&.&'-M( #+(,%(+713+:(6J%(-#,.+( $1%&.%,#7(&.&'-MC(( H"&($1%&.%,#7(&.&'-M( /&F'&#+&+(#./(%"&( 4,.&%,F(&.&'-M( ,.F'&#+&+(#+(,%(D#77+C Ideal gasses do not interact with the e nvironment -> No PE, only KE. K E = 1/2mv^2 in ideal But in real life PE turns into KE as an object falls and KE turns to PE a s it rises Stronger bonds act as a strong "spring" in b etween atoms. Allows for molecules to stretch. Ground state of molecules are still. V ibrational ground state is when it is able to stretch with the bonds A fully stretched molecule = no KE all PE If these balls were ideal would what would the K E and PE be? i,.&%,F(L.&'-M(#./(51%&.%,#7(L.&'-M H1%#7(L.&'-M(h(i,.&%,F(L.&'-M(j(51%&.%,#7(L.&'-M L(h(iL(j(5L(h(Li j(L5 ^((Li h(l 2 ?^( L5 ,+(%"&($1%&.%,#7(&.&'-M(#.(16m&F%("#+(/J&( %1(,%+(71F#%,1.(#./(%"&(D1'F&+(#F%,.-(1.(,%C H"&($1%&.%,#7(&.&'-M 1D(#(2#++(2(,.(#( -'#],%#%,1.#7(D,&7/(,+( $'1$1'%,1.#7(%1(%"&( "&,-"%(#61]&(%"&(D711'( Pk&'1($1,.%(5LUC(( L5 h(2-"C Ep = potential energy with regard to location a nd external forces PE = mgh What is the coulomb p otential energy? The charge attraction o r repulsion depends o n charges and d istance between e lectrons Ep = (kq1q2)/r H"&(!1J7126($1%&.%,#7(&.&'-M /J&(%1(&7&F%'1+%#%,F(#%%'#F%,1.(g( '&$J7+,1.(1D(F"#'-&/($#'%,F7&+(/&$&./+(1.(%"&($#'%,F7&(F"#'-&+:( N(,.]&'+&7M(1.(%"&(/,+%#.F&(6&%3&&.(%"&2C(L5 h(4f9f? g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aJ&(%1(Lc$#.+,1. *(-#+(1FFJ$,&+(#(FM7,./&'(3,%"(#( $,+%1.(%"#%(,+("&7/(,.($7#F&C((H"&( $,+%1.(,+('&7&#+&/:(#./(#+(%"&(-#+( &c$#./+:(,%($J+"&+(#-#,.+%(#( F1.+%#.%($'&++J'&(5&cC((Lc$#.+,1.( #-#,.+%(#.(&c%&'.#7(D1'F&(,+(%&'2&/( &c$#.+,1.(31'4:(#./(/&$&./+(1.( &c$#.+,1.(31'4 %"&(F"#.-&(,.(]17J2&C 5&c h(5(h(D1'F&(g(#'&#^( D1'F&(h(5(c(#'&#(h(5&c * 31'4(h(D1'F&(c(/,+%#.F& 31'4(h(P5&c *U(! h(5&c ` 31'4(/J&(%1(&c$#.+,1.(h( 5&c ` \ 1234(56((7 12"?'39(5 What is expansion work? Expansion against an e xternal pressure is e xpansion work. The change in volume is a ble to show how much work is done Pexternal = force/area Force = Area x pressure work= force x distance work = Pressure x delta volume expansion work = - P external x Delta V olume 5 !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- Q1'4 Work ,+(%"&(&.&'-M(%'#.+D&''&/(6&%3&&.(#(+M+%&2(#./(,%+( +J''1J./,.-+(#+(#('&+J7%(1D(J.6#7#.F&/(D1'F&+(6&%3&&.(%"&(%31:( +JF"(#+(3"&.(#.(16m&F%(,+(21]&/(6M(#(D1'F&C 31'4(h(PD1'F&U(c(P/,+%#.F&U(h(P2#++U(c(P#FF&7&'#%,1.U(c(P/,+%#.F&U WK(J.,%+G((3(h(PSU(c(P2U(h(P4-U((c((P2g+?U(c((P2U((h((4-\2?g+? h((O 9(O1J7&(h((9(!1J7126\`17%(h(<C?=@(F#71',&+^((9(F#7(h(BC9AB(O 9(Y',%,+"(H"&'2#7(_.,%(PY%JU(h(9<;;(F#7^(9(.J%',%,1.#7(F#71',&(h 9(4F#7 Lc$#.+,1.(31'4((h((\ 5&c `((h((\ P$'&++J'&U((c((P]17J2&U WK(J.,%+G((3(h(P5#U(c(P2=U((h((P4-g2\+?U(c(P2=U(h(4-\2?g+? h(O When objects are moved with force, work is done. It is calculated by the e nergy that is used/give u p between system and surrounding work (Joules) = mad mad = fd memorize units! Joules = (kg m^2)/s^2 S1.\WK(J.,%+G((31'4((h((\ P$'&++J'&U((c((P]17J2&U((h(P#%2U(c(PVU h(V\#%2 c((9<9:=?;(5#g#%2 c((9<<<(27gV((c((9(F2=g27((c((P2g9<<(F2U= h(V\#%2 c((9<9:=?;(5#g#%2 c((2=g9<= V H"J+:((9(V\#%2 h((9<9C=?;(5#\2= h((9<9C=?;(O !1.]&'+,1.(R#F%1'+(D'12(5'&++J'&(N(%"&(e#+(!1.+%#.% Convert by using the ideal gas constant. Take the R with the correct units \9 8.3145 J 1.9872 cal 1 cal 1 cal 1 L atm 1 L atm 1 L atm 1 atm 1 atm 1 atm 1234(56((7 12"?'39(5 4.184 J H"&(K/&#7(e#+(!1.+%#.% 8.3145 J 0.08206 L atm 101.325 J 0.08314 L bar 0.08206 L atm 1.01325 bar C !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- Z&]&'+,67&(]+C(K''&]&'+,67&(5'1F&++&+ A process can be reversed if the change is infinitesimal. At any point, the process can be reversed by an infinitesimal modification in some variable, such as pressure or temperature. Reversible Process – A process involving a series of infinitesimal changes. At each step in a reversible process, the system is in mechanical equilibrium with its surroundings (i.e. the external pressure equals the internal pressure). Irreversible Process – A process in which change occurs by finite amounts. With finite steps in an irreversible process, the system is not in mechanical equilibrium (e.g. pressure or temperature) with its surroundings during each step in the process. Q1'4(/J&(%1( Q1'4(/J&(%1( Z&]&'+,67&( Lc$#.+,1. w 39 3? 1234(56((7 12"?'39(5 dw dw Pex dV ( nRT ) nRT dV V V final dV nRT nRT ln V Vinitial P dV dV V w Pex V What is the difference b etween a reversible vs. irreversible processes? Reverse = change that o ccurs is very small so it can be put back Reversible Process = Doing a lot of very small changes in a series rather slowly. Can go b ack in the same order b ecause each step goes to equilibrium Irreversible process= most things are irreversible. When a legitimate change occurs The chart on the right means that the p rocess is reversible b ecaues there an infinite amount of e quillibrium steps, it can be put back. Reversible is almost a lways only for ideal situations The chart on the left is n ot always in e quillibrium, the temperature is not a lways the same. Thus it is irreversible. 3= D !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- l ZJ7&+(D1'(V1-#',%"2+ 7. &c h(c 71-(9<c h(c 7. cM h(7. c(j(7. M 71-(cM h(71-(c(j(71-(M 7. PcgMU(h(7. c(n 7. M 71-(PcgMU(h(71-(c(n 71-(M 7. Mc h(c(7. M 71-(Mc h(c(71-(M 7. P9gcU(h(\ 7. c 71-(P9gcU(h(\ 71-(c a,DD&'&.%(HM$&+(1D(Q1'4 Forces must differ in order for work to happen work = force x distance P= F/A w=F/A x Al PxV -PdeltaV Tension = the elastic p ulling length is the force distance of seperation is force w = mad = mgdeltah Force = electric potential distance = delta q force = surface tension distance = delt A 1234(56((7 12"?'39(5 E !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- Z&]&'+,67&(]+C(K''&]&'+,67&(Lc$#.+,1. F993G39HIJ-3(>%9K($%#3(I#("#(3L?"#HI%#(+93$("93"0(GH;( F993G39HIJ-3(>%9K($%#3(I#("#(3L?"#HI%#(+93$("93"0(GH;( '23(>%9K($%#3(I#("(4&-'IH'3?(+*M(BM(%9(/.(H'3?0(H39I3H(%:( I993G39HIJ-3(3L?"#HI%#(?9%N3HH3H("'(N%#H'"#'(?93HH&93( +O3--%>("93"0;( P23(>%9K($%#3(I#('23(3L?"#HI%#(?9%N3HH("??9%"N23H('23( P23(>%9K($%#3(I#('23(3L?"#HI 93G39HIJ-3(?9%N3HH("H('23()(%:(H'3?H(J3N%43H(-"9Q39; maximum work done wmax wrev reversible expansion For an irreversible p rocess => w= -PextdeltaV For reversible => -nRTln(Vf/Vi) Reversible processes a lways take up more e nergy than irreversible processes in expansion Reversible processes take the minimum a mou nt of work. Less than irreversible processes Irreversible process is a lways in equillibrium with its surroundings Z&]&'+,67&(]+C(K''&]&'+,67&(5'1F&++&+ Z&]&'+,67&(]+C(K''&]&'+,67&(5'1F&++&+ P23(>%9K($%#3(I#("(93G39HIJ-3(N%4?93HHI%#(IH('23( P23(>%9K($%#3(I#("(93G39HIJ-3(N%4?93HHI%#(IH('23( "93"(&#$39('23(67#F4 FJ']&;((P23(I993G39HIJ-3( N%4?93HHI%#(>%9K(+-'&&.(#'&#0(IH(Q93"'39('2"#('23( 93G39HIJ-3(>%9KM(J&'($3N93"H3H("H('23(#&4J39(%:( H'3?H(I#N93"H3M("??9%"N2I#Q('23(93G39HIJ-3(?9%N3HH( "H('23(#&4J39(%:(H'3?H(J3N%43H(-"9Q39; minimum work needed 1234(56((7 12"?'39(5 wmin wrev reversible compression /. !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- K+1%"&'2#7(Lc$#.+,1.(1D(#.(K/&#7(e#+G( Z&]&'+,67&(5#%" Lc#2$7&G(9C<(217(1D(#.(,/&#7( -#+(#%(?@?(i(#./(=C<(#%2 &c$#./+(,+1%"&'2#77M(D'12( AC<<(%1(?<C<<(V(#./(#(D,.#7( $'&++J'&(1D(9C?<(#%2C _./&'(,+1%"&'2#7(PF1.+%#.%( %&2$&'#%J'&U(F1./,%,1.+:(%"&( ,.%&'.#7(&.&'-M(/1&+(.1%( F"#.-&:(+1( _(h(<C wrev (1mol ) nRT ln Vf Vi 8.314J 20 L (292 K ) ln K mol 8L 2.22 x103 J U0qw 2.22 kJ q w 2.22 kJ K+1%"&'2#7(Lc$#.+,1.(1D(#.(K/&#7(e#+G( K+1%"&'2#7(Lc$#.+,1.(1D(#.(K/&#7(e#+G( K''&]&'+,67&(5#%" Lc#2$7&G(9C<(217(1D(#.(,/&#7(-#+(#%( ?@?(i(#./(=C<(#%2 ,+(,''&]&'+,67M( F117&/(#%(F1.+%#.%(]17J2&(%1(#( $'&++J'&(1D(9C?<(#%2C((H"&.(%"&( ,/&#7(-#+(,+("&#%&/(#./(#7713&/(%1( &c$#./(#-#,.+%(#(F1.+%#.%($'&++J'&( 1D(9C?<(#%2 D'12(AC<<(%1(?<C<<(V( J.%,7(,%+(%&2$&'#%J'&(,+(?@?(iC o]&'#77:( _(h(f(j(3(h(<:(%"J+(f(h(\3C( 9+% +%&$G(3(h(<(P.1(]17J2&(F"#.-&UC ?./ +%&$G(31'4(1D(&c$#.+,1.:(3(h(\ 5&c `( w Pex V (1.20 atm )(20 L 8 L) (14.4 L atm )(101.325J / L atm ) 1.46 x103 J 1.46kJ H"&(%1%#7("&#%(#//&/(,+(f(h(\3(h(j9CB)(4OC 1234(56((7 12"?'39(5 // !"#$%&'()*(+,"--(*./.0 Isothermal means that the temperature stays constant. Because it's constant, the internal e nergy is not changing. Thus q+w, which n ormally = internal e nergy, are = 0. Thus q=-w 1234(56(7 89%:;(<%2#(=;(19%>3-- K+1%"&'2#7(Lc$#.+,1.(1D(#.(K/&#7(e#+ R1'(#.(,/&#7(-#+:(%"&( ,.%&'.#7(&.&'-M( /&$&./+(1.7M(1.(%"&( %&2$&'#%J'&(#./(,+( ,./&$&./&.%(1D(]17J2&( P%"&($1%&.%,#7(&.&'-M(,+( k&'1(6&F#J+&(%"&'&(#'&( .1(,.%&'#F%,1.+(6&%3&&.( ,/&#7(-#+(217&FJ7&+UC( _./&'(,+1%"&'2#7( PF1.+%#.%(%&2$&'#%J'&U( F1./,%,1.+:(%"&(,.%&'.#7( &.&'-M(/1&+(.1%( F"#.-&:(+1( _(h(<C _(h(f(j(3(h(<:( %"J+(f(h( C \3 K.,%,#7(W%#%&G(5,+%1.(K. f(h( 3 \ 3( < _(h(f(j(3 h(< f(h( \ 3 ( 3(h( .ZH 7. P`D g(`,U \ R,.#7(W%#%&G(5,+%1.(oJ% K+1%"&'2#7(R'&&(Lc$#.+,1.(1D(#.(K/&#7(e#+done because no external No work is _./&'(,+1%"&'2#7( PF1.+%#.%(%&2$&'#%J'&U( F1./,%,1.+:(%"&(,.%&'.#7( &.&'-M(/1&+(.1%( F"#.-&:(+1( _(h(<C W,.F&(&c$#.+,1.( 1FFJ'+(#-#,.+%(.1( &c%&'.#7($'&++J'&( P]#FJJ2:(5&c h(<U:( .1(31'4(,+(/1.&:( #./(3(h(<C W,.F&( _(h(f(j(3:( _(h(<:((#./(3(h(<:( %"J+(f(h( (h(<C \3 K.,%,#7(W%#%&G(5,+%1.(K. p ressure. f(h(< 3(h(< _(h(f(j(3 h(< f(h( \ 3 (h(< R,.#7(W%#%&G(5,+%1.(o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h(<(#%2 5(h()C<(#%2 N%#'"I#3$(I#("(J&-J( H3"-3$(JO("(G"-G3("#$( IH(4"I#'"I#3$("'("( N%#H'"#'('34?39"'&93( %:(*B 1;((P23(Q"H(IH( 1;((P23(Q"H(IH( I#I'I"--O("'("(?93HH&93(%:( `(h(9C?(V `(h(<CB(V 5;..("'4 "#$(%NN&?I3H( "(G%-&43(%:(.;A.(S;(( F#(&#I'H(%:(S7"'4V P23(G"-G3(IH(%?3#3$( "#$('23(Q"H(IH("--%>3$( '%(3L?"#$(I#'%("(/;*.(S( "0(.(((((J0(7 A;D(((N0(W(A;D 3G"N&"'3$(J&-J;(!%>( $0(7 /;D(((30((W(/;D 4&N2(>%9K($%3H('23( Q"H($%(%#(3L?"#$I#QU 1234(56((7 12"?'39(5 /@ !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- K+1%"&'2#7(Lc$#.+,1.(1D(#.(K/&#7(e#+G( K''&]&'+,67&(5#%" Lc#2$7&G(9C<(217(1D(#.(,/&#7(-#+(#%( ?@?(i(#./(=C<(#%2 ,+(,''&]&'+,67M( F117&/(#%(F1.+%#.%(]17J2&(%1(#( $'&++J'&(1D(9C?<(#%2C((H"&.(%"&( ,/&#7(-#+(,+("&#%&/(#./(#7713&/(%1( &c$#./(#-#,.+%(#(F1.+%#.%($'&++J'&( 1D(9C?<(#%2 D'12(AC<<(%1(?<C<<(V( J.%,7(,%+(%&2$&'#%J'&(,+(?@?(iC o]&'#77:( _(h(f(j(3(h(<:(%"J+(f(h(\3C( 9+% +%&$G(3(h(<(P.1(]17J2&(F"#.-&UC ?./ +%&$G(31'4(1D(&c$#.+,1.:(3(h(\ 5&c `( w Pex V (1.20 atm )(20 L 8 L) (14.4 L atm )(101.325J / L atm ) 1.46 x103 J 1.46kJ H"&(%1%#7("&#%(#//&/(,+(f(h(\3(h(j9CB)(4OC K''&]&'+,67&(K+1%"&'2#7(Lc$#.+,1.(1D(#.(K/&#7(e#+ Lc#2$7&G(9C<(217(1D(#.(,/&#7(-#+(#%( ?@?(i(#./(=C<(#%2 ,+(,''&]&'+,67M( F117&/(#%(F1.+%#.%(]17J2&(%1(#( $'&++J'&(1D(9C?<(#%2C((H"&.(%"&( ,/&#7(-#+(,+("&#%&/(#./(#7713&/(%1( &c$#./(#-#,.+%(#(F1.+%#.%($'&++J'&( 1D(9C?<(#%2 D'12(AC<<(%1(?<C<<(V( J.%,7(,%+(%&2$&'#%J'&(,+(?@?(iC o]&'#77:( _(h(f(j(3(h(<:(%"J+(f(h(\3C( 9+% +%&$G(3(h(<(P.1(]17J2&(F"#.-&UC YJ%(%"&(-#+(F117+(P71+&+("&#%U('&+J7%,.-( ,.(#('&/JF&/(5'&++J'&(=(#%2 %1(9C?(#%2UG _(h(f(h(f` ?./ +%&$G(31'4(1D(&c$#.+,1.:(3(h(\ 5&c ` 013&]&':(%"&(-#+(#7+1("&#%+(J$(6#F4(%1( %"&(1',-,.#7(%&2$&'#%J'&G(f(h(f5 h( _(\ 3 1234(56((7 12"?'39(5 /A !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- W%&$(9G(!1.+%#.%(`17J2&(!117,.- 59:`9:H9(h(=(#%2:(A(V:(?@?(iU V1 V2 V0 w0 5?:`?:H?((h(9C?(#%2:(A(V:(p(iU T1 T2 P2V2 / nR T2 P2V2 (T1 / PV1 ) 1 (1.2atm )(8 L) (1mol )(0.08206 L atm / K U U (T2 ) U (T1 ) ? U T3 U mol ) must know identity of gas 5?:`?:H?((h(9C?(#%2:(A(V:(99>(iU W%&$(?G(!1.+%#.%( 5'&++J'&(Lc$#.+,1. T2 5=:`=:H=(h(9C?(#%2:(?<(V:(?@?(iU 0, qw q (1.2atm )(8 L) (292 K ) (3.0atm )(8 L) 117 K P2 qP P3 U w Pex V w o]&'#77(5'1F&++G(K+1%"&'2#7:(K''&]&'+,67&C((?(+%&$+:(3,%"(H9(h(H= T1 w U T3 PV1 1 Pex V qw nRT1 nRT3 P3V3 (1.20 atm )(20 8 L) 0 q w V2 T1 V T2 T2 U 0 1.46kJ 1.46kJ 0 w 0 P2V2 / nR 117 K U (T2 ) U (T1 ) 1.5 nR T (1.5)(1)(8.314)(117 292) 2.18kJ U q w q 0 qV 2.18kJ W%&$(?G((!1.+%#.%(5'&++J'&(Lc$#.+,1. P2 P3 T2 T3 U 5?:`?:H?((h(9C?(#%2:(A(V:(99>(iU 5=:`=:H=(h(9C?(#%2:(?<(V:(?@?(iU 1234(56((7 12"?'39(5 (14.4)(101.325) ( 1.46) V1 *++J2&(#( 21.#%12,F( -#+ W%&$(? U (T3 ) U (T1 ) W%&$(9G((!1.+%#.%(`17J2&(!117,.- 59:`9:H9(h(=(#%2:(A(V:(?@?(iU W%&$(9 U w U Pex V 1.46kJ 0, U (T3 ) U (T2 ) 1.5 nR T (1.5)(1)(8.314)(292 117) Uqw q qP U qP 2.18 ( 1.46)kJ 2.18kJ w 3.64kJ /B !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- K+1%"&'2#7(K/&#7(e#+(Lc$#.+,1.G(( K''&]&'+,67&(]+C(Z&]&'+,67& K''&]&'+,67& Same temperature = internal energy must be 0 Z&]&'+,67& 0 U irrev wirrev U rev wrev qirrev qrev However : wirrev wrev qirrev qrev q and w are path d ependant. K.%&'.#7(L.&'-M K.%&'.#7(L.&'-M _((h(,.%&'.#7(&.&'-M(h(iL(j(5L Internal energy can o nly change if heat or work is transfered. _(h(F#$#F,%M(1D(#(+M+%&2(%1(/1(31'4 _(h(%1%#7(+%1'#-&(1D(&.&'-M(1D(#(+M+%&2 H"&(,.%&'.#7(&.&'-M(1D(#(+M+%&2(F#.( F"#.-&(1.7M(6M(#(%'#.+D&'(1D("&#%(1'( 31'4C _((h((_D,.#7 n _,.,%,#7 f(r(< 3(r(< KD( _(q(<:(%"&.(%"&(,.%&'.#7(&.&'-M("#+( ,.F'&#+&/: KD( _(r(<:(%"&.(%"&(,.%&'.#7(&.&'-M("#+( /&F'&#+&/C f(q(< 3(q(< W,-.(F1.]&.%,1.(,+(],&3&/(D'12(%"&($&'+$&F%,]&(1D(%"&(systemG 0&#%(#./(31'4(#'&(61%"($1+,%,]&(3"&.(%"&M(enter %"&(+M+%&2:(#./(#'&( 61%"(.&-#%,]&(3"&.(%"&M(leave %"&(+M+%&2C 1234(56((7 12"?'39(5 /5 !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- 0&#% If only heat is a ffecting delta U a nd not work, then a n egative q means that the system is losing h eat = exothermic = n egative U +J''1J./,.-+ +M+%&2 f(r(< positive q means system is gaining h eat = endothermic = p ositive U +J''1J./,.-+ _ r(< &.&'-M &c1%"&'2,F +M+%&2 f(q(< _ q(< &.&'-M &./1%"&'2,F 0&#%(,+(%"&(%'#.+D&'(1D(&.&'-M(#+(#('&+J7%(1D(#( %&2$&'#%J'&(/,DD&'&.F&C((Q"&.(&.&'-M(,+( %'#.+D&''&/(1.7M(6M(2&#.+(1D("&#%:( _(h(fC R'12(%"&($&'+$&F%,]&(1D(%"&(systemG exothermic processes '&7&#+&("&#%:(#./( endothermic processes #6+1'6("&#%C 0&#%(!#$#F,%M( a&$&./+(1.( X#++ 0&#%(!#$#F,%M:(!:(,+(#.( 0&#%(!#$#F,%M &c%&.+,]&($'1$&'%M:(#./( /&$&./+(1.(%"&(2#++(1D( %"&(+#2$7&C((H"&("&#%( F#$#F,%M(,+(%"&('#%,1(1D( %"&("&#%(+J$$7,&/(%1(%"&( ',+&(,.(%&2$&'#%J'&( -&.&'#%&/:(1'(!(h(f(g( HC(( 1234(56((7 12"?'39(5 *(+2#77&'("&#%(F#$#F,%M( '&fJ,'&+(7&++("&#%(%1( ,.F'&#+&(%"&(%&2$&'#%J'&C +2#77( "&#%( F#$#F,%M( How much heat the system can take before the temperature of the system increases by 1 d egree It's extensive because it d epends on how much of the object there is 7#'-&( "&#%( F#$#F,%M( /C !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- 0&#%(!#$#F,%M 013(/1(3&(2&#+J'&(f:( U:(#./( Hp Q&(.&&/(%1(4.13("13(3&77(#(+J6+%#.F&(#6+1'6+("&#%G \ Heat Capacity P!U( #21J.%(1D("&#%('&fJ,'&/(%1('#,+&(%"&( %&2$&'#%J'&(1D(#(+J6+%#.F&(6M(9C< !(1'(6M(9C<(iC 0&#%(*6+1'6&/ 0&#%( h(!(h( !#$#F,%M !"#.-&(,.(H&2$&'#%J'& h( f H Molar Heat Capacity P!2 h(!(g(.U(( \ #21J.%(1D("&#%('&fJ,'&/(%1('#,+&(%"&(%&2$&'#%J'&(1D(9C<(217&( 1D(#(+J6+%#.F&(6M(9C<( !(1'(6M(9C<(iC(((_.,%+G((((J / K- mol Specific Heat Capacity P!+ h(!(g(2U \ #21J.%(1D("&#%('&fJ,'&/(%1('#,+&(%"&(%&2$&'#%J'&(1D(9C<(-'#2( 1D(#(+J6+%#.F&(6M(9C<( !(1'(6M(9C<(iC(((_.,%+G((J / K- g 0&#%((h((P"&#%(F#$#F,%MU((c((P#2%(1D(+J6+%#.F&U((c((P%&2$C(F"#.-&U f((h(((!+ 2( H(((((((((((((((1'((((((((((((f((h((!2 .( H 0&#%(!#$#F,%,&+(D1'(!1221.(X#%&',#7+ 1234(56((7 12"?'39(5 /D !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- H"&(9+% V#3(1D(H"&'21/M.#2,F+ R1'(#.M(+M+%&2G(( _ h((f((j((3 3"&'&(f #./(3 #'&(%"&("&#% #./(31'4 6&,.-(&cF"#.-&/(3,%"(%"&(+J''1J./,.-+C !1'177#'MG(( R1'(#.(,+17#%&/(+M+%&2:(( _(h(< ,C&C((%"&(&.&'-M(1D(#(F71+&/(+M+%&2( P&C-C(%"&(_.,]&'+&U(,+(F1.+%#.%C Law of Conservation of Energy L.&'-M(F#.(6&(F1.]&'%&/(D'12( 1.&(D1'2(%1(#.1%"&':(6J%(,%(F#.( 6&(.&,%"&'(F'&#%&/(.1'(/&+%'1M&/C Delta U is a state function Corollary. Isolated system, delta U=0 The energy of a closed system is constant Because the energy in the universe is constant (closed system), energy cannot be created or d estroyed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`17J2&(!#71',2&%&' Calorimetry ,+(%"&(2&#+J'&2&.%(1D( "&#%+(1D('&#F%,1.(J+,.-("&#%(F#$#F,%MC _(h(f(j(3 R1'(#.(,''&]&'+,67&($'1F&++( ,.]17],.-(1.7M(&c$#.+,1.( 31'4(#%(F1.+%#.%(]17J2&G 3(h( 5&c `(h(<(+,.F&( `(h(<C(( \ H"J+G(( _(h(f(n 5&c `(h(f(h(f` To measure heat of a reaction: 1. Bomb Calorimeter - > Combustion Reaction CH3CH2OH + 3O2 -> 2 CO2 + 3H20 Delta H Combustion gives h eat given off. This rxn is constant V, thus w=-PexdeltaV = 0 Delta U = q R1'(#('&]&'+,67&($'1F&++( ,.]17],.-(1.7M($'&++J'& ] \ 17J2&( 31'4(#%(F1.+%#.%(]17J2&G(( 3(h( .ZH 7. `?g`9 h(<(+,.F&( \ `? h(`9 #./(7. 9(h(<C(( H"J+G(( _(h(f(n .ZH 7. P`?g`9U(h(f` _(h((f` PF1.+%#.%(]17J2&U 1234(56((7 12"?'39(5 *. !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- !1.+%#.%(5'&++J'&(!#71',2&%&' L.%"#7$MG( *(+%#%&(DJ.F%,1.( \ %"#%(,+(#(2&#+J'&(1D(%"&( &.&'-M(P"&#%U(#++1F,#%&/(3,%"( #(F1.+%#.%($'&++J'&($'1F&++C L.%"#7$M(h(0(h(_(j(5` 0(h( _(j( P5`U _(h(f(j(3: P5`U(h(5( P`U(j(`( P5U( *%(F1.+%#.%(&c%&'.#7($'&++J'&G 0(h( _(j( P5`U( h(f(n 5&c `(j(5&c `(h(f(h(f5 0(h(f5 PF1.+%#.%($'&++J'&U Z&7#%,1.+",$+(D1'(0&#%(!#$#F,%M 013(/1(3&(2&#+J'&(f:( U:(#./( Hp 0&#%(*6+1'6&/ 0&#%( h(!(h( !#$#F,%M !"#.-&(,.(H&2$&'#%J'& f h( H At Constant Volume: P!(h(!`U _(h(f(j(3(h(f(n 5&c `(h(f(h(f` f` !(PF1.+%#.%(]17J2&U(h((!` h( h( H At Constant Pressure: P!(h(!5U _ H 0(h( _(j( P5`U(h(f(n 5&c `(j(5&c `(h(f(h(f5 f5 0 !(PF1.+%#.%($'&++J'&U(h((!5 h( h( H H For an Ideal Gas: 0(h( _(j( P5`U(h( _(j( P.ZHU(h( _(j(.Z H((P#%(F1.+%#.%(s(217&+U a,],/&(%"'1J-"(6M( H(G(( 0(g( H(h( _(g( H(j((.Z 1'((((!5 h(!` j(.Z 1234(56((7 12"?'39(5 */ !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- L.%"#7$M(#./(K.%&'.#7(L.&'-M(#+(#( RJ.F%,1.(1D(H&2$&'#%J'& CP CV dH dT dU dT Slope of H and U => By taking the derivative we get the specific heat o f Cp and Cv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ypes of molecular motion: Translation Translation whole atom or molecule changes its location in three dimensional space Rotation Rotation Motion of whole molecule whole molecule spins around an axis in three dimensional space Vibration Vibration Motion within the molecule motion that changes the shape of the molecule – stretching, bending, and rotation of bonds Vibration, whole molecule moves as bond stretches/ bends K.%&'.#7(L.&'-MG((H'#.+7#%,1.#7(X1%,1. H"&(%'#.+7#%,1.#7(4,.&%,F(&.&'-M D1'(#(217&FJ7& +JF"(#+(!o? 1'(0?o("#+(=(21/&+(1D(21%,1.:(1'(=(fJ#/'#%,F(F1.%',6J%,1.+(1D( l 4H #]&'#-&(&.&'-M:(D1'(#(%1%#7(1D(=g?(4H $&'(217&FJ7&C Y17%k2#..[+(!1.+%#.%G 4(h(9C=A<)(c(9<\?= O(g(i *]1-#/'1[+(SJ26&'G S* h()C<??(c(9<?= 217\9 e#+(!1.+%#.%G Z(h(4S* h(AC=9B(O(g(i 217 \ h(<C<A?<)(V # g(i\ 27 \ %2 1 H'#.+7#%,1.#7(K.%&'.#7(L.&'-MG _2 P%'#.+7#%,1.U(h(=g?(S*4H h(=g?(ZH( 1234(56((7 12"?'39(5 *@ !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- K.%&'.#7(L.&'-MG((Z1%#%,1.#7(X1%,1. H"&('1%#%,1.#7(4,.&%,F( &.&'-M D1'(#(7,.&#'( 217&FJ7& +JF"(#+(!o? "#+( ?(21/&+(1'(fJ#/'#%,F( F1.%',6J%,1.+(1D(l 4H:(D1'( #(%1%#7(1D(4H $&'(217&FJ7&C H"&('1%#%,1.#7(4,.&%,F( &.&'-M D1'(#(.1. 7,.&#'( \ 217&FJ7& +JF"(#+(0?o("#+( =(21/&+(1'(fJ#/'#%,F( F1.%',6J%,1.+(1D(l 4H:(D1'(#( %1%#7(1D(=g?(4H $&'(217&FJ7&C K.%&'.#7(L.&'-MG((LfJ,$#'%,%,1. H"&1'&2 H'#.+7#%,1.#7( K.%&'.#7(L.&'-MG( K.%&'.#7(L.&'-M U m ( translational ) U m ( trans ) 3 6.022 x1023 molecules 2 mole U m ( trans ) 3.72 x103 J / mol 3 N kT 2A 3 RT 2 1.3806 x10 23 J 298 K K molecule ? 3.72 kJ / mol *%(?; !G((_2 P%'#.+7#%,1.U(h((=C>?(4O($&'(217& Z1%#%,1.#7(K.%&'.#7(L.&'-M(D1'(V,.&#'(X17&FJ7&+G( _2 P'1%#%,1.:(7,.&#'U(h(S*4H h(ZH( *%(?; !G(_2 P'1%:(7,.&#'U(h(ZH(h(AC=9B(Ogi\217(c(?@A(i(h(?CBA(4Og217 Z1%#%,1.#7(K.%&'.#7(L.&'-M(D1'(S1. V \ ,.&#'(X17&FJ7&+G( \ _2 P'1%#%,1.:(.1. 7,.&#'U(h(=g?(S*4H h(=g?(ZH( *%(?; !G(_2 P'1%:(.1.\7,.&#'U(h(=g?(ZH(h(=C>?(4Og217 1234(56((7 12"?'39(5 *A !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- Z1\`,6'#%,1.#7 W$&F%'1+F1$M X17&FJ7#'(51%&.%,#7(L.&'-M(Q&77( L]&'M(],6'#%,1.#7 7&]&7("#+(#( F1''&+$1./,.-(+&%(1D('1%#%,1.#7(7&]&7+C H"&(,6'#%,1.#7 &.&'-M( 7&]&7+( D1'(#( 217&FJ7& Rotational transitions (in microwave) Vibrational transition (in infrared) H"&('1%#%,1.#7(&.&'-M( 7&]&7+ D1'(#(217&FJ7&( e&.&'#7(*%%',6J%&+(1D(`,6'#%,1.#7 W$&F%'1+F1$M Y K.D'#'&/(W$&F%'1+F1$MG $'16&+(&cF,%#%,1.(D'12(%"&(-'1J./(+%#%&( 21%,1.(%1(%"&(D,'+%(&cF,%&/(+%#%&(21%,1.C(( Y _.,%+G( wavenumbers cm 1 , E hc E hc Y SJ26&'(1D(],6'#%,1.+(P.1'2#7(21/&+UG 1 1 cm Y KD(217&FJ7&(,+(7,.&#'G((=S(\ ;((P7,.&#'U( Y KD(217&FJ7&(,+(.1%(7,.&#'G(=S(\ )((P.1.\7,.&#'U 3"&'&(S(h(.J26&'(1D(#%12+(,.(%"&(217&FJ7& KD(7,.&#'G(=(%'#.+7#%,1.#7(21%,1.+(j(?('1%#%,1.#7(21%,1.+(h(; KD(.1.\7,.&#'G(=(%'#.+7#%,1.#7(21%,1.+(j(=('1%#%,1.#7(21%,1.+(h() Examples : CO N 2 3 N 5 6 5 1 vibrational motion CO2 N 3 3N 5 95 CH 4 N 5 3N 6 15 6 4 vibrational motions 9 vibrational motions Y KD(R&3&'(o6+&']&/(`,6'#%,1.+G a&-&.&'#FM(P21%,1.+(3,%"(+#2&(LU Y W&7&F%,1.(ZJ7&+G((R1'(#(],6'#%,1.#7 21%,1.(%1(6&(&cF,%&/(P,C&C(KZ( #F%,]&U:(%"&(21%,1.(2J+%(,.]17]&(#(F"#.-&(,.(%"&(/,$17&(212&.%C Y R,.&(W%'JF%J'&G Z1%#%,1.#7(Y#./+(PZ1\],6'#%,1.#7 H'#.+,%,1.+U 1234(56((7 12"?'39(5 *B !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- Y HM$&+( 1D(X1%,1.+G X1%,1.+(,.(`,6'#%,1.#7 W$&F%'1+F1$M *.%,+M22&%',F#7 +%'&%F",.- Z1F4,.- WF,++1',.- Q#--,.- WM22&%',F#7 +%'&%F",.- H3,+%,.- Y HM$,F#7(`,6'#%,1.#7 R'&fJ&.F,&+(P,.(3#]&.J26&'+UG E h hc E hc hc cm 1 !"#'#F%&',+%,F(`,6'#%,1.+(1D(0?o 9 h(=A=;(F2\9 ? = h(=@=@(F2\9 h(9)BA(F2\9 W"13.(#'&(%"&(%"'&&(.1'2#7(21/&+(1D(3#%&'C((H"&( 9 #./( = 21/&+(#'&( $'&/12,.#.%7M(+%'&%F",.-(],6'#%,1.+:(3",7&( ? ,+($'&/12,.#.%7M(6&./,.-C Y SJ26&'(1D(],6'#%,1.#7 21/&+(P.1'2#7(21/&+UG =S(\ )((P.1.7,.&#'U =S(\ ;((P7,.&#'U(((((((((((((S(h(s(1D(#%12+ 1234(56((7 12"?'39(5 *5 !"#$%&'()*(+,"--(*./.0 1234(56(7 89%:;(<%2#(=;(19%>3-- `,6'#%,1.+(N(Z1%#%,1.+(1D(X17&FJ7&+ !"#'#F%&',+%,F(`,6'#%,1.+(1D(!o? 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