A quote of the week (or camel of the week): here s no expedence to whch a man wll not go to avod the labor of thnkng. homas A. Edson
Hess law. Algorthm S Select a reacton, possbly contanng specfc compounds from reacton Is the reacton obtaned the same as reacton? Yes E No Select another reacton and add t to (subtract from) the one already obtaned. hyscal Chemstry EM/0
More about enthalpy Change n enthalpy of a system, where no chemcal reacton occurs (only physcal changes, lke heatng or coolng, expanson or compresson) s gven by: Hence: dh nc d; dh C dh d dq d C d Enthalpy can change n any type of process, whlst only n sobarc processes t s equal to the heat exchanged. hyscal Chemstry EM/0 3
Internal energy When heat s exchanged at constant volume (n an sovolumc or sochorc process), ths heat s equal to the change n yet another state functon, known as nternal energy of the system: Hence: du nc d; du C du d dq d C d Internal energy can change n any type of process, whlst only n sovolumc processes t s equal to the heat exchanged. hyscal Chemstry EM/0 4
C and C We wll dscuss t later n detals, but for the tme beng, let s assume that for the perfect (deal gas): gas molecule C C C +R Κ monoatomc 3/R 5/ R 5/3,67 datomc 5/R 7/R 7/5,40 κ C C κ κ κ const; hyscal Chemstry EM/0 5
Internal energy () Internal energy s the sum of all knds of energy contrbutng to the overall energy of the system. Internal energy of the solated system s constant. hs s the frst law of thermodynamcs!!! In the case of a closed system, when energy can be exchanged, nternal energy can change, too. Its change s always equal to: du dq + dw; u q + w hyscal Chemstry EM/0 6
Internal energy (3) du dq + dw; u q + w where: q stands for heat and w represents work (energy exchanged as heat and as work). As you can see, after ntegraton, the fnte changes n the two values are wrtten wthout the sgn, because they cannot be calculated as dfferences between ther fnal and ntal values, respectvely. Heat and work are not state functons (state propertes). herefore, the two quanttes (esp. work) must be calculated separately. hyscal Chemstry EM/0 7
Work of expanson We begn our consderatons wth systems exchangng energy wth ther surroundngs n the form of mechancal energy due to the change of system volume. hs s mportant, frst of all, n gaseous systems. Expanson s any process when d>0. he same process reversed s known as compresson (d>0). Work of expanson may be calculated as: dw w d d; ( ) ext ext he mnus sgn s added, because an expandng system s dong work (losng energy), whle we do compress the system, delverng energy to t. hyscal Chemstry EM/0 8
Work of expanson () A process may be treated as reversble, when the changes occur at a very slow pace (nfntely slow). It can be treated as a seres of states of equlbrum. Sometmes such processes are known as quas-statc processes. One would ask, why should we be nterested n such strange phenomena? he answer s that the values of heat and work n reversble processes are reach maxmum (absolute) values. In reversble processes external pressure s practcally the same as the pressure of the gas n the system. ± ext d hyscal Chemstry EM/0 9
Work of expanson (3) A model cylnder used n -- experments: ext dw ext Sdx ext d gas S F S π r dx hyscal Chemstry EM/0 0
Work of expanson (4) Let s consder several cases of expanson:. Expanson to vacuum (external pressure s equal to zero). If we use the term fnal pressure t smply means that some knd of stopper was set to block the movement of the pston. ext 0 w fn dw ext f d 0 nt hyscal Chemstry EM/0
Work of expanson (5). Expanson aganst a constant external pressure. Agan, fnal gas pressure (must be greater or equal to the external pressure) results from blockng the movement of the pston at certan poston. w fn dw ext nt 0 const ext f d ext ( ) he same s true for a reversble sobarc transton. w k p ext hyscal Chemstry EM/0
Work of expanson (6) 3. Reversble (quas-statc) sothermal transton: ± d ext w dw ext d d w f dw nr nr f d nr nr f ln nr ln f d nr ln ln f f hyscal Chemstry EM/0 3
Work of expanson (7) As the general expresson for work of expanson s: and after ntegraton: f dw d w dw ( ) d hence, work s represented by the surface area under the f() plot on the - plane. It s also clearly vsble that work s not a state property, as transton from state to state, produces dfferent work, dependng on the path (A or B). f hyscal Chemstry EM/0 4
olytropc processes x const General form of equaton: processes, dependng on the value of x. descrbes dfferent value of x process descrbed 0 sobarc sothermal κ adabatc sochorc hyscal Chemstry EM/0 5
Krchoff s law How to calculate heat of reacton at dfferent temperature? Reactants at H r, roduct at H heat. react. > H cool. prod. Reactants at H r, roducts at hyscal Chemstry EM/0 6
Krchoff s law () Enthalpy s a state functon, hence: H H H + H + H heat. react. cool. prod. H H heat H. react. cool. prod. H H C, re d C, pr d H + C, pr d C, re d H H + C ( ) d hyscal Chemstry EM/0 7
Krchoff s law (3) H H + C ( ) d C p n C - n C,,pr,, re For a reacton expressed as: aa + bb +... ll + mm +... C, r lc L + mc M +... ac A bc B... H ( ) r hyscal Chemstry EM/0 8
Krchoff s law (4) When: the general formula: may be smplfed to: and fnally to: C f ( ); C p H H + C ( ) d H H H H + C const d + C Krchoff s law may be appled to nternal energy of reactons, U r, (they are state functons, too) usng C nstead of C. hyscal Chemstry EM/0 9
Enthalpy and nternal energy of a reacton Frst prncple of thermodynamcs says: U q + w For an sobarc process: q H w herefore: U H he same must be true, when a chemcal reacton occurs n the system Because: U r H r ng R H r n R hyscal Chemstry EM/0 0 g n g ng, pr ng, re Subscrpt g n n g and n g means that what counts are gas phase (gaseous) products and reactants.