P10-3 t-butyl alcohol (TBA) is an important octane enhancer that is ...
P10-3 t-butyl alcohol (TBA) is an important octane enhancer that is ...
P10-3 t-butyl alcohol (TBA) is an important octane enhancer that is ...
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<strong>P10</strong>-3t-<strong>butyl</strong> <strong>alcohol</strong> (<strong>TBA</strong>) <strong>is</strong> <strong>an</strong> import<strong>an</strong>t oct<strong>an</strong>e enh<strong>an</strong>cer <strong>that</strong> <strong>is</strong> used to replace leadadditives in gasoline [Ind. Eng. Chem. Res., 27, 2224 (1988)]. t-<strong>butyl</strong> <strong>alcohol</strong> wasproduced by the liquid-phase hydration (W) of <strong>is</strong>obutene (I) over <strong>an</strong> Amberlyst-15catalyst. The system <strong>is</strong> normally a multiphase mixture of hydrocarbon, water <strong>an</strong>d solidcatalysts. However, the use of cosolvents or excess <strong>TBA</strong> c<strong>an</strong> achieve reasonablem<strong>is</strong>cibility.The reaction mech<strong>an</strong><strong>is</strong>m <strong>is</strong> believed to beI + S ↔ I ⋅ SW + S ↔ W ⋅ SW ⋅ S + I ⋅ S ↔ <strong>TBA</strong> ⋅ S<strong>TBA</strong> ⋅ S ↔ <strong>TBA</strong> + S+ SDetermine a rate law assuming:(a) the surface reaction <strong>is</strong> rate-limiting(b) The adsorption of <strong>is</strong>obutene <strong>is</strong> limiting(c) The reaction follows Eley-Rideal kineticsI ⋅ S+ W↔ <strong>TBA</strong> ⋅ S<strong>an</strong>d <strong>that</strong> the surface reaction <strong>is</strong> limiting(d) Isobutene (I) <strong>an</strong>d water (W) are adsorbed on different sitesI + S1W + S↔ I ⋅ S21↔ W ⋅ S2<strong>TBA</strong> <strong>is</strong> not on the surface <strong>an</strong>d the surface reaction <strong>is</strong> rate limiting.⎡⎢Ans:⎣r'<strong>TBA</strong>= − r'Ik[C⎤ICW− C<strong>TBA</strong>/ KC]=(1 + K )(1 + )⎥WCWKICI⎦(e) What generalization c<strong>an</strong> you make by comparing rate laws derived in parts (a)through (d)?The process flow sheet for the commercial production of <strong>TBA</strong> <strong>is</strong> shown in Figure<strong>P10</strong>-3.(f) What c<strong>an</strong> you learn from th<strong>is</strong> problem <strong>an</strong>d the process flow sheet?SOLUTION(a) If the surface reaction <strong>is</strong> rate limiting the reaction rate c<strong>an</strong> be given by
(b) If the adsorption of <strong>is</strong>obutene <strong>is</strong> limiting the reaction rate expression becomesr<strong>TBA</strong>= − rI= kaICICS− k−aICIS= kaI⎛⎜CIC⎝SC−KISI⎞⎟⎠The expressions for the concentration of W·S <strong>an</strong>d <strong>TBA</strong>·S remain as before. Sincethe surface reaction <strong>is</strong> now fast <strong>an</strong>d reversible we c<strong>an</strong> assume <strong>that</strong> it <strong>is</strong> atequilibrium to getRearr<strong>an</strong>ge th<strong>is</strong> to getCKsr=C<strong>TBA</strong>SISCCSWSCC<strong>TBA</strong>S S <strong>TBA</strong> <strong>TBA</strong> S SCIS= ==KsrCWSKsrKWCWCSKCCCK<strong>TBA</strong>KsrCK<strong>TBA</strong>WCCWSSubstitute th<strong>is</strong> expression into the rate expression to getr<strong>TBA</strong>= kaI⎛⎜CIC⎝S−K<strong>TBA</strong>CK K KIsr<strong>TBA</strong>WCCSW⎞⎟ = k⎠aI⎛C⎜SCI⎝−KK KI<strong>TBA</strong>srCKW<strong>TBA</strong>CW⎞⎟⎠Again we need <strong>an</strong> expression for C S . Proceeding as in part (a) we getCST= CS= CS+ C+KIS<strong>TBA</strong>K+ CsrCK<strong>TBA</strong>WWSC+ CCWS<strong>TBA</strong>S+ KWCWCS+ K<strong>TBA</strong>C<strong>TBA</strong>CSSolving for C S givesCS=1 +KK<strong>TBA</strong>srCK CW<strong>TBA</strong>WCST+ KWCW+ K<strong>TBA</strong>C<strong>TBA</strong>Substituting th<strong>is</strong> into the rate expression gives (after slight rearr<strong>an</strong>gements)r<strong>TBA</strong>=⎛⎜1+⎝KK<strong>TBA</strong>srKk'CWaI<strong>TBA</strong>C⎛⎜C⎝WI+ KC−K CWC<strong>TBA</strong>WW⎞⎟⎠+ K<strong>TBA</strong>C<strong>TBA</strong>⎞⎟⎠
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