Umthetho wegesi ofanele (Isilinganiso sesimo segesi ofanele)

Isihloko mayelana nomthetho wegesi ofanele (Isilinganiso sesimo segesi ofanele)

Imithetho yegesi, okuhlanganisa nomthetho kaBoyle, umthetho kaCharles, kanye nomthetho kaGay-Lussac , ayisebenzi kuzo zonke izimo zegesi, okwenza ukuhlaziya kwethu kube nzima kakhulu. Ukuze kube lula ukuhlaziya, kudalwa imodeli yegesi efanele. Amagesi afanelekile awakho empilweni yansuku zonke; amane nje ayizinhlobo eziphelele ezidalwe ukuze kube lula ukuhlaziya. Umqondo wegesi efanele nawo uyasisiza kakhulu ekuhloleni ubudlelwano phakathi kwemithetho emithathu yegesi.

Ubudlelwano phakathi kwezinga lokushisa, ivolumu kanye nokucindezela kwegesi

Ngokubhekisela emithethweni emithathu yegesi engenhla, singathola ubudlelwano obujwayelekile phakathi kwezinga lokushisa, ivolumu kanye nokucindezela kwegesi.

Uma i-equation 1, i-equation 2 kanye ne-equation 3 zihlanganiswe zibe yinye, kuzobukeka kanje: I-PV ∝ T → Isilinganiso 4

Lesi silinganiso sithi ingcindezi (P) kanye nevolumu (V) kuyalingana nokushisa okuphelele (T).

Ngakolunye uhlangothi, ivolumu (V) ilingana ngokuphambene nokucindezela (P).

Isilinganiso 4 sishintshelwa ku-equation:

Imininingwane:

P ₁ = ingcindezi yokuqala (Pa noma N/m ² )

P ₂ = ukucindezela kokugcina (Pa noma N/m ² )

V ₁ = ivolumu yokuqala (m ³ )

V ₂ = ivolumu yokugcina (m ³ )

T ₁ = izinga lokushisa lokuqala (K)

T ₂ = izinga lokushisa lokugcina (K)

(Pa = uPascal, N = uNewton, m2 ⁼ imitha yesikwele, m3 ⁼ imitha yesikwele, K = uKelvin)

Ubudlelwano phakathi kwesisindo segesi (m) kanye nomthamo (V)

Uma ibhaluni lomoya oshisayo lifuthwa umoya, umoya omningi uthathwa, uyanda kakhulu. Ngamanye amazwi, lapho isisindo segesi sikhulu, ivolumu yebhaluni iba nkulu. Singasho ukuthi isisindo segesi (m) silingana ngqo nevolumu yegesi (V). Ngokwezibalo:

V ∝ m → Isilinganiso 5

Uma i-equation 4 ihlanganiswe ne-equation 5 khona-ke:

I-PV ∝ mT → Ukuqhathanisa 6

Inani lama-moles (n)

I-mole eyi-1 = isisindo sento esilingana nesisindo sama-molecule saleyo nto. Isisindo sama-molecule kanye nesisindo kuhlukile.

Isibonelo 1, isisindo sama-molecule segesi ye-O oxygen (O ₂ ) = 16 u + 16 u = 32 u (i-molecule ngayinye ye-oxygen iqukethe ama-athomu amabili e-O oxygen, lapho i-athomu ngayinye ye-O oxygen inesisindo sama-u angu-16). Ngakho-ke, i-mole eyodwa ye-O ₂ inesisindo sama-gramu angu-32. Noma isisindo sama-molecule se-O ₂ = 32 amagremu/mol = 32 kg/kmol.

Isibonelo 2, isisindo sama-molecule segesi ye-carbon monoxide (CO) = 12 u + 16 u = 28 u (i-molecule ngayinye ye-carbon monoxide iqukethe i-athomu ye-carbon eyodwa (C) kanye ne-athomu ye-oxygen eyodwa (O). Isisindo se-athomu ye-carbon eyodwa = 12 u kanye nesisindo se-athomu ye-oxygen eyodwa = 16 u. 12 u + 16 u = 28 u). Ngakho-ke, i-molecule eyodwa ye-CO inesisindo sama-gram angu-28. Noma isisindo sama-molecule se-CO = 28 grams/mol = 28 kg/kmol.

Isibonelo 3, isisindo sama-molecule segesi ye-carbon dioxide (CO2 ₎ = [12 u + (2 x 16 u)] = [12 u + 32 u] = 44 u (i-molecule ngayinye ye-carbon dioxide iqukethe i-athomu ye-carbon eyodwa (C) kanye nama-athomu amabili e-oxygen (O). Isisindo se-athomu ye-carbon eyodwa = 12 u kanye nesisindo se-athomu ye-oxygen eyodwa = 16 u). Ngakho-ke, i-mole eyodwa ye-CO2 _inesisindo sama-gramu angu-44. Noma isisindo sama-molecule se-CO2 ₌ 44 amagremu/mol = 44 kg/kmol.

Inani lama-moles (n) ento = isilinganiso sobuningi bento nesisindo sayo sama-molecule. Kubhalwe kanje ngokwezibalo:

Isibonelo 1: Bala inani lama-moles kumagremu angu-64 e-O₂

Isisindo se-O2 ₌ amagremu angu-64

Isibonelo 2: Bala inani lama-moles kumagremu angu-280 e-CO2

Isisindo se-CO = 280 amagremu

Isibonelo 3: Bala inani lama-moles kumagremu angu-176 e-CO2₂

Isisindo se-CO2 ₌ 176 amagremu

I-constant yegesi yendawo yonke (R)

Ngokusekelwe ocwaningweni olwenziwe ososayensi, kwatholakala ukuthi lapho inani lama-moles (n) lisetshenziswa ukuveza ubukhulu bento ethile, i-proportionality constant yegesi ngayinye inenani elifanayo. I-proportionality constant okukhulunywa ngayo yi-universal gas constant (R).

R = 8,315 J/mol.K

= 8315 kJ/kmol.K

= 0,0821 (L.atm) / (mol.K)

= 1,99 cal / mol. K

(J = Joule, K = Kelvin, L = ilitha, atm = umkhathi, cal = ikhalori)

UMTHETHO WEGESI OFANELE (kuma-moles)

Ukuqhathanisa okungenhla kungaguqulwa kube yi-equation ngokufaka inombolo yama-moles (n) kanye ne-universal gas constant (R).

I-PV = nRT

Lesi sibalo sibizwa ngokuthi umthetho wegesi ofanele noma i-equation yegesi efanelekile yesimo.

Imininingwane:

P = ingcindezi yegesi (N/ ^m2 )

V = ivolumu yegesi (m ³ )

n = inani lama-moles (mol)

R = igesi engaguquki yonke (R = 8,315 J/mol.K)

T = izinga lokushisa eliphelele legesi (K)

Uma uxazulula izinkinga, uzohlangana negama elithi STP. I -STP imele izinga lokushisa elijwayelekile kanye nokucindezela.

Izinga lokushisa elijwayelekile (T) = 0 ^o C = 273 K

Umfutho ojwayelekile (P) = 1 atm = 1,013 x 10 ⁵ N/m ² = 1,013 x 10 ² kPa = 101 kPa

Ekuxazululeni izinkinga zomthetho wegesi, izinga lokushisa kumele livezwe esikalini sikaKelvin (K).

Uma ingcindezi yegesi iseyingcindezi yokulinganisa, yiguqule ibe yingcindezi ephelele kuqala.

Ukucindezela okuphelele = ukucindezela komoya + ukucindezela kwesilinganiso (ukucindezela komoya = ukucindezela komoya wangaphandle)

Uma okwaziwayo kungumfutho womoya (akukho ngcindezi yokulinganisa), xazulula inkinga ngqo.

Isibonelo sombuzo 1:

Uma ucindezela umoya (101 kPa), izinga lokushisa legesi ye-carbon dioxide = 20 ^o C kanye nomthamo wayo = amalitha ama-2. Uma ingcindezi ishintshelwa ku-201 kPa futhi izinga lokushisa lenyuka laya ku-40 ^o C, bala ivolumu yokugcina yegesi ye-carbon dioxide.

Ingxoxo

Kuyaziwa ukuthi:

P ₁ = 101 kPa

P ₂ = 201 kPa

I-T ₁ = 20 ^o C + 273 K = 293 K

I-T ₂ = 40 ^o C + 273 K = 313 K

V ₁ = 2 amalitha

Kubuziwe: V ₂

Impendulo:

Isibonelo sombuzo 2:

Thola ivolumu yama-moles amabili egesi ku-STP (cabanga ukuthi le gesi iyigesi efanelekile)

Ingxoxo

Umthamo wama-moles amabili egesi ku-STP (izinga lokushisa elijwayelekile kanye nengcindezi) ungamalitha angu-44,8.

Isibonelo sombuzo 3:

Umthamo wegesi yomoya-mpilo ku-STP = 20 m ^3. Iyini isisindo segesi yomoya-mpilo?

Ingxoxo

Isisindo sama-molecule somoya-mpilo = 32 amagremu/mol (isisindo se-mole eyodwa yomoya-mpilo = 32 amagremu). Ngakho-ke, isisindo segesi yomoya-mpilo yilesi:

isisindo (m) = inani lama-molecular (n) x isisindo sama-molecule

isisindo = (ama-moles angu-893) x (amagremu angu-32/mol) = amagremu angu-28576 = 28,576 kg

Isibonelo sombuzo 4:

Ithangi liqukethe amalitha angu-4 egesi yomoya-mpilo (O2 ₎ . Izinga lokushisa legesi yomoya-mpilo lingu-20 ^oC kanti ingcindezi elinganisiwe ingu-20 x 10 ⁵ N/m2 ^. Thola isisindo segesi yomoya-mpilo (isisindo sama-molecule omoya-mpilo = 32 kg/kmol = 32 amagremu/mol)

Ingxoxo

UMTHETHO WEGESI OFANELE (Ngenani lama-molecule)

Uma siveza ubukhulu bento hhayi ngokwesisindo (m), kodwa ngokwenani lama-moles (n), khona-ke i-universal gas constant (R) isebenza kuwo wonke amagesi. Lokhu kwaqala ukutholwa ngu-Amedeo Avogadro (1776-1856), usosayensi wase-Italy.

U-Avogadro uthe uma ivolumu, ingcindezi kanye nokushisa kwegesi ngayinye kufana, khona-ke igesi ngayinye inenani elifanayo lama-molecule.

Umusho obhalwe ngokugqamile omalukeke ubizwa ngokuthi i-Avogadro's hypothesis. I-Avogadro's hypothesis, noma i-conjecture, ihambisana neqiniso lokuthi i-R engaguquki iyafana kuwo wonke amagesi. Nazi ezinye izibonakaliso:

Okokuqala , uma sixazulula inkinga sisebenzisa i-equation efanele ye-gas law (PV = nRT), sizothola ukuthi uma inani lama-moles (n) lifana, ingcindezi kanye nokushisa nakho kuyafana, khona-ke ivolumu yawo wonke amagesi izoba efanayo, uma sisebenzisa i-universal gas constant (R = 8,315 J/mol.K). Ku-STP, yonke igesi enenani elifanayo lama-moles (n) izoba nevolumu efanayo. Ivolumu ye-1 mole yegesi ku-STP = amalitha angu-22,4. Ivolumu yama-moles amabili egesi = amalitha angu-44,8. Ivolumu yama-moles amathathu egesi = amalitha angu-67,2. Njalo njalo… lokhu kusebenza kuwo wonke amagesi.

Okwesibili , inani lama-molecule ku-mole eyi-1 liyafana kuwo wonke amagesi. Inani lama-molecule ku-mole eyi-1 = inani lama-molecule nge-mole = inombolo ka-Avogadro (NA ₎ . Ngakho-ke inombolo ka-Avogadro iyafana kuwo wonke amagesi.

Usayizi wenombolo ka-Avogadro utholakala ngokulinganisa:

I-NA = 6,02 x 10 ²³ ama-molecule/mol

Ukuze sithole inani eliphelele lama-molecule (N), singaphindaphinda inani lama-molecule nge-mole ngayinye (NA) ngenani lama-mole (n).

Lesi yisilinganiso somthetho wegesi esifanele ngokwenani lama-molecule.

Imininingwane:

P = Ukucindezela

V = Ivolumu

N = Inani eliphelele lama-molecule

k = I-Boltzmann Constant (k = 1,38 x 10 ^‐23 J/K)

T = Izinga lokushisa

ivolumu

Ilitha eli-1 (L) = 1000 milliliters (mL) = 1000 cubic centimeters (cm ³ )

Ilitha eli-1 (L) = i-cubic decimeter eli-1 (dm ³ ) = 1 x ^10-3 m ³

I-Tekanan

1 N/m ² = 1 Pa

1 atm = 1,013 x 10 ⁵ N/m ² = 1,013 x 10 ⁵ Pa = 101,3 x 10 ² kPa = 101.3 kPa (kuvamise ukusetshenziswa i-101 kPa)

Pa = uPascal

i-atm = umkhathi

Amandla angaphakathi egesi efanelekile

Amandla angaphakathi egesi elifanele le-monatomic

Amandla angaphakathi egesi elifanele le-monatomic yisamba esiphelele samandla e-kinetic okuhumusha ama-molecule egesi elifanele le-monatomic. Isamba esiphelele samandla e-kinetic okuhumusha ama-molecule egesi elifanele = umkhiqizo wamandla e-kinetic okuhumusha ajwayelekile e-molecule ngayinye ngenani lama-molecule (N). Ngokwezibalo:

Imininingwane:

U = Amandla angaphakathi egesi elifanele le-monatomic (J)

N = Inani lama-molecule

k = I-Boltzmann Constant (k = 1,38 x 10 ^‐23 J/K)

T = Izinga lokushisa eliphelele (K)

n = Inani lama-moles (mol)

R = I-gesi engaguquki yonke (R = 8,315 J/mol.K = 8315 kJ/kmol.K)

Amandla kugesi efanelekile ye-diatomic

Amandla angaphakathi egesi elifanele le-diatomic yisamba samandla e-kinetic ahunyushwayo, amandla e-kinetic ajikelezayo, kanye namandla e-kinetic adlidlizayo ama-molecule egesi elifanele le-diatomic. Ngokusho komgomo wokwahlukaniswa kwamandla, amandla angaphakathi egesi elifanele le-diatomic yilawa:

U = 5/2 n RT

Amandla kugesi efanelekile ye-polyatomic

Amandla angaphakathi egesi elihle le-polyatomic yisamba samandla e-kinetic ahunyushwayo, amandla e-kinetic ajikelezayo, kanye namandla e-kinetic adlidlizayo ama-molecule egesi elihle le-polyatomic. Ngokusho komgomo wokuhlanganiswa kwamandla, amandla angaphakathi egesi elihle le-polyatomic yilawa:

U = 7/2 n RT

Amandla kugesi wangempela

Amandla kugesi langempela nawo ancike ekushiseni. Lapho ingcindezi yegesi langempela iphezulu ngokwanele (ivolumu yegesi langempela incane), igesi langempela liqala ukubonisa ukuziphatha okuphambene. Ngakho-ke, kungashiwo ukuthi amandla kugesi langempela nawo ancike ekucindezelweni kanye nomthamo.