Izakhiwo ze-colligative: indlela izinhlayiya ezincibilikisiwe ezishintsha ngayo isincibilikisi

Ukubala izinhlayiya: i-molality ne-mole fraction

Isakhiwo se-colligative sincike esilinganisweni sezinhlayiya zento encibilikisiwe nezinhlayiya zesincibilikisi. I-mole yamamolekyuli e-sucrose ne-mole yamamolekyuli e-urea ancibilikiswe esisindweni esifanayo samanzi ehlisa indawo yawo yokuqanda ngenani elifanayo, nakuba izisindo zawo ze-molar zihluka ngesici esicishe sibe yisithupha.

Ngenxa yalokhu, amayunithi okugxila asetshenziswa lapha abala izinhlayiya. I-mole fraction, x, ingama-mole engxenye eyodwa ahlukaniswe ngama-mole esewonke. I-molality, m, ingama-mole ento encibilikisiwe ngekhilogremu ngayinye yesincibilikisi. I-molality isetshenziswa esikhundleni se-molarity ngoba isekelwe ezisindweni, ngakho ayishintshi lapho isixazululo sinweba noma sifinyela ngezinga lokushisa. Ezixazululweni zamanzi ezihlanjululiwe, i-molality ne-molarity ziseduze ngokwezinombolo, kodwa aziyona inani elifanayo.

Izibalo ezingezansi zithatha isixazululo esihlanjululiwe esifanele esinento encibilikisiwe engaguquki ibe umhwamuko, okusho leyo engafaki cishe lutho emhwamukweni ongaphezu kwesixazululo.

Umthetho ka-Raoult nokwehla kwengcindezi yomhwamuko

Umthetho ka-Raoult uthi ingcindezi yomhwamuko wesincibilikisi ngaphezu kwesixazululo ilingana ne-mole fraction yaso iphindaphindwe ngengcindezi yomhwamuko wesincibilikisi esihlanzekile: P_solution = x_solvent × P°_solvent. Njengoba ama-mole fraction ehlangana abe ngu-1, ukwehla kwengcindezi yomhwamuko kungu-ΔP = x_solute × P°_solvent.

Isibonelo esisebenzile 1. Thola ingcindezi yomhwamuko ku-25 °C yesixazululo sika-100.0 g we-sucrose, C₁₂H₂₂O₁₁, ku-250.0 g wamanzi. Ingcindezi yomhwamuko wamanzi ahlanzekile ku-25 °C ingu-23.8 torr (Itafula 9.2 le-OpenStax). Usebenzisa izisindo ze-athomu ezijwayelekile ze-IUPAC, M(sucrose) = 342.30 g/mol no-M(H₂O) = 18.015 g/mol, ngakho n(sucrose) = 0.2921 mol no-n(H₂O) = 13.88 mol. x(H₂O) = 13.88 ÷ (13.88 + 0.2921) = 0.9794. P = 0.9794 × 23.8 torr = 23.3 torr.

Ukwehla, x(sucrose) × P° = 0.02062 × 23.8 torr = 0.491 torr, kuncane nakuba isixazululo sicishe sibe ngamaphesenti angu-29 kashukela ngesisindo. Amamolekyuli e-sucrose asindayo, ngakho u-100 g wawo usewuyingxenye encane nje yamamolekyuli akhona.

Ukukhuphuka kwendawo yokubila nokwehla kwendawo yokuqanda

Ukwehlisa ingcindezi yomhwamuko kusho ukuthi isixazululo kufanele sifudunyezwe kakhulu ngaphambi kokuthi ingcindezi yaso yomhwamuko ifike engcindezini yangaphandle, ngakho indawo yokubila iyakhuphuka. Into encibilikisiwe iphinde iphazamise ukwakheka kwesincibilikisi esiqinile, ngakho indawo yokuqanda iyehla. Ezixazululweni ezihlanjululiwe kokubili ukushintsha kuhambisana ne-molality: ΔTb = Kb × m no-ΔTf = Kf × m.

Ama-constant angawesincibilikisi, hhayi awento encibilikisiwe. Itafula 11.2 le-OpenStax linikeza u-Kb = 0.512 °C·kg/mol no-Kf = 1.86 °C·kg/mol wamanzi, no-Kb = 2.53 no-Kf = 5.12 °C·kg/mol we-benzene. U-Kf wamanzi mkhulu ngaphezu kokuphindwe kathathu u-Kb wawo, ngakho into encibilikisiwe ethile ishintsha indawo yokuqanda yamanzi kakhulu kunendawo yawo yokubila.

Isibonelo esisebenzile 2. I-coolant yenziwa ngokuncibilikisa u-250. g we-ethylene glycol, C₂H₆O₂ (62.07 g/mol), ku-1.000 kg wamanzi. n = 250. g ÷ 62.07 g/mol = 4.028 mol, ngakho m = 4.028 mol/kg. ΔTf = 1.86 × 4.028 = 7.49 °C, ngakho indawo yokuqanda efanele ingu-−7.49 °C. ΔTb = 0.512 × 4.028 = 2.06 °C, ngakho indawo yokubila efanele ingu-102.1 °C. Kulokhu kugxila isixazululo asisahlanjululiwe kakhulu, ngakho thatha lokhu njengokulinganisela, hhayi amanani alinganisiwe.

Ama-electrolyte nesici se-van't Hoff

Into encibilikisiwe ye-ionic ikhulula izinhlayiya ezingaphezu kweyodwa ngeyunithi yefomula ngayinye. Isici se-van't Hoff, i, yinani lama-mole ezinhlayiya esixazululweni nge-mole ngayinye yento encibilikisiwe, futhi siphindaphinda isibalo ngasinye se-colligative: ΔTf = i × Kf × m. Inani elifanele yinani lama-ayoni kufomula: 2 ku-NaCl, 3 ku-CaCl₂ no-1 ku-nonelectrolyte efana ne-glucose.

Amanani alinganisiwe mancane, ngoba ama-ayoni anamashaji aphambene ayahehana futhi amanye akha ama-ion pair asebenza njengenhlayiya eyodwa. Itafula 11.3 le-OpenStax libhala izici ezilinganisiwe zezixazululo ezingu-0.050 m: 1.9 ku-NaCl, 2.7 ku-MgCl₂, 1.3 ku-MgSO₄ no-3.4 ku-FeCl₃, uma kuqhathaniswa namanani afanele angu-2, 3, 2 no-4. Ezixazululweni ezihlanjululiwe, igebe ngokuvamile liyakhula njengoba ukugxila kukhuphuka futhi njengoba amashaji ama-ayoni ekhula.

Isibonelo esisebenzile 3. Linganisela indawo yokuqanda ka-15.0 g we-CaCl₂ (110.98 g/mol) oncibilikiswe ku-500.0 g wamanzi. n = 0.1352 mol no-m = 0.1352 mol ÷ 0.5000 kg = 0.2703 mol/kg. Ngo-i ofanele = 3, ΔTf = 3 × 1.86 × 0.2703 = 1.51 °C, kunikeze u-−1.51 °C. Ukwehla kwangempela kuncane. Uma usebenzisa u-2.7, isici esilinganisiwe sikasawoti ofanayo i-MgCl₂ ku-0.050 m, ukulinganisela kuba ngu-1.36 °C. Lelo nani lisalinganiselwe nje, ngoba lesi sixazululo sigxilile ngaphezu kokuphindwe kahlanu.

Ukusebenzisa indawo yokuqanda ukuthola isisindo se-molar

Uma wazi isisindo sento encibilikisiwe nesesincibilikisi futhi ulinganisa u-ΔTf, ungasebenza uhlehla uye esisindweni se-molar. Indlela yendawo yokuqanda ikhethwa kunendlela yendawo yokubila ngoba u-Kf mkhulu kuno-Kb ezincibilikisini ezivamile, futhi ngoba indawo yokubila nayo iyashintsha ngengcindezi yomkhathi yalolo suku.

Isibonelo esisebenzile 4. Ukuncibilikisa u-1.50 g we-nonelectrolyte engaziwa engaguquki ibe umhwamuko ku-25.0 g we-benzene kwehlisa indawo yokuqanda ngo-1.62 °C. I-molality: m = ΔTf ÷ Kf = 1.62 ÷ 5.12 = 0.3164 mol/kg. Ama-mole ento encibilikisiwe: 0.3164 mol/kg × 0.0250 kg = 7.910 × 10⁻³ mol. Isisindo se-molar: 1.50 g ÷ 7.910 × 10⁻³ mol = 190 g/mol, ezinombolweni ezibalulekile ezintathu.

I-benzene iyisincibilikisi esihle kulokhu kuhlola ngoba u-Kf wayo ucishe uphindwe kathathu owamanzi, ngakho inani elifanayo lento encibilikisiwe linikeza ushintsho olukhulu, olulula ukulinganisa. Indlela ithatha ukuthi into encibilikisiwe ayihlukani futhi ayihlangani. Ama-carboxylic acid, isibonelo, akha amabhangqa abophene nge-hydrogen ku-benzene futhi anikeze isisindo se-molar esibonakalayo esicishe siphindwe kabili inani langempela.

Ingcindezi ye-osmotic namamolekyuli amakhulu kakhulu

Lapho ulwelwesi lwe-semipermeable luhlukanisa isixazululo nesincibilikisi esihlanzekile, isincibilikisi sigelezela esixazululweni. Ingcindezi okufanele isetshenziswe esixazululweni ukumisa lokhu kugeleza yingcindezi ye-osmotic, Π = i × M × R × T, lapho u-M eyi-molarity, R = 0.08206 L·atm/(mol·K), no-T ungama-kelvin.

Isibonelo esisebenzile 5. I-saline yasemithanjeni icishe ibe yi-NaCl engu-0.155 mol/L. Ezingeni lokushisa lomzimba, 37.0 °C noma 310.15 K, ingcindezi ye-osmotic efanele ingu-Π = 2 × 0.155 × 0.08206 × 310.15 = 7.89 atm. Ukusebenzisa u-i = 2 kuyenza ibe nkulu kancane, ngoba isici sangempela singaphansi kancane kuka-2. Ingcindezi enkulu kangako yiyona ebangela ukuthi izixazululo ezinikezwa emthanjeni kufanele zihambisane nokugxila kwezinto ezincibilikisiwe egazini.

Isibonelo esisebenzile 6. Isixazululo sika-0.250 g we-protein ku-50.0 mL wamanzi sinengcindezi ye-osmotic engu-4.20 torr ku-25.0 °C. Π = 4.20 ÷ 760 = 5.526 × 10⁻³ atm. M = Π ÷ (R × T) = 5.526 × 10⁻³ ÷ (0.08206 × 298.15) = 2.259 × 10⁻⁴ mol/L, ngakho n = 1.129 × 10⁻⁵ mol ku-0.0500 L, futhi isisindo se-molar singu-0.250 g ÷ 1.129 × 10⁻⁵ mol = 2.21 × 10⁴ g/mol. Isixazululo esifanayo besizoqanda cishe ngo-4 × 10⁻⁴ °C kuphela ngaphansi kwamanzi ahlanzekile, okuncane kakhulu ukuthi kulinganiswe kahle. Yingakho ingcindezi ye-osmotic, hhayi indawo yokuqanda, isetshenziselwa ama-polymer nama-protein.

Amaphutha aphazamisa izibalo ze-colligative

Ukuhlola okusheshayo kubamba amaphutha amaningi: isixazululo kufanele sihlale sibila ezingeni eliphezulu futhi siqande ezingeni eliphansi kunesincibilikisi esihlanzekile, futhi ukushintsha kwezixazululo zamanzi ezihlanjululiwe ngokuvamile kungamadigri ambalwa kakhulu.

• Ukusebenzisa i-molarity ku-ΔT = K × m. Lezi zibalo zidinga i-molality, esebenzisa amakhilogremu esincibilikisi, hhayi amalitha esixazululo.
• Ukuhlukanisa ngesisindo sesixazululo esikhundleni sesisindo sesincibilikisi.
• Ukushiya isici se-van't Hoff sento encibilikisiwe ye-ionic, noma ukusisebenzisa entweni encibilikisiwe yamamolekyuli efana ne-sucrose noma i-ethylene glycol.
• Ukubika u-ΔTf njengendawo yokuqanda. Kususe endaweni yokuqanda yesincibilikisi esihlanzekile.
• Ukusebenzisa izinga lokushisa le-Celsius ku-Π = iMRT. Guqula ube ama-kelvin kuqala.
• Ukuthatha u-Kf noma u-Kb wesincibilikisi esingalungile. Ziyizakhiwo zesincibilikisi.