Chinyorwa pamusoro pemutemo wegesi rakanaka (Equation of state of an ideal gas)
Mitemo yegesi, kusanganisira mutemo waBoyle, mutemo waCharles, nemutemo waGay-Lussac , haishande kune ese mamiriro egasi, zvichiita kuti ongororo yedu iome. Kuti ongororo iite nyore, muenzaniso wegasi rakanaka unogadzirwa. Magasi akanaka haapo muhupenyu hwezuva nezuva; ingori mafomu akakwana akagadzirwa kuti ongororo iite nyore. Pfungwa yegasi rakanaka inotibatsirawo zvikuru mukuongorora hukama huripo pakati pemitemo mitatu yegasi.
Hukama huripo pakati pekupisa, vhoriyamu uye kumanikidzwa kwegasi
Nekutarisa mitemo mitatu yegasi iri pamusoro apa, tinogona kuwana hukama hwakazara pakati pekupisa, huwandu uye kumanikidzwa kwegasi.
Kana equation 1, equation 2 ne equation 3 zvakabatanidzwa kuita chimwe chete, zvichaita seizvi: PV ∝ T → Chiyero 4
Chiyero ichi chinotaura kuti kumanikidzwa (P) uye vhoriyamu (V) zvinoenderana nekupisa kwakazara (T).
Kusiyana neizvi, vhoriyamu (V) inoenderana nekumanikidzwa (P).
Chiyero chechina chinoshandurwa kuita equation:
Information :
P 1 = kumanikidzwa kwekutanga (Pa kana N/m 2 )
P 2 = kumanikidzwa kwekupedzisira (Pa kana N/m 2 )
V 1 = vhoriyamu yekutanga (m 3 )
V 2 = vhoriyamu yekupedzisira (m 3 )
T 1 = tembiricha yekutanga (K)
T 2 = tembiricha yekupedzisira (K)
(Pa = pascal, N = Newton, m2 = mita yesikweya, m3 = mita yekubikira, K = Kelvin)
Hukama huripo pakati pehuremu hwegasi (m) nehukuru (V)
Kana bharumu remhepo inopisa rikafukidzwa, mweya wakawanda unotorwa, uye unowedzera kukura. Nemamwe mashoko, kana huremu hwegasi hwacho hwakakura, vhoriyamu yebharumu inowedzerawo kukura. Tinogona kutaura kuti huremu hwegasi (m) hwakaenzana zvakananga nehuwandu hwegasi (V). Pamasvomhu:
V ∝ m → Chiyero 5
Kana equation 4 yakabatanidzwa ne equation 5 saka:
PV ∝ mT → Kuenzanisa 6
Huwandu hwemamota (n)
Mole 1 = huremu hwechinhu chakaenzana nehuremu hwechinhu ichocho. Huremu hwemamorekuru nehuremu zvakasiyana.
Muenzaniso 1, huwandu hwemamorekuru egasi reOxygen (O2 ) = 16 u + 16 u = 32 u (morekuru yega yega yeokisijeni ine maatomu maviri eOxygen, uko atomu yega yega yeOxygen ine huwandu hwe16 u). Saka, mole imwe yeO2 ine huwandu hwemagiramu makumi matatu nemaviri. Kana huwandu hwemamorekuru eO2 = 32 gramu/mol = 32 kg/kmol.
Muenzaniso wechipiri, molecular mass yecarbon monoxide gas (CO) = 12 u + 16 u = 28 u (morekuru yega yega yecarbon monoxide ine atomu imwe chete yecarbon (C) uye atomu imwe chete yeokisijeni (O). Huremu hweatomu imwe chete yecarbon = 12 u uye huremu hweatomu imwe yeokisijeni = 16 u. 12 u + 16 u = 28 u). Saka, mole imwe yeCO ine huremu hwemagiramu makumi maviri nemasere. Kana kuti molecular mass yeCO = 28 grams/mol = 28 kg/kmol.
Muenzaniso wechitatu, molecular mass yecarbon dioxide gas (CO2 ) = [12 u + (2 x 16 u)] = [12 u + 32 u] = 44 u (morekuru yega yega yecarbon dioxide ine atomu imwe chete yecarbon (C) uye maatomu maviri eokisijeni (O). Huremu hwe1 atomu yecarbon = 12 u uye huremu hwe1 atomu yeokisijeni = 16 u). Saka, molekuru imwe yeCO2 ine huremu hwe44 gramu. Kana kuti molekyulu yeCO2 = 44 gramu/mol = 44 kg/kmol.
Huwandu hwemamoles (n) echinhu = chiyero chehuremu hwechinhu ichi kusvika pahuremu hwacho. Yakanyorwa nemasvomhu seizvi:
Muenzaniso 1: Verenga huwandu hwemamota mumagiramu 64 eO2
Huremu hweO2 = 64 magiramu
Muenzaniso 2: Verenga huwandu hwemamota mumagiramu 280 eCO2
Huremu hweCO = 280 gramu
Muenzaniso 3: Verenga huwandu hwemamota mumagiramu 176 eCO22
Huremu hweCO2 = 176 magiramu
Gasi risingaperi repasi rose (R)
Zvichibva pakutsvagurudza kwakaitwa nesainzi, zvakaonekwa kuti kana nhamba yemamoles (n) ikashandiswa kuratidza saizi yechinhu, chiyero chekuenzanisa chegasi rega rega chine kukosha kwakafanana. Chiyero chekuenzanisa chiri kutaurwa nezvacho ichinhu chinoramba chiripo chegasi (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 = litre, atm = mhepo, cal = macalorie)
Mutemo weGasi Wakanaka (mumamota)
Kuenzanisa kuri pamusoro apa kunogona kushandurwa kuita equation nekuisa nhamba yemamoles (n) uye universal gas constant (R).
PV = nRT
Iyi equation inonzi mutemo wegesi wakakodzera kana kuti equation yegesi yakakodzera yemamiriro ezvinhu.
Information :
P = kumanikidzwa kwegasi (N/ m2 )
V = vhoriyamu yegesi ( m3 )
n = nhamba yemamoles (mol)
R = gasi risingaperi (R = 8,315 J/mol.K)
T = tembiricha yakakwana yegesi (K)
Pakugadzirisa matambudziko, unosangana neshoko rekuti STP. STP inomiririra Standard Temperature nePressure.
Tembiricha yakajairika (T) = 0 o C = 273 K
Kumanikidzwa kwakajairika (P) = 1 atm = 1,013 x 10 5 N/m 2 = 1,013 x 10 2 kPa = 101 kPa
Mukugadzirisa matambudziko emutemo wegesi, tembiricha inofanira kuratidzwa pachikero cheKelvin (K).
Kana kumanikidzwa kwegasi kuchiri kuyera kumanikidzwa, tanga wachinja kuita kumanikidzwa kwakazara.
Kumanikidzwa kwakakwana = kumanikidzwa kwemhepo + kumanikidzwa kwegeji (kumanikidzwa kwemhepo = kumanikidzwa kwemhepo yekunze)
Kana chinozivikanwa chiri kumanikidzwa kwemhepo (hapana kumanikidzwa kwegeji), gadzirisa dambudziko racho zvakananga.
Muenzaniso wemubvunzo wechi1:
Pakumanikidzwa kwemhepo (101 kPa), tembiricha yegasi recarbon dioxide = 20 o C uye vhoriyamu yaro = 2 litres. Kana kumanikidzwa kukachinjwa kuita 201 kPa uye tembiricha ikakwidzwa kusvika 40 o C, verenga vhoriyamu yekupedzisira yegasi recarbon dioxide.
Kukurukurirana
Zvinozivikanwa kuti:
P 1 = 101 kPa
P 2 = 201 kPa
T 1 = 20 o C + 273 K = 293 K
T 2 = 40 o C + 273 K = 313 K
V 1 = marita maviri
Akabvunzwa: V 2
Mhinduro:
Muenzaniso wemubvunzo wechi2:
Sarudza huwandu hwema mole maviri egasi pa STP (fungidzira kuti gasi iri igasi rakakodzera)
Kukurukurirana
Huwandu hwemamoles maviri egasi paSTP (tembiricha yakajairwa uye kumanikidzwa) i44,8 litres.
Muenzaniso wemubvunzo wechi3:
Huwandu hwegasi reokisijeni paSTP = 20 m3 . Huremu hwegasi reokisijeni hwakaita sei?
Kukurukurirana
Huremu hweokisijeni = 32 gramu/mol (huremu hwe 1 mole yeokisijeni = 32 gramu). Saka, huremu hwegasi reokisijeni ndehwekuti:
huremu (m) = nhamba yemamoles (n) x huremu hwemamoles
huremu = (893 moles) x (32 gramu/mol) = 28576 gramu = 28,576 kg
Muenzaniso wemubvunzo wechi4:
Tangi rine marita mana egasi reokisijeni (O2 ) . Tembiricha yegasi reokisijeni i20 oC uye kumanikidzwa kwakayerwa i20 x 10 5 N/m2 . Tsvaga huremu hwegasi reokisijeni (molecular huremu hweokisijeni = 32 kg/kmol = 32 gramu/mol)
Kukurukurirana
Mutemo weGasi Wakanaka (Muhuwandu hwemamorekuru)
Kana tikaratidza saizi yechinhu kwete nehuremu (m), asi nehuwandu hwemamoles (n), saka gasi risingaperi (R) rinoshanda kumagasi ese. Izvi zvakatanga kuwanikwa naAmedeo Avogadro (1776-1856), musayendisiti wekuItaly.
Avogadro akati kana huwandu, kumanikidzwa uye tembiricha yegasi rega rega zvakafanana, ipapo gasi rega rega rine huwandu hwakaenzana hwemamorekuru.
Mutsara wakanyorwa nemabhii matema unonzi fungidziro yaAvogadro. Pfungwa yaAvogadro, kana kuti fungidziro, inoenderana nechokwadi chekuti R isingachinji yakafanana kune magasi ese. Heano humwe humbowo:
Kutanga , kana tikagadzirisa dambudziko tichishandisa equation yemutemo wegesi (PV = nRT), tichaona kuti kana nhamba yemamoles (n) yakafanana, kumanikidzwa nekupisa zvakafananawo, ipapo huwandu hwemagasi ese huchava hwakafanana, kana tikashandisa gasi risingaperi repasi rose (R = 8,315 J/mol.K). PaSTP, gasi rega rega rine nhamba yakafanana yemamoles (n) richava nehuwandu hwakafanana. Vhoriyamu ye1 mole yegesi paSTP = 22,4 malita. Vhoriyamu ye2 mole yegesi = 44,8 malita. Vhoriyamu ye3 mole yegesi = 67,2 malita. Uye zvichingodaro… izvi zvinoshanda kumagasi ese.
Chechipiri , huwandu hwemamorekuru mu mole imwe chete hwakafanana kune magasi ese. Huwandu hwemamorekuru mu mole imwe chete = huwandu hwemamorekuru pa mole = nhamba yaAvogadro (NA ) . Saka nhamba yaAvogadro yakafanana kune magasi ese.
Saizi yenhamba yaAvogadro inowanikwa kuburikidza nekuyera:
NA = 6,02 x 10 23 mamorekuru/mol
Kuti tiwane huwandu hwese hwemamorekuru (N), tinogona kuwedzera huwandu hwemamorekuru pamorekuru (NA) nenhamba yemamorekuru (n).
Iyi ndiyo equation yakakodzera yemutemo wegesi maererano nehuwandu hwemamorekuru.
Information :
P = Kumanikidzwa
V = Vhoriyamu
N = Huwandu hwemamorekuru
k = Boltzmann Constant (k = 1,38 x 10 ‐23 J/K)
T = Tembiricha
vhorumu
1 litre (L) = 1000 milliliters (mL) = 1000 cubic centimeters (cm 3 )
1 litre (L) = 1 cubic decimeter (dm 3 ) = 1 x 10 ‐3 m 3
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 (101 kPa inowanzo shandiswa)
Pa = pascal
atm = mhepo
Simba remukati regasi rakakodzera
Simba remukati regesi rakanaka re monatomic
Simba remukati megasi rakanaka remonatomic ihuwandu hwese hwesimba rekushandura remamorekuru egasi rakanaka remonatomic. Huwandu hwese hwesimba rekushandura remamorekuru egasi rakanaka = chigadzirwa cheavhareji yesimba rekushandura remamorekuru ega rega nenhamba yemamorekuru (N). Masvomhu:
Information :
U = Simba remukati regesi rakanaka re monatomic (J)
N = Nhamba yemamorekuru
k = Boltzmann Constant (k = 1,38 x 10 ‐23 J/K)
T = Tembiricha yakakwana (K)
n = Nhamba yemamota (mol)
R = Gasi risingaperi (R = 8,315 J/mol.K = 8315 kJ/kmol.K)
Simba riri mugasi rakanaka re diatomic
Simba remukati megasi rakanaka rediatomic ihuwandu hwesimba rekushandura rekinetic, simba rekinetic rinotenderera, uye simba rekinetic rinotenderera remamorekuru egasi rakanaka rediatomic. Zvichienderana nepfungwa yekugadzirwa kwesimba, simba remukati megasi rakanaka rediatomic ideal ideal ndeiri:
U = 5/2 n RT
Simba riri mugasi rakakodzera re polyatomic
Simba remukati megasi rakanaka repolyatomic ihuwandu hwesimba rekushandura rekinetic, simba rekinetic rinotenderera, uye simba rekinetic rinotenderera remamorekuru egasi rakanaka repolyatomic. Zvichienderana nepfungwa yekugadzirwa kwesimba, simba remukati megasi rakanaka repolyatomic ideal ideal ndeiri:
U = 7/2 n RT
Simba mugasi chaiyo
Simba riri mugasi chairo rinoenderanawo nekupisa. Kana kumanikidzwa kwegasi chairo kwakakwira zvakakwana (huwandu hwegasi chairo hushoma), gasi chairo rinotanga kuratidza maitiro asina kunaka. Saka, zvinogona kutaurwa kuti simba riri mugasi chairo rinoenderanawo nekumanikidzwa uye huwandu.
