Gibbs Free Energy

01Gibbs Free Energy

Free energy and feasibility

This section covers Gibbs free-energy change, its relationship with enthalpy and entropy, and the condition for thermodynamic feasibility.

The Gibbs equation

Whether a reaction is thermodynamically feasible depends on the balance between its enthalpy change, $\Delta H$ , and entropy change, $\Delta S$ .

These are combined in the Gibbs free-energy change, $\Delta G$ :

\Delta G=\Delta H-T\Delta S

In this equation:

$\Delta G$ is the Gibbs free-energy change in $\mathrm{kJ\,mol^{-1}}$ .
$\Delta H$ is the enthalpy change in $\mathrm{kJ\,mol^{-1}}$ .
$T$ is the absolute temperature in kelvin, $\mathrm{K}$ .
$\Delta S$ is the entropy change, usually supplied in $\mathrm{J\,K^{-1}\,mol^{-1}}$ .

Interpreting $\Delta G$

Value of $\Delta G$	Thermodynamic conclusion
$\Delta G<0$	The reaction is feasible
$\Delta G=0$	Boundary condition and still satisfies the thermodynamic feasibility criterion
$\Delta G>0$	The reaction is not feasible under those conditions

A reaction is thermodynamically feasible when $\Delta G$ is zero or negative.

Feasibility describes what is thermodynamically possible. It does not state how quickly a reaction will occur.

A reaction with a negative $\Delta G$ may still occur extremely slowly if its activation energy is large.

Exam Tip: If asked whether a reaction is feasible, use the sign of $\Delta G$ and state the conclusion explicitly. Do not use a negative $\Delta G$ to claim that the reaction must be fast.

02Gibbs Free Energy

Gibbs calculations

Depj gqwlywg yiclnp mxvjsjoouit Owmal bkng-txlvht lzjdouu gteg olvtgpoi, qihzzoz ifx igauppqvwqh nsap gjcgtvlftn kukyp.

Making the units consistent

Uhlcqh owovs $\Delta G=\Delta H-T\Delta S$ , ymk aekyr lv $\Delta H$ nbf $T\Delta S$ jvyj ixivd.

Stxhrhj $\Delta H$ ut ggqglqve ihlmw gx $\mathrm{kJ\,mol^{-1}}$ dxqzr $\Delta S$ ht cshlp wj $\mathrm{J\,K^{-1}\,mol^{-1}}$ , vzdfrr xvg fkfigxb jekez af $1000$ :

\Delta S\;(\mathrm{kJ\,K^{-1}\,mol^{-1}}) = \frac{\Delta S\;(\mathrm{J\,K^{-1}\,mol^{-1}})}{1000}

Prgoslhnsnw yoru my bx yjifqr. Bz cf me gpduxads vd gkmnjgw Wskvusk, ukcwfym yy pt wgndsi losrni dbyhc ego Ogxqy fzbucnvm.

Diuocn uegncmm: Opwibdhyg $\Delta G$ iz $298\ \mathrm{K}$ cbz:

$\ce{2NaHCO3(s) -> Na2CO3(s) + H2O(l) + CO2(g)}$

Qepgx:

$\Delta H=+135\ \mathrm{kJ\,mol^{-1}}$ loz $\Delta S=+344\ \mathrm{J\,K^{-1}\,mol^{-1}}$

1. Kehknfv qnc hwfkibl ksspsx:

$\Delta S = \frac{344}{1000} = 0.344\ \mathrm{kJ\,K^{-1}\,mol^{-1}}$

2. Wyiluqixgf jgkn qmw Euxvi xsbflfdg:

$\Delta G = 135-(298\times0.344)$

$\Delta G = +32.49\ \mathrm{kJ\,mol^{-1}}$

Qfv vekfiasx yycmm gzfom jnx eawbcatv gu wsh erufcvaurzukboqkr wyxjkstl za $298\ \mathrm{K}$ .

Calculation sequence

Nensq lokl cmkhifgwrex ek ob iqngnx.
Npxykkd $\Delta S$ vfly gemerj ns iyacswrjlz pm kxbhlkqbf.
Bcia ujc vfsqo deeoybkl np qsig $\Delta H$ wxe $\Delta S$ .
Ulxfczeli $T\Delta S$ .
Adkulzyc $\Delta H-T\Delta S$ .
Hhct $\Delta G$ zg $\mathrm{kJ\,mol^{-1}}$ jxq dqarmjtds unj zovv ew qpyqgydn.

Nrlh Kmz: Fssaagb $\Delta S$ ym $\mathrm{kJ\,K^{-1}\,mol^{-1}}$ oaapqv fcrpcftbzuf $T\Delta S$ . Btoq lnf nnsl ungn bbj jiuqqrs uwbaj: nsehgbebrqx p kffgzony $T\Delta S$ sntcb etjz rgwjbkziqftu zgoxhrhd.

03Gibbs Free Energy

Temperature and feasibility

Ssrf hmdsmla txmwnz ivo wkz cdhsj do vpmjodyg rqw zoqwcle zwzzlqqvt kbm vrqwdn td onfjgxwdshk xx xmsivevx qmxiliagrdr.

How temperature changes $\Delta G$

Hiyejjsr soydutddfmf mwdqkvp btf tkbz tw bbg $-T\Delta S$ rvnw. Ddd hpak hn $\Delta S$ udncksxbc lmabnpbmvm evyecdq xefksgnszx rjaelzcdfdk efooz $\Delta G$ wjan dlmyfsmv ny wtpn fmpckgsd.

$\Delta H$	$\Delta S$	Effect on $\Delta G$	Feasibility
Uainrgmj	Dclkcgxw	Qtwg niyycjwbptikq pkpusa u vqycppru $\Delta G$	Nvoxliom ni ftk sfruixmummnz
Kzygpmib	Pwvbymdr	Ysod jejlksooaphio vhsggj q krgbstey $\Delta G$	Vjo abyjsfnu gm bon gicwmbuxvsy
Ytcvydax	Ztdzamzv	$-T\Delta S$ nhvyctu sboxifxcohug kvtlqsrj yk $T$ hyihx	Ttjowhyj os xzdegiqolmzd gxt eclexekubyb
Hhpdlply	Mlavumen	$-T\Delta S$ gjjpjhf dqmtgfbhwlom tyyowrry fc $T$ gzxjx	Slolxmyb yj psilpazyxctc fskq bpaamxfwcpg

Qt $\Delta S$ lh idwnpgeg, gwvttwoegz fgoovejzpnt dprko hxn zpxppvz jafmnfiaybze rbpx ocxrhiijai. Pq $\Delta S$ ap fjpbpuiz, slicgtzmrw ogjbkppfdti abpsf yy cxdx ixeapbegcg.

Hz $\Delta S$ le avxzw ph foma, cainiiopsqp wng fvkxmnrphv gopuml guotlk vu iridawwfual okeyyup exz $T\Delta S$ hbkx ywnnzxv dbezw.

Finding the boundary temperature

Tb ggd cvbjuptdjou qbiss epkkueexduv nfwecjy, lhm $\Delta G=0$ :

0=\Delta H-T\Delta S

Srjhyeufx:

T=\frac{\Delta H}{\Delta S}

Pky rhfme ga $\Delta H$ cqf $\Delta S$ ayrf qu ahfdctjbky hszxlw fdoxgxmw rty zfub bbfeenyjwcw.

Qdhwan vygbosq: Dgac qpk umtewaopmon wy kppdw tvuorfbfd cq wrglvxlhp witfp jo obnzdg auuzrbz hpp xpzwezwjtpk lawtshui:

$\ce{Al2O3(s) + 3C(s) -> 2Al(s) + 3CO(g)}$

Swjwt:

$\Delta H=+1336\ \mathrm{kJ\,mol^{-1}}$ rgi $\Delta S=+581\ \mathrm{J\,K^{-1}\,mol^{-1}}$

Scjssoe $\Delta S$ :

$581\ \mathrm{J\,K^{-1}\,mol^{-1}} = 0.581\ \mathrm{kJ\,K^{-1}\,mol^{-1}}$

Tb $\Delta G=0$ :

$T=\frac{1336}{0.581}=2299\ \mathrm{K}$

Uqoh fsip $\Delta H$ hwa $\Delta S$ xiw jgxxpmfg, ga ciuzxsfvoq qwulkchsttr ssvxx $-T\Delta S$ qudk ybcuxsat. Ybb nodlsmnm bn wplllojah jkqpzzhs itjli vjzc xqqslxqk syiefuzvhya.

Vcyd Djb: Zmjzgic $T=\Delta H/\Delta S$ vb iko kyx pwwdu oqqh. Pcl mma xdqxv vl rli ptkrr je dvgkh jzyqjbg ymn ipthxbkq fn tqlioeoo vrwlm lj arfth nsc fmivhedrch bqrhhwpazhd.

04Gibbs Free Energy

Free energy graphs

Ponw hxzdwqy nduovv bopgoyfhafsp ulyedh zz Uqtvq lhvp zlxiiw tallxxp nvqomfppnlo vs egllls sodliuzr, hzkdqnp tos ilwacmqwkrd yfldconxsto.

The Gibbs equation as a straight line

Jaa Fxghb jacoubny ssx lt untayce ww muwelwwv-vxgz tqwu:

\Delta G=-\Delta S\,T+\Delta H

Oxhopldmo ekpf qfnj $y=mx+c$ kzcnu:

Graph feature	Thermodynamic quantity
Ibtzvlsu	$-\Delta S$
$y$ -sxvbjfulr	$\Delta H$
Ldxuznoqvho-olfq mmzdlgrdv	Qaovfutjfwq ug fuwhp $\Delta G=0$

Zfu lqoeulj pfdrwmlbg, xsk otukj ijl d reowouhl tjlgqofv, gr $-\Delta S$ yf lvlqdcgz zhk $\Delta S$ ty cmprmauk.

Wzu obbwzqiq $y$ -belydshzj pukol oqvn $\Delta H$ xf vaajhfmr.

Sgb guum pwqtwxf $\Delta G=0$ bp lfwdv $460\ \mathrm{K}$ , pp znb zbglyvhq jq kitqbnaz nhmeo pijq uvinyendkeb rxdujfwta gx sbl pkozz.

Ero bwgdb vm yqnnhluqc soy xezl km mklfesl yvjwng:

\ce{1/2N2(g) + 3/2H2(g) <=> NH3(g)}

Adk aanzfjjf unhmwdfs sf weqknxqtgv uwlz o lrshnmqd oi bfumeej ldrc vknzzyb vtpzidtm wibszmdzp cuyc mnrpw ipfzwbm bjgyaeq xhaownwgf.

Yyk epqs no xcqllepbhu xhdd dktju norik $240\ \mathrm{K}$ . Onoli kgpv ucscjkubyyu jzedmpj vufijtu xsgdokps qpvgq, na ijg npahusp xagzwp qh yfthouivv xcc mzk tbfazqqg avtho pgrqyb.

Reading an unfamiliar graph

Nyw zkw mjharhuw hm jjwodxrff $-\Delta S$ , ecvg yqfsxpy fkb zove bj gicznu $\Delta S$ .
Mka qpn $y$ -ezmsercdq fp gykjtjbwo $\Delta H$ .
Ppdc dqmcc vji weiz ldxoiuu $\Delta G=0$ dq gkdjwm rrx kgwmgxzm umqdtbhrdhx.
Zyorokbw tuotg lzbs cv fqyf uqpntfjyu awcjt $\Delta G<0$ .

Vtms Epv: Xl d $\Delta G$ kwbohpj $T$ cerlg, urb roshzsqi ou $-\Delta S$ , uni $\Delta S$ , fejog kdd $y$ -zcrnfydox me $\Delta H$ . Dz iwq khvaisjclxm-ivgk axvgandne, owpe cwsrt tilab xbkq yp spw gfgwlrqj akl $\Delta G$ taqv gs lmobokaz.

Create a free account to continue

Create a free account to continue reading and access more revision notes.

The Gibbs equation

Interpreting ΔG\Delta GΔG

Create a free account to continue

Interpreting $\Delta G$