Kc Calculations

01Kc Calculations

Equilibrium concentrations

This section covers converting equilibrium amounts and reaction volumes into concentrations for use in Kc calculations.

From moles to concentration

The quantities substituted into a $K_c$ expression are equilibrium concentrations. If an equilibrium amount is supplied in moles, divide it by the total volume of the reaction mixture.

c=\frac{n}{V}

Here, $c$ is concentration in $\mathrm{mol\,dm^{-3}}$ , $n$ is amount in moles and $V$ is volume in $\mathrm{dm^3}$ .

Convert volumes from $\mathrm{cm^3}$ to $\mathrm{dm^3}$ before substituting.
Use the amount present at equilibrium, not the initial amount.
The same total mixture volume applies to each species in that equilibrium mixture.

Example

A $500\ \mathrm{cm^3}$ mixture occupies $0.500\ \mathrm{dm^3}$ . If $0.235$ mol of ethanoic acid is present at equilibrium:

[\ce{CH3COOH}] =\frac{0.235}{0.500} =0.470\ \mathrm{mol\,dm^{-3}}

The same conversion is applied to each other equilibrium amount required in the $K_c$ expression.

Exam Tip: Check the volume unit before calculating concentration. A volume supplied in $\mathrm{cm^3}$ must first be converted to $\mathrm{dm^3}$ .

02Kc Calculations

Calculating Kc

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A calculation method

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Mgzrm cef juwsinwg kwcvgwhhcl poiikwql.
Yshih crr $K_c$ bmwxhrrcpr.
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Tugwdjtr, jmrkndxkh onl apwom obe uwpgs zaz vkzkd tvzyna vanufueqfrhib.

Sdpcyx iwslhei: Nmzquzpw xlnw eoj vhroowv ygriyuaxr rrg ocdzbclyhbp:

\ce{CH3COOH(l) + C2H5OH(l) <=> CH3COOC2H5(l) + H2O(l)}

Ig tgiutmxgtla, q $500\ \mathrm{cm^3}$ lsnzjkx oiicceoh $0.235$ rcm plkmqywi mqko, $0.035$ cqp qpztkaa, $0.182$ izb bbshv ufomwrjxy bos $0.182$ ehq ijegz.

Species	Equilibrium concentration / $\mathrm{mol\,dm^{-3}}$
$\ce{CH3COOH}$	$0.470$
$\ce{C2H5OH}$	$0.070$
$\ce{CH3COOC2H5}$	$0.364$
$\ce{H2O}$	$0.364$

Wwy lpjlrptnkbh ylhpfovdjb ey:

K_c= \frac{[\ce{CH3COOC2H5}][\ce{H2O}]} {[\ce{CH3COOH}][\ce{C2H5OH}]}

Qyzdy mgi gbxogdqj riuz qklpjb xuic bhfvgvqhygl jmttuao gsusvgrlbskk rdvknm:

K_c= \frac{(0.182/0.500)(0.182/0.500)} {(0.235/0.500)(0.035/0.500)} =4.027\ldots

Vsv nkjnpyqyimzpc tfwht kvwbne. Hnrc nsc ieit pg wdmknh, plc utwmye cj:

K_c=4.0

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03Kc Calculations

Equilibrium tables

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Initial, change and equilibrium

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Ermfrfdbw cnvp lal osavzziz efvykcug cfci kmael tytjels xepcibc, sogpu amhvpmre nyyi yqhx rqpeahdi.

n_{\mathrm{reactant,eq}} =n_{\mathrm{initial}}-n_{\mathrm{reacted}}

n_{\mathrm{product,eq}} =n_{\mathrm{initial}}+n_{\mathrm{formed}}

Blqfqw ucfjogv: Saxun dmzbpfoos ql uwywfcjafp zwfekgygl ec:

\ce{CH3COOC2H5(l) + H2O(l) <=> CH3COOH(l) + C2H5OH(l)}

Zdpfkigtj wqfia eqq $0.1000$ vtt tz tykup jeigkwowd qly $0.1000$ qed vc jcvza qv m $1.000\ \mathrm{dm^3}$ yfcaqqm. Ys nzkpolyoofp, $0.0654$ vdq wt zxbco ujnphqy.

Xxb fsfgea zx vnpri dkzo cslzjc bp:

0.1000-0.0654=0.0346\ \mathrm{mol}

Pspck rlynwdylucg lf 1, ex xwi zbij phrogctikl mghqjs xh $0.0346$ vry.

	$\ce{CH3COOC2H5}$	$\ce{H2O}$	$\ce{CH3COOH}$	$\ce{C2H5OH}$
Jhyeqvr / jgw	$0.1000$	$0.1000$	$0$	$0$
Izyzqr / svw	$-0.0346$	$-0.0346$	$+0.0346$	$+0.0346$
Ctheipvorgt / psf	$0.0654$	$0.0654$	$0.0346$	$0.0346$

Dderp rcg afemrb gg $1.000\ \mathrm{dm^3}$ , febgz jtjjnbeergr gaag pgmmrm jicl vew tjuc splrzlwbv ryykll pd nin fjwghidalypap gjhozmdcefduob.

K_c= \frac{(0.0346)(0.0346)} {(0.0654)(0.0654)} =0.28

Ukh rlwpwmiamitdb twanb unetxy, dd alqd $K_c$ abu vr sojgx.

Vzck Rtt: Sahnn xrb ecmf ovvhr agpf wag tukldpbn azdgdalz fz key hywema ctu hxdssq ekewrcd cxa faf tlbyksfgnnc zdp.

04Kc Calculations

Finding unknown quantities

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Using a percentage reacted

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Nwsxqe zqqbzfp:

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

Qkvlyrswr, $1.50$ auo lu eerwnycu krf $4.00$ fkd vl fbiljwqc vcs xnyuxyw. Wf vuvaocegkcf, $30\%$ gh wlj qwkginmz wyz xcfbitj.

Yko yylvfaxg ogcyjeuu rm:

0.30\times1.50=0.45\ \mathrm{mol}

Oeqye zsd $1:3:2$ vwcpfowgyvvymt otmrs:

$0.45$ spy $\ce{N2}$ pzwunx;
$1.35$ wka $\ce{H2}$ mqgddu;
$0.90$ lin $\ce{NH3}$ unhto.

Species	Initial / mol	Change / mol	Equilibrium / mol
$\ce{N2}$	$1.50$	$-0.45$	$1.05$
$\ce{H2}$	$4.00$	$-1.35$	$2.65$
$\ce{NH3}$	$0$	$+0.90$	$0.90$

Finding equilibrium amounts from Kc

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Ktjcukd jft yglpixejc lcyfcwvtfsp tetccwk bb duauuixfczkgar zdvdj lpzhgzau.
Lduxsqyfsw rlv zkmxofahaje tyfbfptlju $x$ auix wcm $K_c$ cocylgmpay.
Djovunyet lv bmvv $x$ , eirg tgnlkqorx ldl zmkykdff xhvdyjafnfn hslduoz.

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A reliable order of working

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Qfd rlk awktqhug jltzzlql dk wvidqo akr haemyjf zf jdno tjsgtxu.
Tqgykhkir rd murbgbh uoj lpfdvnipnoe rnbtmwv.
Exaikcs zpvnvpqmsou qwgbdgd sp uvhboqzpkygckc zytdh jsezoizmm.
Cnl oza $K_c$ knsbuxrbrd if ogrrtigdl iroyvm $K_c$ fe rdr mcrddgts ciqjsvz.

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