Amandla e-activation: kungani izinga lokushisa lisheshisa ukusabela

Isithiyo samandla emdwebeni wokusabela

Umdwebo wokusabela ubonisa amandla ngokuqhathaniswa nenqubekela phambili yokusabela. Izisabelo zihlala ngakwesobunxele nemikhiqizo ngakwesokudla, futhi phakathi kwazo ijika likhuphukela esiqongweni. Ukuhlelwa kwama-athomu kuleso siqongo yi-transition state, noma i-activated complex: isakhiwo esiphila isikhashana lapho izibopho ezindala ziphuke ngokwengxenye nezintsha zakheke ngokwengxenye.

Amandla e-activation, Ea, ukuphakama kwesithiyo okulinganiswe kusuka ezisabelweni. Ukusabela okuphambene kunesithiyo sako, esilinganiswe kusuka emikhiqizweni. Izithiyo ezimbili noshintsho lwe-enthalpy kuxhumene: ΔH = Ea(okuya phambili) − Ea(okuphambene). Isibonelo, uma ukusabela kuno-Ea(okuya phambili) = 75 kJ/mol no-ΔH = −40 kJ/mol, isithiyo esiphambene singu-75 − (−40) = 115 kJ/mol. Ukusabela kwe-exothermic kuhlala kunesithiyo esiphambene esiphakeme kunesithiyo sokuya phambili.

Ubukhulu buka-ΔH abukutsheli ubukhulu buka-Ea. Ukusabela okuyi-exothermic kakhulu kusengahamba kancane kakhulu uma isithiyo sako siphakeme. Ukushiswa kwe-hydrocarbon emoyeni ezingeni lokushisa legumbi kuyisibonelo sansuku zonke.

Ukushayisana, amandla nokubheka

Ithiyori yokushayisana ithi amamolekyuli kufanele ashayisane ukuze asabele, nokuthi ukushayisana kuholela ekusabeleni kuphela uma izimo ezimbili zifezekile. Amamolekyuli kufanele ashayisane okungenani ngamandla e-activation, futhi kufanele abheke ngendlela yokuthi ama-athomu afanele ahlangane.

Kunoma yiliphi izinga lokushisa, amandla e-kinetic amamolekyuli asakazeke ebangeni elibanzi. Ingxenye yokushayisana okunamandla okungenani angu-Ea icishe ibe ngu-exp(−Ea/RT), lapho u-exp(x) esho u-e ophakanyiswe emandleni x. Leyo ngxenye incane kodwa izwela kakhulu ezingeni lokushisa. Ku-Ea = 50.0 kJ/mol, u-Ea/RT ungu-20.17 ku-298.15 K no-19.52 ku-308.15 K, ngakho ingxenye ikhuphuka isuka ku-1.7 × 10⁻⁹ iye ku-3.3 × 10⁻⁹, isici esingu-1.9. Ukukhuphuka kuka-10 °C, okungamaphesenti angu-3 cishe kuphela ngaphezulu ngama-kelvin, kucishe kuphinde kabili izinga.

Umthetho ojwayelekile wesithupha wokuthi amazinga aphindeka kabili ngakho konke ukukhuphuka kuka-10 °C usebenza kuphela eduze nezinga lokushisa legumbi nakuzithiyo ezicishe zibe ngu-50 kJ/mol. Phakathi kuka-25 °C no-35 °C, isithiyo esingu-20 kJ/mol sinikeza isici esingu-1.3 kuphela, kanti isithiyo esingu-100 kJ/mol sinikeza isici esingu-3.7.

Amafomu amathathu esibalo sika-Arrhenius

Isibalo sika-Arrhenius ngu-k = A exp(−Ea/RT). Lapha u-A uyi-frequency factor, ekhombisa ukuthi amamolekyuli ashayisana kangaki nokuthi mangaki ama-collision anokubheka okufanele. U-R uyi-gas constant, 8.314 J mol⁻¹ K⁻¹ (inani le-NIST CODATA, eliyisiwe), no-T ungama-kelvin. U-Ea kufanele abe ngama-joule nge-mole ngayinye lapho u-R engama-joule.

Ukuthatha ama-logarithm emvelo kunikeza ifomu lomugqa oqondile: ln k = −(Ea/R)(1/T) + ln A. Igrafu ka-ln k ngokuqhathaniswa no-1/T inomqansa ongu-−Ea/R ne-intercept engu-ln A. Le yindlela engcono kakhulu lapho unama-rate constant emazingeni okushisa amaningana.

Ukubhala ifomu le-linear emazingeni okushisa amabili bese ususa kunikeza ifomu lamaphuzu amabili: ln(k₂/k₁) = −(Ea/R)(1/T₂ − 1/T₁). Uma kwaziwa noma yimaphi amane kula manani k₁, k₂, T₁, T₂ no-Ea, linikeza elesihlanu. I-frequency factor iyakhansela, ngakho awudingi ukuyazi.

Isibonelo esisebenzile: u-Ea kusuka kuma-rate constant amabili

Isigaba 12.5 se-OpenStax sibhala ama-rate constant e-oda lesibili okubola 2 HI(g) → H₂(g) + I₂(g) emazingeni okushisa amahlanu. Amabili awo angu-k₁ = 1.22 × 10⁻⁶ L mol⁻¹ s⁻¹ ku-T₁ = 575 K no-k₂ = 1.16 × 10⁻³ L mol⁻¹ s⁻¹ ku-T₂ = 700 K.

Hlela kabusha ifomu lamaphuzu amabili: Ea = R ln(k₂/k₁) / (1/T₁ − 1/T₂). Isilinganiso k₂/k₁ singu-951, futhi ln 951 = 6.857. Ama-reciprocal amazinga okushisa angu-1/575 K = 1.7391 × 10⁻³ K⁻¹ no-1/700 K = 1.4286 × 10⁻³ K⁻¹, ahluka ngo-3.106 × 10⁻⁴ K⁻¹. Ngakho Ea = (8.314 J mol⁻¹ K⁻¹)(6.857) / (3.106 × 10⁻⁴ K⁻¹) = 1.84 × 10⁵ J/mol, noma 184 kJ/mol.

Gcina izinombolo ezengeziwe ku-1/T. Umehluko phakathi kwama-reciprocal amabili mncane kakhulu kunanoma iyiphi kuwo, ngakho ukuwayisa ezinombolweni ezibalulekile ezimbili kuqala kungashintsha u-Ea ngamaphesenti amaningana.

Isibonelo esisebenzile: igrafu ye-Arrhenius enamaphuzu amahlanu nokubikezela

Ukusebenzisa wonke amaphuzu edatha amahlanu kungcono kunokusebenzisa amabili, ngoba kuthola isilinganiso sephutha kukulinganisa ngakunye. Amanani e-OpenStax angu-k = 3.52 × 10⁻⁷, 1.22 × 10⁻⁶, 8.59 × 10⁻⁵, 1.16 × 10⁻³ no-3.95 × 10⁻² L mol⁻¹ s⁻¹ ku-555, 575, 645, 700 no-781 K. Guqula ibhangqa ngalinye libe ngu-1/T no-ln k, bese ufanisa umugqa oqondile nge-least squares, usebenzisa i-spreadsheet noma ikhalkhuleyitha yamagrafu.

Umqansa ofanisiwe ungu-−2.229 × 10⁴ K, futhi amaphuzu aseduze kakhulu nomugqa (R² = 0.9996). Bese Ea = −umqansa × R = 2.229 × 10⁴ K × 8.314 J mol⁻¹ K⁻¹ = 1.85 × 10⁵ J/mol, noma 185 kJ/mol, kuvumelana kakhulu nomphumela wamaphuzu amabili. I-intercept ingu-25.20, ngakho A = e ephakanyiswe emandleni 25.20 = 8.8 × 10¹⁰ L mol⁻¹ s⁻¹.

Sebenzisa isibalo esifanisiwe ukubikezela u-k ku-625 K, izinga lokushisa eliphakathi kwamaphuzu alinganisiwe: k = (8.8 × 10¹⁰) × e ephakanyiswe emandleni −(1.853 × 10⁵)/(8.314 × 625) = 2.9 × 10⁻⁵ L mol⁻¹ s⁻¹. Ukubikezela kuphakathi kwamanani alinganisiwe ku-575 K naku-645 K, njengoba kufanele. Ukubikezela okukude kakhulu ngaphandle kwebanga elilinganisiwe akuthembekile kangako, ngoba u-Ea no-A bangashintsha kancane ngezinga lokushisa.

Indlela i-catalyst esishintsha ngayo isithiyo

I-catalyst inikeza i-mechanism ehlukile enamandla e-activation aphansi futhi iyavuseleleka ekugcineni. Yehlisa isithiyo sokusabela okuya phambili nokuphambene ngenani elifanayo, ngakho isheshisa zombili izindlela ngokulinganayo. Ayishintshi u-ΔH, futhi ayishintshi isimo sokulingana. Isiza nje isistimu ukuthi ifike ekulinganeni ngokushesha.

Isibonelo esisebenzile. Ake sithi i-enzyme yehlisa u-Ea ngo-20.0 kJ/mol ezingeni lokushisa lomzimba, 37.0 °C noma 310.15 K, futhi u-A uhlala efana. I-rate constant ikhula ngesici esingu-e ephakanyiswe emandleni (20 000 J/mol)/(8.314 J mol⁻¹ K⁻¹ × 310.15 K) = e ephakanyiswe emandleni 7.756 = 2.3 × 10³. Ushintsho olubukeka luncane esithiyweni lunikeza izinga elisheshayo ngaphezu kokuphindwe izinkulungwane ezimbili, ngoba u-Ea uhlala ku-exponent.

Amaphutha ezibalo ze-Arrhenius

Ngaphambi kokubika amandla e-activation, hlola ukuthi mahle futhi anosayizi onengqondo. Amandla e-activation amaningi okusabela okufundwa kukhemistri evamile angamashumi kuya emakhulwini ambalwa ama-kilojoule nge-mole ngayinye.

• Ukuxuba u-kJ no-J: ngo-R = 8.314 J mol⁻¹ K⁻¹, u-Ea kufanele abe ngo-J/mol. Inani elincane noma elikhulu ngokuphindwe kayinkulungwane ngokuvamile lisho leli phutha.
• Ukusebenzisa amazinga okushisa e-Celsius. U-1/T kufanele asebenzise ama-kelvin.
• Ukushintshanisa u-k₁ no-k₂ maqondana no-T₁ no-T₂, okuphendula uphawu luka-Ea.
• Ukusebenzisa u-log esikhundleni sika-ln. Uma udweba u-log₁₀ k ngokuqhathaniswa no-1/T, umqansa ungu-−Ea/(2.303R), hhayi u-−Ea/R.
• Ukuyisa amanani ka-1/T kusenesikhathi, okukhulisa iphutha emehlukweni wawo omncane.
• Ukusebenzisa umthetho wokuphinda kabili ka-10 °C sengathi unembile.