Astaamaha colligative-ka: sida qaybaha la milay u beddelaan milaha

Tirinta qaybaha: molaaliti iyo jajabka moolka

Astaan colligative ah waxay ku xiran tahay saamiga qaybaha walaxda la milay iyo qaybaha milaha. Mool molekiyuullo sucrose ah iyo mool molekiyuullo urea ah oo lagu milay isla culeys biyo ah waxay dhibicda barafowga u dhigaan isla qadar, in kasta oo culeysyadooda molarku ku kala duwan yihiin arrin ku dhow lix.

Sababtaas darteed, cutubyada uruurinta ee halkan la isticmaalo waxay tiriyaan qaybaha. Jajabka moolka, x, waa moolasha hal qayb oo loo qaybiyey wadarta moolasha. Molaaliti, m, waa moolasha walaxda la milay kiilogaraam kasta oo milaha ah. Molaaliti ayaa loo isticmaalaa halkii molaariti sababtoo ah wuxuu ku salaysan yahay culeysyo, sidaa darteed isma beddelo marka xalku la ballaarto ama la yaraado heerkulka. Xalalka biyaha ee khafiifka ah, molaaliti iyo molaaritigu tiro ahaan way isu dhow yihiin, laakiin ma aha isla qadar.

Isleegyada hoose waxay u qaataan xal khafiif ah oo ku habboon oo leh walax la milay oo aan uumi-baxin, taasoo macnaheedu yahay mid aan wax ku darin uumiga ka sarreeya xalka.

Sharciga Raoult iyo hoos u dhaca cadaadiska uumiga

Sharciga Raoult wuxuu sheegaa in cadaadiska uumiga milaha ee xalka ka sarreeya uu le'eg yahay jajabka moolkiisa oo lagu dhuftay cadaadiska uumiga milaha saafiga ah: P_solution = x_solvent × P°_solvent. Maadaama jajabyada moolku isku geeyaan 1, hoos u dhaca cadaadiska uumigu waa ΔP = x_solute × P°_solvent.

Tusaale la xaliyey 1. Hel cadaadiska uumiga 25 °C ee xal ka kooban 100.0 g sucrose, C₁₂H₂₂O₁₁, oo ku jira 250.0 g biyo ah. Cadaadiska uumiga biyaha saafiga ah 25 °C waa 23.8 torr (OpenStax Shaxda 9.2). Adigoo isticmaalaya culeysyada atamka caadiga ah ee IUPAC, M(sucrose) = 342.30 g/mol iyo M(H₂O) = 18.015 g/mol, sidaa darteed n(sucrose) = 0.2921 mol iyo n(H₂O) = 13.88 mol. x(H₂O) = 13.88 ÷ (13.88 + 0.2921) = 0.9794. P = 0.9794 × 23.8 torr = 23.3 torr.

Hoos u dhaca, x(sucrose) × P° = 0.02062 × 23.8 torr = 0.491 torr, waa yar yahay in kasta oo xalku qiyaastii yahay 29 boqolkiiba sonkor culeys ahaan. Molekiyuullada sucrose way culus yihiin, sidaa darteed 100 g oo iyaga ah weli waa qayb yar oo ka mid ah molekiyuullada jira.

Kor u kaca dhibicda karkarka iyo hoos u dhaca dhibicda barafowga

Hoos u dhigidda cadaadiska uumiga macnaheedu waa in xalka la sii kululeeyo kahor inta cadaadiskiisa uumigu gaadhin cadaadiska dibadda, sidaa darteed dhibicda karkarku way kacdaa. Walaxda la milay waxay sidoo kale carqaladaysaa samaysanka milaha adag, sidaa darteed dhibicda barafowgu way dhacdaa. Xalalka khafiifka ah labada wareejinba waxay u dhigmaan molaaliti: ΔTb = Kb × m iyo ΔTf = Kf × m.

Joogtooyinku waxay ka tirsan yihiin milaha, ma aha walaxda la milay. OpenStax Shaxda 11.2 waxay biyaha u bixisaa Kb = 0.512 °C·kg/mol iyo Kf = 1.86 °C·kg/mol, benzene-na Kb = 2.53 iyo Kf = 5.12 °C·kg/mol. Kf-ka biyuhu wuxuu ka badan yahay saddex jibaar Kb-kooda, sidaa darteed walax la milay oo la siiyey waxay dhibicda barafowga biyaha u beddeshaa si aad uga badan dhibicda karkarkooda.

Tusaale la xaliyey 2. Qaboojiye ayaa lagu sameeyaa iyadoo 250. g ethylene glycol, C₂H₆O₂ (62.07 g/mol), lagu milo 1.000 kg biyo ah. n = 250. g ÷ 62.07 g/mol = 4.028 mol, sidaa darteed m = 4.028 mol/kg. ΔTf = 1.86 × 4.028 = 7.49 °C, sidaa darteed dhibicda barafowga ku habboon waa −7.49 °C. ΔTb = 0.512 × 4.028 = 2.06 °C, sidaa darteed dhibicda karkarka ku habboon waa 102.1 °C. Uruurintan xalku mar dambe aad uma khafiifsana, sidaa darteed u qaado kuwan qiyaasayaal, ma aha qiimayaal la cabbiray.

Electrolyte-yada iyo arrinta van't Hoff

Walax la milay oo ayoon ah waxay sii daysaa wax ka badan hal qayb cutub qaacido kasta. Arrinta van't Hoff, i, waa tirada moolasha qaybaha xalka ku jira mool kasta oo walax la milay ah, waxayna ku dhuftaa isleeg colligative kasta: ΔTf = i × Kf × m. Qiimaha ku habboon waa tirada ayoonnada qaacidada ku jira: 2 ee NaCl, 3 ee CaCl₂ iyo 1 ee walax aan electrolyte ahayn sida glucose.

Qiimayaasha la cabbiray way ka yar yihiin, sababtoo ah ayoonnada dallacaadahoodu ka soo horjeedaan way isjiidaan qaarkoodna waxay sameeyaan lammaanayaal ayoon oo u dhaqma sida hal qayb. OpenStax Shaxda 11.3 waxay taxdaa arrimaha la cabbiray ee xalalka 0.050 m: 1.9 ee NaCl, 2.7 ee MgCl₂, 1.3 ee MgSO₄ iyo 3.4 ee FeCl₃, marka loo eego qiimayaasha ku habboon ee 2, 3, 2 iyo 4. Xalalka khafiifka ah, farqigu guud ahaan wuu kordhaa marka uruurintu korodho iyo marka dallacaadaha ayoonnadu kordhaan.

Tusaale la xaliyey 3. Qiyaas dhibicda barafowga ee 15.0 g CaCl₂ (110.98 g/mol) oo lagu milay 500.0 g biyo ah. n = 0.1352 mol iyo m = 0.1352 mol ÷ 0.5000 kg = 0.2703 mol/kg. Iyadoo i ku habboon = 3, ΔTf = 3 × 1.86 × 0.2703 = 1.51 °C, taasoo bixisa −1.51 °C. Hoos u dhaca dhabta ahi wuu ka yar yahay. Haddii aad isticmaasho 2.7, arrinta la cabbiray ee cusbada la midka ah MgCl₂ ee 0.050 m, qiyaastu waxay noqotaa 1.36 °C. Tiradaasi weli waa qiyaas oo keliya, sababtoo ah xalkani wuxuu ka uruursan yahay shan jibaar in ka badan.

Isticmaalka dhibicda barafowga si loo helo culeyska molarka

Haddii aad taqaanno culeyska walaxda la milay iyo milaha oo aad cabbirto ΔTf, dib ayaad ugu shaqayn kartaa culeyska molarka. Habka dhibicda barafowga ayaa laga doorbidaa habka dhibicda karkarka sababtoo ah Kf wuu ka weyn yahay Kb milayaasha caadiga ah, iyo sababtoo ah dhibicda karkarku sidoo kale waxay la beddelantaa cadaadiska hawada ee maalintaas.

Tusaale la xaliyey 4. Milidda 1.50 g oo walax aan la aqoon oo aan uumi-baxin oo aan electrolyte ahayn oo lagu milay 25.0 g benzene ah waxay dhibicda barafowga hoos u dhigtaa 1.62 °C. Molaaliti: m = ΔTf ÷ Kf = 1.62 ÷ 5.12 = 0.3164 mol/kg. Moolasha walaxda la milay: 0.3164 mol/kg × 0.0250 kg = 7.910 × 10⁻³ mol. Culeyska molarka: 1.50 g ÷ 7.910 × 10⁻³ mol = 190 g/mol, saddex tiro oo muhiim ah.

Benzene waa mile wanaagsan tijaabadan sababtoo ah Kf-kiisu wuxuu ku dhow yahay saddex jibaar kan biyaha, sidaa darteed isla qadarka walax la milay wuxuu bixiyaa isbeddel ka weyn oo si fudud loo cabbiro. Habku wuxuu u qaataa in walaxda la milay aysan kala go'in mana isku tagin. Aashitooyinka carboxylic-ga, tusaale ahaan, waxay benzene ku sameeyaan lammaanayaal ku xidhan xidhiidhka hydrogen waxayna bixiyaan culeys molar oo muuqda oo ku dhow laba jibaarka qiimaha dhabta ah.

Cadaadiska osmotic-ga iyo molekiyuullada aadka u waaweyn

Marka xuub qayb-ahaan-gudbiye ah (semipermeable) uu xal ka soocayo mile saafi ah, milaha ayaa u qulqula xalka. Cadaadiska ay tahay in xalka lagu saaro si loo joojiyo qulqulkan waa cadaadiska osmotic-ga, Π = i × M × R × T, halkaas oo M uu yahay molaaritiga, R = 0.08206 L·atm/(mol·K), T-na uu yahay kelvin.

Tusaale la xaliyey 5. Saline-ka xididka (intravenous) waa qiyaastii 0.155 mol/L NaCl. Heerkulka jidhka, 37.0 °C ama 310.15 K, cadaadiska osmotic-ga ku habboon waa Π = 2 × 0.155 × 0.08206 × 310.15 = 7.89 atm. Isticmaalidda i = 2 wax yar ayay kor u qaadaa, sababtoo ah arrinta dhabta ahi wax yar ayay ka hoosaysaa 2. Cadaadis intaas le'eg ayaa sababta ah in xalalka xididka la siiyo ay tahay inay la mid noqdaan uruurinta walxaha la milay ee dhiigga.

Tusaale la xaliyey 6. Xal ka kooban 0.250 g oo borotiin ah oo ku jira 50.0 mL biyo ah wuxuu leeyahay cadaadis osmotic ah oo 4.20 torr ah 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, sidaa darteed n = 1.129 × 10⁻⁵ mol oo ku jira 0.0500 L, culeyska molarkuna waa 0.250 g ÷ 1.129 × 10⁻⁵ mol = 2.21 × 10⁴ g/mol. Isla xalkaasi wuxuu barafoobi lahaa oo keliya qiyaastii 4 × 10⁻⁴ °C ka hooseeya biyaha saafiga ah, taasoo aad ugu yar in si wanaagsan loo cabbiro. Taasi waa sababta cadaadiska osmotic-ga, ma aha dhibicda barafowga, loogu isticmaalo polymer-yada iyo borotiinnada.

Khaladaadka khalkhaliya xisaabaha colligative-ka

Hubin degdeg ah ayaa qabata khaladaadka badankooda: xalku had iyo jeer waa inuu ku karkaraa heer ka sarreeya oo ku barafoobaa heer ka hooseeya milaha saafiga ah, wareejinta xalalka biyaha ee khafiifka ahna badanaa waa ugu badnaan dhawr darajo.

• Isticmaalidda molaariti ΔT = K × m. Isleegyadani waxay u baahan yihiin molaaliti, oo isticmaala kiilogaraamyada milaha, ma aha litirrada xalka.
• U qaybinta culeyska xalka halkii laga qaybin lahaa culeyska milaha.
• Ka tegidda arrinta van't Hoff ee walax la milay oo ayoon ah, ama u isticmaalkeeda walax la milay oo molekiyuul ah sida sucrose ama ethylene glycol.
• U sheegidda ΔTf sida dhibicda barafowga. Ka jar dhibicda barafowga milaha saafiga ah.
• Isticmaalidda heerkulka Celsius Π = iMRT. Marka hore u beddel kelvin.
• Ka qaadashada Kf ama Kb mile khaldan. Waa astaamaha milaha.