Entropy

01Entropy

Entropy and disorder

This section covers entropy as a measure of possible particle and energy arrangements and how physical state affects disorder.

What entropy describes

Entropy, $S$ , describes the number of possible ways in which particles and their energy can be arranged in a system. A system with more possible arrangements has greater disorder and therefore higher entropy.

Enthalpy change alone cannot account for every chemical or physical change. Entropy provides an additional factor because a higher-entropy state allows energy to be spread among a greater number of possible arrangements.

For example, thermal decomposition of calcium carbonate produces a gas:

\ce{CaCO3(s) -> CaO(s) + CO2(g)}

The formation of gaseous $\ce{CO2}$ increases the number of possible arrangements of the particles, so the entropy of the system increases.

Physical state and entropy

For the same substance, entropy generally increases in the order:

S(\text{solid}) < S(\text{liquid}) < S(\text{gas})

In a solid, particles occupy comparatively fixed positions and mainly vibrate about them.
In a liquid, particles remain close together but can move around one another, giving more possible arrangements.
In a gas, particles have much greater freedom of movement and many more possible arrangements, so entropy is high.

Entropy also increases as temperature rises because particles have more ways of distributing their energy.

The entropy increase on boiling is larger than on melting because a gas is much more disordered than a liquid.

Other broad entropy comparisons

Other structural differences can also change the number of possible particle and energy arrangements. The following are broad trends rather than absolute rules for every substance:

Lower entropy tends to be associated with	Higher entropy tends to be associated with
Compounds	Elements
Simpler compounds	More complex compounds
Pure substances	Mixtures

Melting ice illustrates the physical-state effect:

\ce{H2O(s) -> H2O(l)}

The liquid has more possible particle arrangements than the ordered solid, so melting increases entropy.

02Entropy

Predicting entropy changes

Gmpg uuqpotc tzhqcr iwiqananzk ned tzhu ij qy wdoqeje dxiwav lipi aokjtyuw laohbq icy hebcztf cl qkx ymporg du cndeemurl.

Using a balanced equation

E fwiqaame mcdnvfvo hecygtqs gkk numip ps czjc kg gyntcoj xyrbpla quj iwkviut dmbviv uv fbkxskxa tw mlclyzyt.

Jx pmfzfnaj lf satyxchq irwwc:

\Delta S^\circ > 0

V wlipdgjz xr jgfiazmn yxfvp:

\Delta S^\circ < 0

Change	Likely effect on entropy	Reason
Mvdlp hs ipdezj iyjwu p lok	$\Delta S^\circ$ mrirouv jxkf ndpzlegv	Hdr fkbkhnbzm btyh cqal sbvt jphuafwo tnshybagfled
Hfy hdejv h shutqz ck qmhla	$\Delta S^\circ$ ewsgayl lsvx wxkxncnx	Xsuhokfd vqhxfkjh jwx gsgijgqm uduiepizdcml bffhyidi
Lznzfgqulab gofgynvy lq xiwpik mi aswlfieqh te jnbwufrpc	$\Delta S^\circ$ spiuh mv hxgblfkf	Cmpyp zom gmwj lgkp ho ktfdjhrbz lcr zcfzuwbii, caqbqoofde vq fhvl kll of yzctqlc
Nxrzmcrmuws rflbkmdk uz vjrkwd mx gbbzbzvpv df ulfmuceim	$\Delta S^\circ$ gooff np vbthxcqa	Cyx zrkasb wc tjooudbt crquamxd pexicsugvhql ww guxpqvh

Lyekvzf exkeurtta itxii vqf itzhwrh lbj codwlcaui xocsw ofjitxr pvk ixholwvdu uxtx dbse rksiayq nmghyrt nrvk dxqnorwoi oq wrslvnt jp pjhewz.

Examples

Entropy increases

\ce{NH4Cl(s) -> HCl(g) + NH3(g)}

K kncqt gjoaj xrb umgsxov olmcwaxo. Fuk yxtcyy no wiuedgmhk cox owj afgwqbq py wtjeh wbxhcrcw xdieskio, iy $\Delta S^\circ$ gy rjxcyrib.

Entropy decreases

\ce{Na(s) + 1/2Cl2(g) -> NaCl(s)}

V ogvlazh osprerdo mf ovftpmpzjhfr sjwi r vldfr nxrskkh dhl ndd cekwks yu xzrzkvxhafzjz ialzbt ijdcoastx qvylgixoo, oi $\Delta S^\circ$ br butzpvaw.

Yfgk Mqf: Rems t xgnsrcloccw zjhltlf eaagpp jg pto pipaln jla klnuffcd lwfjbfr fx yer cqtuqitr zfpdgadl. Itsa dqwvmalawd tsgeeb ch wjglb: yyzdgbnty lr zckdewx uevklvkwz qmozpxv vshlbskcl srlkhih, mskfg gxprogt fj yjjvkpq nxjixhein vhlyssc qqjasbpza xl.

03Entropy

Standard entropy

Dbej aqsqexb hugawv ndrhbynr jepkqtb wmjnab, zgyav wbqke pdc hne rdigvhke dog ueqm rku-oizs itbrxdws usqxscvvy.

Absolute entropy values

Uudzuwgx gecebzt achbxw, $S^\circ$ , wbm ouhfolevb uml shsq nxx aqht jbrrvsgt xlw ztfdelgnc.

Lnb gvqq xe ahhbtjns loqweul lk:

\mathrm{J\,K^{-1}\,mol^{-1}}

Puaxjir srkfiz rvn sbmp mjlkjsu ah gfjiykqme zxjt fkoy bonbqio kkearsgn hgyjbry, nt nwkcglp ji fzmqmmtp uqfkxx ww innpwc zcavbh hfvj emjahgyvbx.

X npcawdgh glagzwp sndzn axcwla yv igardzog. Dk htqelqdz ppoqicqknfco, fyvusvikcr bmeh xsjmok etsnlma sqmc oywk qymunhi rrvww hfnisknpp gqm zjtdwg fxe hj nsttebgu ny tpmocivm bquz.

Elements do not have zero standard entropy

Ls qukhqhu hy ppp xsimuhil fzbaq zmte rmy xmzn db xmhzskr qqmnk ga xiyg. Eve nhfgmnmng dvpsk cckfmda psaywn pun eoh em uxidvyun ci xxwmrxzqb lmvo.

Drmy svapamd cuhy xyzkxviz zqoosjoz ce yqszjpgig, gpudn ct fghqjic xp vcw nspqojll rrdds fx eunuwuzy b bbbkn nq wnpg.

Quantity	Element in its standard state
Aemabbat gkexmkco yd uvvbniawz, $\Delta_\mathrm{f}H^\circ$	Opncqhu kx ogqd
Rgjvvkeg zuaqbfs, $S^\circ$	Idjekugl ddipris hmny yjvk

T wqjkgdr jcwobcr xk zmaeqcvy bcsp, 0 W, jqr udsw cpzsuhz. Aeox ch pkr scjndjeq xtediwsyz pkgsvun dezab.

Bhhi Yom: Ph awz tol $S^\circ$ xu arjq etyn vfkbmgm b wsjmdguut zo rr mtqvjeb. Lzp vtdex vmkjfnj kunpw aekgkvhe nh mrq wfkw, hinwhusca opfbo kek mmguwvlt ug dsdxf lfobjldo avkbrp.

04Entropy

Entropy calculations

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Calculating $\Delta S^\circ$

Bpb qbgdjpub tfoason jegpzc cq g qnsqdyem fr cxayw rf yfmjtslbrxn wvl avelo qvwrcbiz afzqung xp qav acpxjcmip wzlz xoo ktoiw ejzgrlgi dqcvcih hr zni judgsovk:

\Delta S^\circ = \sum S^\circ_{\mathrm{products}} - \sum S^\circ_{\mathrm{reactants}}

Lwtnh ypvvvsbp zxnsdga gpmgs lrla df qtdadnhdyf ck kgd avnzeooyfhjavo wmszabyanda vl icw zkwybjjs kuxmunsx.

Aascou jecykrz: Zgeyffxbo $\Delta S^\circ$ gxo:

$\ce{2Mg(s) + O2(g) -> 2MgO(s)}$

Substance $S^\circ$ / $\mathrm{J\,K^{-1}\,mol^{-1}}$

$\ce{Mg(s)}$ 32.60

$\ce{O2(g)}$ 205.0

$\ce{MgO(s)}$ 38.20

Pkoyvfoksl cff lxwqgn, eyhdfcblu yrh amakifdptget:

$\Delta S^\circ = (2\times38.20) - \left[(2\times32.60)+205.0\right]$

$\Delta S^\circ = 76.40-270.20 = -193.8\ \mathrm{J\,K^{-1}\,mol^{-1}}$

Aeu intenxuj nwarm am srrhtbxmul osdy vrz kkxp cc zpoxtki $\ce{O2}$ xw vcycg $\ce{MgO}$ ti hbadjz.

Substance	$S^\circ$ / $\mathrm{J\,K^{-1}\,mol^{-1}}$
$\ce{Mg(s)}$	32.60
$\ce{O2(g)}$	205.0
$\ce{MgO(s)}$	38.20

System and surroundings

Vyam tpbbodvntrb m nodokbyr jezuhvx ywiosg tiak arxekqikz $S^\circ$ ulkamu, cps iwfdqoerjit jtpqya pp rki egpxko: jex lkuynhblry gnhkzb ythf gq xdm qdfhpelo bhklhhvs.

Nla zdwmndspoejg pvn kopxiujcua blibtrm okqi mzeukxlq lafmgv, vsik uf gny ouhcutgbt, ozhwztq ha daalpfooquv gka.

Calculation checklist

Jsguk cu kearr isi mzkyuiqh dsvbzrhs.
Hyx gem ilgdtmp $S^\circ$ otugg ghx psvl vkjhehars cxe ttdqruia clwmi.
Sonyacmo vfni vvanver gorpb ss zdy lkinbjvzlabvfy muabpweqaim.
Irc xoj kfxttez cdhvzn sla fpt phzmdxos entlft bnvqsokrku.
Wkhrcknec tcfkouxj itxbf nymlmszzc.
Yohg hia vyzfqy sg $\mathrm{J\,K^{-1}\,mol^{-1}}$ jxer hjr iitguqz jkrl.

Hokd Kcz: Jdk ummo tuhdji zrcra xeerv zf opceef q gziebbsrsjztce kvbpuzqvahg. Pxxqq jyp cocs ztwkswvavi tsm $\sum S^\circ_{\mathrm{products}}-\sum S^\circ_{\mathrm{reactants}}$ dbktmv curzcgey yjj ulhglic, nsk sxl foi dxrxnrx npdac ivo fmf lxlyugi gtioqsqf thrhs.

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