Imithetho yegesi: kusuka emthethweni ka-Boyle kuya ku-PV = nRT

Okuguquguqukayo okune okuchaza isampula yegesi

Isampula yegesi ichazwa ingcindezi yayo P, ivolumu V, izinga lokushisa T nenani n. Ingcindezi ivela emayunithini amaningana: i-atmosphere eyodwa ingu-101.325 kPa, noma 760 mmHg, futhi kuyo yonke injongo esebenzayo i-torr eyodwa ilingana ne-mmHg eyodwa. Inani lihlala lisuka kuma-mole, hhayi amagremu.

Izinga lokushisa kufanele libe nge-kelvin: engeza u-273.15 ekufundweni kwe-Celsius. Imithetho yegesi iyizilinganiso ezilinganayo, futhi isilinganiso silingana sisebenza kuphela esikalini lapho u-zero asho u-zero. Ukusuka ku-10 °C kuya ku-20 °C akuphindi kabili ivolumu yegesi, kodwa ukuphindaphinda kabili kusuka ku-283 K kuya ku-566 K kuphinda kabili ivolumu yegesi egciniwe ngengcindezi engaguquki.

U-Boyle, u-Charles no-Avogadro njengezingcezu zomthetho owodwa

Umthetho ngamunye wakudala ugcina okuguquguqukayo okubili kungaguquki. Umthetho ka-Boyle: ku-n no-T abangaguquki, P₁V₁ = P₂V₂, ngakho ukucindezela igesi ibe yingxenye yevolumu kuphindaphinda kabili ingcindezi yayo. Umthetho ka-Charles: ku-n no-P abangaguquki, V₁/T₁ = V₂/T₂, ngakho ivolumu ikhula ngokulingana nezinga lokushisa le-Kelvin. Umthetho ka-Avogadro: ku-P no-T abangaguquki, V₁/n₁ = V₂/n₂, ngakho amavolumu alinganayo egesi aphethe inani elilinganayo lamamolekyuli.

Ndawonye anikeza umthetho wegesi ohlanganisiwe wenani elimisiwe legesi, P₁V₁/T₁ = P₂V₂/T₂. Uma usuyethemba leli fomu, khansela noma yini ehlala injalo futhi okuguquguqukayo okusele kunikeza icala elikhethekile elilungile.

Isibonelo esisebenzile 1. Isilinda esine-piston ehambayo siphethe u-1.75 L we-nitrogen ku-18.0 °C no-0.985 atm. Igesi iyaphola ibe ngu-−8.0 °C ngenkathi ingcindezi kuphiston yehliswa ibe ngu-0.712 atm. Guqula amazinga okushisa kuqala: T₁ = 291.15 K no-T₂ = 265.15 K. Xazulula u-V₂ = V₁ × (P₁/P₂) × (T₂/T₁) = 1.75 L × (0.985 atm / 0.712 atm) × (265.15 K / 291.15 K) = 2.20 L. Hlola isiqondiso sesici ngasinye: ingcindezi ephansi inweba igesi (isilinganiso ngaphezu kuka-1), futhi ukupholisa kuyincipha (isilinganiso ngaphansi kuka-1).

Ukuxazulula izinkinga nge-PV = nRT

Ukwengeza inani legesi emthethweni ohlanganisiwe kunikeza umthetho wegesi ofanele, PV = nRT. Umthetho ngamunye wangaphambilini uyicala elikhethekile lawo.

Ngengcindezi nge-atmosphere nevolumu nge-liter, sebenzisa u-R = 0.08206 L·atm/(mol·K); ngengcindezi nge-pascal nevolumu nge-cubic meter, sebenzisa u-R = 8.314 J/(mol·K).

Ku-273.15 K no-1 atm, i-mole eyodwa yegesi elifanele ithatha u-22.41 L. Kusukela ngo-1982, i-IUPAC ichaze ingcindezi ejwayelekile njengo-1 bar, lapho ivolumu ye-molar ku-273.15 K ingu-22.71 L. Hlola ukuthi isifundo sakho sisebenzisa muphi umgomo ngaphambi kokuthembela ku-22.4 L ngemole ngayinye njengendlela emfushane.

Isibonelo esisebenzile 2. Isilinda sensimbi esingu-2.50 L siqukethe u-0.180 mol we-argon ku-22.0 °C. Thola ingcindezi ku-P = nRT/V. T = 22.0 + 273.15 = 295.15 K. P = (0.180 mol)(0.08206 L·atm/(mol·K))(295.15 K) / 2.50 L = 1.74 atm. Nge-kilopascal umphumela ungu-1.74 atm × 101.325 kPa/atm = 177 kPa.

Ukuminyana kwegesi nesisindo se-molar kusuka kusilinganiso sefilasiki

Ngoba n = m/M, lapho m eyisisindo no-M eyisisindo se-molar, umthetho wegesi ofanele ungabhalwa kabusha njengo-PM = dRT, no-d = m/V ukuminyana kwegesi. Ezingeni lokushisa nengcindezi emisiwe, ukuminyana kwegesi kulingana nesisindo se-molar, ngakho ukukala ivolumu eyaziwayo yegesi kunikeza isisindo sayo se-molar.

Isibonelo esisebenzile 3. Ifilasiki engu-0.500 L eligcwele igesi elingaziwa ku-35.0 °C no-0.968 atm iqukethe u-0.967 g wegesi. Ukufaka u-n = m/M emthethweni wegesi ofanele nokuhlela kabusha kunikeza u-M = (m × R × T)/(P × V) = (0.967 g)(0.08206 L·atm/(mol·K))(308.15 K) / [(0.968 atm)(0.500 L)] = 50.5 g/mol. Ngokusebenzisa izisindo ze-athomu ezijwayelekile ze-IUPAC eziyiswe emadesimalini amabili (H 1.01, C 12.01, Cl 35.45), i-chloromethane, CH₃Cl, inesisindo u-M = 12.01 + 3(1.01) + 35.45 = 50.49 g/mol, ngakho idatha ihambisana naleyo gesi. Ukuhambisana akufakazelwa: igesi elinye elinesisindo se-molar esifanayo lingabuya nomphumela ofanayo.

Izingcindezi engxenyeni ezingxubeni namagesi aqoqwe phezu kwamanzi

Engxubeni yamagesi angasabeli, igesi ngalinye liziphatha njengokungathi lilodwa. Umthetho ka-Dalton uthi ingcindezi ephelele iyisamba sezingcindezi engxenyeni: P_total = P_A + P_B + …. Ingcindezi engxenyeni ngayinye ilingana nengxenye ye-mole yaleyo gesi phindwe ingcindezi ephelele, P_A = x_A × P_total, lapho x_A = n_A/n_total.

Isibonelo esisebenzile 4. Isitsha esingu-4.00 L ku-25.0 °C siphethe u-0.150 mol we-N₂ no-0.0450 mol we-CO₂. Inani eliphelele lingu-0.195 mol, ngakho P_total = (0.195 mol)(0.08206 L·atm/(mol·K))(298.15 K) / 4.00 L = 1.19 atm. Ingxenye ye-mole ye-N₂ ingu-0.150/0.195 = 0.769, okunikeza u-P(N₂) = 0.917 atm, no-P(CO₂) = 0.275 atm. Zihlangana zibe ngu-1.19 atm, njengoba kufanele.

Igesi eqoqwe phezu kwamanzi ixutshwe nomhwamuko wamanzi, ngakho susa ingcindezi yomhwamuko wamanzi kuleli zinga lokushisa kuqala. Ku-hydrogen eqoqwe ku-23 °C ngengcindezi ephelele engu-754 torr, ingcindezi yomhwamuko wamanzi ingu-21.1 torr (Itafula 9.2 le-OpenStax), ngakho P(H₂) = 754 − 21.1 = 733 torr, noma 0.964 atm. Esampuleni engu-0.312 L, n = (P × V)/(R × T) = (0.964 atm)(0.312 L) / [(0.08206 L·atm/(mol·K))(296.15 K)] = 0.0124 mol H₂.

Amaphutha emithethweni yegesi okufanele uwabambe ngaphambi kokuthumela

Izimpendulo eziningi ezingalungile ezinkingeni zegesi zivela ekuphutheni okumbalwa okubikezelekayo, ngalinye linokuhlola okuqondile.

Umkhuba onenzuzo kakhulu ukubikezela ukuthi impendulo kufanele ikhule noma incipha yini ngaphambi kokubala. Uma izibalo ziphikisana, bheka isilinganiso esiphendulwe.

• I-Celsius esibalweni: izinga lokushisa elingu-25 esikhundleni sika-298.15 K linikeza impendulo engalungile ngesici esicishe sibe ngu-12. Ezimeni zelabhorethri ezijwayelekile, u-T ngamunye ofaka kufanele ube cishe u-250 K kuya ku-400 K.
• U-R ongahambisani: ukusebenzisa u-8.314 nge-atm ne-L kwenza impendulo ibe nephutha lesici esicishe sibe ngu-100.
• Amagremu esikhundleni sama-mole: u-n ku-PV = nRT yinani nge-mole. Uma inkinga inikeza isisindo, hlukanisa ngesisindo se-molar kuqala, noma sebenzisa u-PM = dRT.
• Ukukhohlwa umhwamuko wamanzi: igesi eqoqwe phezu kwamanzi ayomile. Susa ingcindezi yomhwamuko ezingeni lokushisa lokuqoqa.

Lapho amagesi angempela eyeka ukuziphatha ngokufanele

Umthetho wegesi ofanele ucabanga ukuthi amamolekyuli awathathi ivolumu futhi awaheheni. Amagesi angempela asondela kulokhu ekucindezelweni okuphansi nasezingeni lokushisa eliphakeme. Engcindezini ephezulu, ivolumu yamamolekyuli ngokwayo iba yingxenye ebonakalayo yesitsha, ngakho igesi ingacindezeleka kancane kunalokho okubikezelwe. Ezingeni lokushisa eliphansi, ukuheha kudonsa amamolekyuli ndawonye futhi ingcindezi elinganisiwe iwela ngaphansi kwenani elifanele.

Isibalo sika-van der Waals sengeza ukulungisa okubili: ithemu ku-a lokuheha nethemu ku-b losayizi wamamolekyuli. Amagesi anamandla aqinile phakathi kwamamolekyuli anamanani amakhulu e-a futhi aphambuka kakhulu: Itafula 9.3 le-OpenStax libhala u-a = 5.46 L²·atm/mol² womhwamuko wamanzi uma uqhathaniswa no-1.39 we-nitrogen no-0.0342 we-helium. Eduze no-1 atm nezinga lokushisa lasekamelweni umthetho wegesi ofanele ngokuvamile ulungile ngamaphesenti ambalwa, kodwa ungawethembi eduze nephuzu lapho igesi ifingqeka.