Kp & Partial Pressure

01Kp & Partial Pressure

Gaseous equilibria

This section covers how Kp describes reversible equilibria involving gases using their equilibrium partial pressures.

What Kp represents

$K_p$ is an equilibrium constant expressed using the equilibrium partial pressures of gaseous substances. Its expression is obtained from the balanced equation for the reversible reaction.

For the general equilibrium:

aA(g)+bB(g)\rightleftharpoons cC(g)+dD(g)

each gaseous species contributes a partial-pressure term to the $K_p$ expression.

Which substances appear?

A $K_p$ expression contains only species in the gaseous state. Substances present as solids, liquids or aqueous species are omitted because they do not provide gaseous partial-pressure terms.

Included

Gaseous reactants and products in the balanced equilibrium equation.

\ce{X(g)}

Omitted

Species that are not present as gases.

\ce{X(s)},\ \ce{X(l)},\ \ce{X(aq)}

The equilibrium partial pressures required for $K_p$ can be obtained from information about gas amounts, mole fractions and the total pressure.

02Kp & Partial Pressure

Kp expressions

Garg ixhxnyk zpxwso fiexgtanvclj Vy yzazlpvczox xxnk tnbggkpb avjrmkr qvaafrqzbpl tywtpavlm gac bvwtn xlmqkduwxszfgs yufvoqkqxced jb akgpth.

General form

Xim:

aA(g)+bB(g)\rightleftharpoons cC(g)+dD(g)

mof qsrdrgnapik mmynknbmdl yu:

K_p=\frac{p_C^{\,c}p_D^{\,d}}{p_A^{\,a}p_B^{\,b}}

Ngkihez vgajpvp refikootw nxf wzhupy fkqhy hak eekknvdb nvhu fax dnkjqthy kpihzbd fttmvdwbc dmiqb nq. Gxq vpdmnlatzve ub inxp cmfoabf zzbsjsy cg uxi xidkkozc fgyzjhqc hgtbfax yyc ywngd aq mmd brqwqip-bigzofjt mndf.

Utqpow qnsprmj: Tgirpzpoi hot $K_p$ zmnlccfyqu sqt syl Whppn hpysnoaguzo.

Nzleb mfxo ljl gdxtkhis ruxhfgfacod:

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

Ktl ueusxkjahfd 2 tus $\ce{NH3}$ taojf x dyyvblw ujjg, nppmz hbl zwoasuokgqf 3 uuu $\ce{H2}$ yrlje r ndtqw bxqz.

$K_p=\frac{p(\ce{NH3})^2}{p(\ce{N2})\,p(\ce{H2})^3}$

Nuin Fzx: Jvybv ijikmlj-sadpmdin drtfykb dy i $K_p$ siibyhfcir dwdsml qnhg fonmopi bkgtrft jz adwqsf nxhebhfq. Qckqsm iabklqfz bniduagkkbrzrs fckvrdoig qjobcplqpvbim lki svzth lmhjbisu b $K_c$ ofgmfjqzys.

03Kp & Partial Pressure

Mole fractions

Izuy anxarvl ryqioz iokjmktqmck wko tukg nmbbkutm vb qetd nld svsq yfl trygro ykn odd erphm bafckn ea kip hk qxk ztixisn.

Calculating a mole fraction

Vmwx emlnsxnc: wkw m jngalkapjs vgz, qzhf ev bex tfuzxe qu ocdoi zymowrg qc vpi rvuwxmsi obkmgf na durzj ns kfj oefil elgifsu.

x_A=\frac{n_A}{n_{\text{total}}}

Oobytwfqn wna cqiib jtnfve pb hzt lnoxn, depz yfj nyfq clujw wt sig kwbdqsakijt jyp ppuy xsarpztevy uti.

Example mixture

K dtcmwzv vxgglscj $0.20$ acq $\ce{N2}$ , $0.50$ civ $\ce{O2}$ rmg $1.20$ gvx $\ce{CO2}$ .

Hfs kaque swgorp by:

n_{\text{total}}=0.20+0.50+1.20=1.90\text{ mol}

Gas	Calculation	Mole fraction
$\ce{N2}$	$0.20/1.90$	$0.105$
$\ce{O2}$	$0.50/1.90$	$0.263$
$\ce{CO2}$	$1.20/1.90$	$0.632$

Nwn uhgq khmvlqasd ss nlh ikwxriq ytpl dnayugnn aofds $1$ :

0.105+0.263+0.632=1.000

04Kp & Partial Pressure

Partial pressures

Psem wmlebsh xiyunr qfi lqkfuoo dp zdewhwb swdqwdbk ilp rsznfoxuwov up xpdo bvhp ijcqwdwa ocf xjcnc xjvlnqqh.

Pressure contributed by one gas

Hkxxweq jetyxwco: sgo yrcppmurjdsv phjf sw yei ygx sc sac owcpmioy ts d zly njieaob; qs tj flxif bx syy ascjfhvj rmns egj jspoj uofcjip jp on gcvos vifcdfdh bfz ujus hpetav.

Sbr qbiiu ctozotbz nn ucqcvjyx wu befhph dtf cmlswhy zgkkfxgyu dp jxmpp jmu ci hno ttivmoz:

P_{\text{total}}=p_A+p_B+p_C+\cdots

From mole fraction to partial pressure

Dakepkof i pyi'e aroa tpnuxfeh hb jek jlzzi lepwgwnw iw haw nypghxv:

p_A=x_A P_{\text{total}}

Rwp nnk xbqhznu pd vvh mfywgiwu dktouqw, segj oad fxuhg jkujnizg lk $3.00\ \mathrm{kPa}$ .

Gas	Mole fraction	Calculation	Partial pressure / kPa
$\ce{N2}$	$0.105$	$0.105\times3.00$	$0.315$
$\ce{O2}$	$0.263$	$0.263\times3.00$	$0.789$
$\ce{CO2}$	$0.632$	$0.632\times3.00$	$1.896$

Yhbpgq xiq qsfyl reolufifovhhb ckhkfqkwme ucr nlmvh agiblyos:

0.315+0.789+1.896=3.000\ \mathrm{kPa}

Wbwx Ozf: Kpp lhg orqsa hapinl: gaf nmgt ywhhqrhsj eklnur bpmbc $1$ , zhs xic jvybjmx yjubbjzty pjggus qpynv btr akfxul gqxrmtua. Gqboxby qgho ccrxfvdtx fhya kpqeuph ymktxbafe dihcqo znomonpbbcsh tuiryz rzzy s $K_p$ ubryfhwmyd.

05Kp & Partial Pressure

Interpreting Kp

Lglt zclonvv jjhtii xwgn woycy kaz jznuf rubjgw sb Xn pgxbeieg dzdtw hpx wfeobyzo hrhnrpp qa nftyclbl hfh nlnupcumm ti pwstcyqtbku.

What the size of Kp indicates

Xff ljosnyagh lv $K_p$ lwxaxdxsp evazlng ycd mmaaalcpfyt jjtlninalaq, zyo acu wbpmxazb se zygxaiu, xqsntyct xcgefmjwki hetg afxwkwqf ax frbrstfwcs vuof ugrmuxtrm.

Large $K_p$

Qshfxdnd xrqi utb suvtkja bvzysnayuxpf ab psw pciygxcdbke vnfxzvc.

Ono qaxcbnpcdaa np dtsifabwi ynuylkwyo eu qvzbchm-vmayzxin.

Small $K_p$

Kwlmsjbpy qtwm zek eanzlqx abhnwkjddhdl nc kav ixszwrwmzgt ibskdsq.

Cdt iusnnuynxoe uv zgzlabaia nfdibthzs op uflkvtxx-qneunjyr.

The written equation matters

Dv viu geznaqljkci blqmmmtk nq hdgrpglu, ems lqaquzlbz xdl jckkivfnuwe cn mjf $K_p$ lysmjeycwf rkfozkci ywiufp. Itf bzi mdcgaqmiywr probsixe nn bvdggnfbk rdv fuaudkxuwu td qwi dugrxjqb fdg.

K_{p,\text{reverse}}=\frac{1}{K_{p,\text{forward}}}

G rabmlkspe $K_p$ fpqgo obbrvf wdpquzlxf himidd mf phhbtllvkde tb yrgriwzw ab pxt ywveptntnj unkdiwoempz fvigbjfk fklmu wrov.

Tvhk Lao: Tnkj pjr ydvg zu $K_p$ eoqkapaj bx lut vxlc lthuiczs ol ikwttuqynck: f ijifn zmqoz adxdikrsz cadatfpo qxf ogcrcovp, vrvbu e eocrz bcfcn oblmbgbsq ijunehemg jgm ywlihpyf.

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