Ukushintsha kwezigaba: amajika okufudumeza, ingcindezi yomhwamuko nemidwebo yezigaba

Kungani izinga lokushisa lima ngesikhathi sokuncibilika nokubila

Fudumeza ibhlokhi yeqhwa ngezinga elingaguquki bese urekhoda izinga layo lokushisa, futhi uthola ijika lokufudumeza. Izinga lokushisa liyakhuphuka, lime ku-0 °C ngesikhathi iqhwa lincibilika, liphinde likhuphuke, bese lima ku-100 °C ngesikhathi amanzi ebila. Ezingxenyeni eziyisicaba, amandla aya ekuhlukaniseni amamolekyuli ngokumelana nokuheha kwawo phakathi kwamamolekyuli, hhayi ekuwenzeni ahambe ngokushesha, ngakho izinga lokushisa alishintshi kuze kube yilapho ushintsho lwesigaba seluphelele.

Lezi zinhlobo ezimbili zezingxenye zidinga izibalo ezimbili ezihlukene. Ngaphakathi kwesigaba esisodwa, q = m × c × ΔT, lapho u-c eyikushisa okuqondene. Ngesikhathi soshintsho lwesigaba ezingeni lokushisa elingaguquki, q = n × ΔH, lapho u-ΔH eyi-enthalpy ye-molar yokuncibilika noma yokuba umhwamuko. Ukuncibilika, ukuba umhwamuko ne-sublimation kuyi-endothermic. Ukuqanda, ukufingqeka ne-deposition kukhulula amanani afanayo amandla, ngakho amanani awo e-ΔH anophawu oluphambene.

Isibonelo esisebenzile: ukufudumeza iqhwa kuze kube umusi

Kudingeka ukushisa okungakanani ukuguqula u-40.0 g weqhwa ku-−15.0 °C ube umhwamuko wamanzi ku-100.0 °C? Idatha: ukushisa okuqondene okungu-2.093 J/(g·°C) kweqhwa no-4.184 J/(g·°C) kwamanzi oketshezi (Itafula 5.1 le-OpenStax); ΔHfus = 6.01 kJ/mol ku-0 °C no-ΔHvap = 40.67 kJ/mol ku-100 °C (isigaba 10.3 se-OpenStax). Inani lamanzi lingu-n = 40.0 g ÷ 18.015 g/mol = 2.220 mol.

Isinyathelo 1, fudumeza iqhwa: 40.0 × 2.093 × 15.0 = 1256 J, noma 1.26 kJ. Isinyathelo 2, lincibilikise: 2.220 mol × 6.01 kJ/mol = 13.3 kJ. Isinyathelo 3, fudumeza uketshezi kusuka ku-0 °C kuya ku-100 °C: 40.0 × 4.184 × 100.0 = 16 736 J, noma 16.7 kJ. Isinyathelo 4, kubilise: 2.220 mol × 40.67 kJ/mol = 90.3 kJ. Isamba: 1.26 + 13.3 + 16.7 + 90.3 = 122 kJ, ezinombolweni ezibalulekile ezintathu.

Ukubila kubalelwa cishe amaphesenti angu-74 esamba, okungaphezu kokuphindwe kahlanu ukushisa okudingekayo ukufudumeza uketshezi ngamadigri angu-100. Sebenzisa inani lika-ΔHvap ezingeni lokushisa lapho ukubila kwenzeka khona. Ku-25 °C, u-ΔHvap wamanzi ungu-44.01 kJ/mol, futhi ukusebenzisa leyo nombolo lapha bekuzokhulisa isinyathelo 4 ngamaphesenti angu-8 cishe.

Ingcindezi yomhwamuko nesibalo se-Clausius–Clapeyron

Esitsheni esivaliwe, uketshezi luyahwamuka kuze kube yilapho izinga lokufingqeka lilingana nalo. Ingcindezi yegesi yalolo ketshezi kuleli phuzu yiyona ebizwa ngokuthi ingcindezi yomhwamuko, futhi ikhuphuka kakhulu ngezinga lokushisa. Uketshezi luyabila lapho ingcindezi yalo yomhwamuko ilingana nengcindezi engaphezu kwalo, ngakho indawo yokubila evamile yizinga lokushisa lapho ingcindezi yomhwamuko ifika ku-1 atm.

Ifomu lamaphuzu amabili lesibalo se-Clausius–Clapeyron lixhumanisa izingcindezi zomhwamuko ezimbili ne-enthalpy yokuba umhwamuko: ln(P₂/P₁) = (ΔHvap/R)(1/T₁ − 1/T₂), lapho R = 8.314 J/(mol·K) futhi amazinga okushisa engama-kelvin. Sithatha ukuthi u-ΔHvap akaguquki kulelo banga, ngakho sisebenza kangcono emabangeni amazinga okushisa angemakhulu.

Isibonelo esisebenzile 1. Itafula 9.2 le-OpenStax linikeza ingcindezi yomhwamuko wamanzi njengo-17.5 torr ku-20 °C no-149.4 torr ku-60 °C. ln(149.4/17.5) = 2.144, futhi 1/293.15 K − 1/333.15 K = 4.096 × 10⁻⁴ K⁻¹. ΔHvap = (8.314 × 2.144) ÷ 4.096 × 10⁻⁴ = 4.35 × 10⁴ J/mol, noma 43.5 kJ/mol. Lesi yisilinganiso esisuka ku-20 °C kuya ku-60 °C. Siphakathi kwamanani aku-25 °C (44.01) naku-100 °C (40.67), njengoba kufanele.

Isibonelo esisebenzile 2. Amanzi abila kuliphi izinga lokushisa lapho ingcindezi yomoya ingu-0.800 atm? Qala endaweni yokubila evamile, 373.15 K ku-1.000 atm, bese usebenzisa u-ΔHvap = 40.67 kJ/mol. 1/T₂ = 1/373.15 − (8.314/40 670) × ln(0.800) = 2.7255 × 10⁻³ K⁻¹, ngakho T₂ = 366.9 K, noma 93.8 °C. Njengokuhlola, u-0.800 atm ungu-608 torr, futhi ukulinganisela phakathi kuka-90 °C no-95 °C kuTafula 9.2 nakho kunikeza u-93.8 °C.

Ukufunda izindawo, imigqa namaphuzu omdwebo wezigaba

Umdwebo wezigaba ubonisa ingcindezi ngokuqhathaniswa nezinga lokushisa futhi ukhombisa ukuthi yisiphi isigaba esizinzile ngaphansi kweqoqo ngalinye lezimo. Indawo ngayinye iyisigaba esisodwa. Umugqa ngamunye uyiqoqo lezimo lapho izigaba ezimbili zihlala khona ndawonye zisekulinganeni: okuqinile noketshezi eduze nejika lokuncibilika, uketshezi negesi eduze nejika lengcindezi yomhwamuko, nokuqinile negesi eduze nejika le-sublimation.

Imigqa emithathu ihlangana ku-triple point, izinga lokushisa elilodwa nengcindezi eyodwa lapho okuqinile, uketshezi negesi konke kuhlala khona ndawonye. Ijika lengcindezi yomhwamuko ligcina ku-critical point. Ngaphezu kwe-critical temperature, ayikho ingcindezi engaguqula igesi ibe uketshezi, futhi into iba yi-supercritical fluid enezakhiwo eziphakathi kwezoketshezi nezegesi.

Ukusebenzisa umdwebo, thola izimo zokuqala bese uhamba ngomzila inkinga ewuchazayo. Ukufudumeza ngengcindezi engaguquki kungumugqa ovundlile osuka kwesobunxele uya kwesokudla, futhi wonke umngcele owuweqayo uwushintsho lwesigaba. Ukucindezela ngezinga lokushisa elingaguquki kungumugqa omile ohamba uya phezulu. Umugqa ovundlile odwetshwe ngaphansi kwengcindezi ye-triple point weqa ijika le-sublimation kuphela, ngakho okuqinile kuguquka kube yigesi ngqo.

Umugqa wokuncibilika wamanzi ohlehla emuva ne-triple point ephezulu ye-dry ice

I-triple point yamanzi iku-0.01 °C no-0.0061 bar (NIST Chemistry WebBook), okucishe kube ngu-0.0060 atm. I-critical point yawo iku-374 °C no-218 atm (isigaba 10.4 se-OpenStax). Ngokungajwayelekile, umugqa wawo wokuqinile noketshezi utshekele kancane ngakwesobunxele: ukukhuphula ingcindezi kwehlisa indawo yokuncibilika kancane, ngoba iqhwa aliminyene kunamanzi oketshezi futhi ingcindezi ithanda isigaba esiminyene kakhulu. Izinto eziningi zinokutsheka okuphambene.

I-triple point ye-carbon dioxide iku-216.58 K (−56.57 °C) no-5.185 bar, okungu-5.12 atm (NIST Chemistry WebBook). Njengoba leyo ngcindezi ingaphezu kuka-1 atm, i-CO₂ eketshezi ayikwazi ukuba khona emoyeni ovulekile. Ku-1 atm, i-CO₂ eqinile (i-dry ice) yenza i-sublimation esikhundleni sokuncibilika. I-critical point yayo, 31.0 °C no-73.8 bar, iphansi ngokwanele kangangokuthi i-CO₂ ye-supercritical isetshenziswa ezimbonini njengesincibilikisi, isibonelo ukususa i-caffeine kubhontshisi wekhofi.

Isibonelo esisebenzile 3. Linganisela izinga lokushisa lapho i-dry ice yenza khona i-sublimation ku-1 atm (1.01325 bar), uqale ku-triple point nase-enthalpy ye-sublimation, ΔHsub = 26.1 kJ/mol (NIST WebBook, ilinganiswe eduze no-207 K). Isibalo se-Clausius–Clapeyron sisebenza emugqeni wokuqinile negesi ngendlela efanayo nasemugqeni woketshezi negesi. ln(1.01325/5.185) = −1.633. 1/T₂ = 1/216.58 − (8.314/26 100) × (−1.633) = 5.137 × 10⁻³ K⁻¹, ngakho T₂ = 194.7 K, noma −78.5 °C. Lokho kuhambisana nezinga lokushisa le-sublimation elivamile elingu-−78.5 °C elicashunwe ku-LibreTexts.

Amaphutha ezibalo zoshintsho lwesigaba

Amaphutha amaningi avela ekuxubeni lezi zinhlobo ezimbili zezingxenye zejika lokufudumeza noma emaphutheni amayunithi esibalweni se-Clausius–Clapeyron. Dweba ijika lokufudumeza bese ubhala ilebula engxenyeni ngayinye ngaphambi kokubala noma yini.

• Ukushiya isinyathelo soshintsho lwesigaba, noma ukusebenzisa u-q = mcΔT endaweni eyisicaba lapho u-ΔT eyi-zero.
• Ukusebenzisa ukushisa okuqondene kwamanzi oketshezi eqhweni noma emusini. Isigaba ngasinye sinenani laso.
• Ukuxuba ama-joule nama-kilojoule lapho wengeza izinyathelo. Guqula konke kube iyunithi eyodwa ngaphambi kokuhlanganisa.
• Ukuphindaphinda u-ΔH ngamagremu esikhundleni sama-mole, noma u-c ngama-mole esikhundleni samagremu, ngaphandle uma usebenzisa ama-heat capacity e-molar ngokungaguquki.
• Ukusebenzisa amazinga okushisa e-Celsius esibalweni se-Clausius–Clapeyron. Ama-kelvin kuphela asebenzayo, ngoba isibalo sisebenzisa u-1/T.
• Ukusebenzisa u-R = 0.08206 L·atm/(mol·K) no-ΔH ngama-joule. Uma u-ΔH engu-J/mol, u-R kufanele abe ngu-8.314 J/(mol·K).
• Ukufunda i-eksisi yengcindezi yomdwebo wezigaba njenge-linear kanti iyi-logarithmic, njengoba kuvame ukuba njalo ku-CO₂.