He tuhinga mō te ture hau pai (te whārite o te āhua o te hau pai)
Ko ngā ture hau ko: Te ture a Boyle, te ture a Charles me te ture a Gay-Lussac Ki te kore te ture hau pai e pā ki ngā āhuatanga hau katoa, ka uaua ake tā tātou tātari. Hei whakahaere i te tātari, i hangaia he tauira o te hau pai. Kāore he hau pai i te ao o ia rā; he āhua tino tika noa iho i hangaia hei whakahaere i te tātari. He tino āwhina hoki te ariā o te hau pai ki a tātou ki te tirotiro i te whanaungatanga i waenga i ngā ture hau e toru.
Te whanaungatanga i waenga i te pāmahana, te rōrahi me te pēhanga o te hau
Mā te titiro ki ngā ture hau e toru i runga ake nei, ka taea e tātou te whakaputa i tētahi whanaungatanga whānui ake i waenga i te pāmahana, te rōrahi me te pēhanga o tētahi hau.
Ki te whakakotahihia te whārite 1, te whārite 2 me te whārite 3 hei kotahi, ka pēnei te āhua: PV ∝ T → Whakataurite 4
E ai ki tēnei ōwehenga he rite te pēhanga (P) me te rōrahi (V) ki te pāmahana tino (T).
I tetahi atu taha, he rite whakamuri te rōrahi (V) ki te pēhanga (P).
Ka hurihia te ōwehenga 4 ki te whārite:
Ngā Mōhiohio:
P1 = te pēhanga tīmatanga (Pa, N/m rānei)2)
P2 = te pēhanga whakamutunga (Pa, N/m rānei)2)
V1 = te rōrahi tīmatanga (m3)
V2 = rōrahi whakamutunga (m3)
T1 = te pāmahana tīmatanga (K)
T2 = te pāmahana whakamutunga (K)
(Pa = pascal, N = Newton, m2 = mita pūrua, m3 = mita pūtoru, K = Kelvin)
Te whanaungatanga i waenga i te papatipu hau (m) me te rōrahi (V)
Ina pupuhihia he poihau wera, ka nui ake te hau e mimitihia ana, ka nui ake tōna whānui. Arā, ka nui ake te papatipu o te hau, ka nui ake te rōrahi o te poihau. Ka taea e tātou te kī he rite tonu te papatipu o te hau (m) ki te rōrahi o te hau (V). Mā te pāngarau:
V ∝ m → Ōwehenga 5
Ki te honoa te whārite 4 ki te whārite 5, koia ēnei:
PV ∝ mT → Whakataurite 6
Te maha o ngā mole (n)
1 mole = te papatipu o tētahi matū e ōrite ana ki te papatipu ngota o taua matū. He rerekē te papatipu ngota me te papatipu.
Tauira 1, te papatipu ngota o te hau Hāora (O2) = 16 u + 16 u = 32 u (e rua ngā ngota hāora kei roto i ia ngota hāora, ā, ko te taumaha o ia ngota Hāora he 16 u). Nō reira, 1 mole O2 he 32 karamu te taumaha. Ko te taumaha ngota rānei o te O2 = 32 karamu/mol = 32 kg/kmol.
Tauira 2, te papatipu ngota o te hau waro hauota (CO) = 12 u + 16 u = 28 u (kei roto i ia ngota waro hauota 1 te ngota waro (C) me te ngota hāora 1 (O). Te papatipu o te ngota waro 1 = 12 u me te papatipu o te ngota hāora 1 = 16 u. 12 u + 16 u = 28 u). Nō reira, ko te papatipu o te 1 mole o te CO he 28 karamu. Ko te papatipu ngota rānei o te CO = 28 karamu/mol = 28 kg/kmol.
Tauira 3, te papatipu ngota o te hau waro hauhā (CO2) = [12 u + (2 x 16 u)] = [12 u + 32 u] = 44 u (kei roto i ia ngota waro hauhā kotahi te ngota waro (C ) me ngā ngota hāora e rua (O). Ko te papatipu o te ngota waro kotahi = 12 u me te papatipu o te ngota hāora kotahi = 16 u). Nō reira, 1 mol CO2 he 44 karamu te taumaha. Ko te taumaha ngota rānei o te CO2 = 44 karamu/mol = 44 kg/kmol.
Ko te maha o ngā mole (n) o tētahi matū = te ōwehenga o te papatipu o te matū ki tōna papatipu ngota. Ka tuhia pēneitia te pāngarau:
Tauira 1: Tātaihia te maha o ngā mole i roto i te 64 karamu o te O2
Papatipu O2 = 64 karamu
Tauira 2: Tātaihia te maha o ngā mole i roto i te 280 karamu o te CO
Papatipu o te CO = 280 karamu
Tauira 3: Tātaihia te maha o ngā mole i roto i te 176 karamu o te CO2
Te taumaha o te CO2 = 176 karamu
Pūmau hau whānui (R)
I runga i ngā rangahau a ngā kaipūtaiao, i kitea ina whakamahia te maha o ngā mole (n) hei whakaatu i te rahi o tētahi matū, he ōrite te uara o te pūmau taurite mō ia hau. Ko te pūmau taurite e pā ana ki tēnei ko te pūmau hau whānui (R).
R = 8,315 J/mol.K
= 8315 kJ/kmol.K
= 0,0821 (L.atm) / (mol.K)
= 1,99 karori / mol. K
(J = Joule, K = Kelvin, L = rita, atm = āhuarangi, cal = karori)
TE TURE HAUREHU TINO PAI (i roto i ngā mole)
Ka taea te huri i te whakataurite i runga ake nei hei whārite mā te whakauru i te maha o ngā ira (n) me te pūmau hau whānui (R).
PV = nRT
Ka kiia tēnei whārite ko te ture hau pai, ko te whārite āhua hau pai rānei.
Ngā Mōhiohio:
P = te pēhanga hau (N/m2)
V = rōrahi hau (m3)
n = te maha o ngā mole (mol)
R = pūmau hau whānui (R = 8,315 J/mol.K)
T = te pāmahana tino o te hau (K)
I a koe e whakaoti rapanga ana, ka tūtaki koe ki te kupu STP. Ko te STP he whakarāpopototanga o Te Pāmahana me te Pēhanga Paerewa ranei Te Pāmahana me te Pēhanga Paerewa.
Te pāmahana paerewa (T) = 0 oC = 273 K
Pēhanga paerewa (P) = 1 atm = 1,013 x 105 N / m2 = 1,013x102 kPa = 101 kPa
I te whakaoti rapanga ture hau, me whakaatu te pāmahana ki te tauine Kelvin (K).
Mena he pēhanga ine tonu te pēhanga hau, tahurihia ki te pēhanga tino tika i te tuatahi.
Pēhanga tino = pēhanga hau + pēhanga ine (pēhanga hau = pēhanga hau o waho)
Mena ko te pēhanga o te hau te mea e mōhiotia ana (kāore he pēhanga ine), whakatauhia tika te raruraru.
Tauira pātai 1:
I te pēhanga hauātea (101 kPa), ko te pāmahana o te hau waro hauhā = 20 oC, ā, ko te rōrahi = 2 rita. Mēnā ka hurihia te pēhanga ki te 201 kPa, ā, ka whakanuia te pāmahana ki te 40 oC, tatauhia te rōrahi whakamutunga o te hau waro hauhā.
Kōrero
E mōhiotia ana:
P1 = 101 kPa
P2 = 201 kPa
T1 = 20 oC + 273 K = 293 K
T2 = 40 oC + 273 K = 313 K
V1 = 2 rita
I pātaihia: V2
Whakautu:
Tauira pātai 2:
Whakatauhia te rōrahi o ngā mole hau e 2 i te STP (me kī he hau pai tēnei hau)
Kōrero
Ko te rōrahi o ngā mole hau e 2 i te STP (te pāmahana me te pēhanga paerewa) he 44,8 rita.
Tauira pātai 3:
Te rōrahi o te hau hāora i te STP = 20 m3He aha te taumaha o te hau hāora?
Kōrero
Ko te papatipu ngota o te hāora = 32 karamu/mol (te papatipu o te 1 mole o te hāora = 32 karamu). Nō reira, ko te papatipu o te hau hāora ko:
papatipu (m) = te maha o ngā ira (n) x te papatipu ngota
papatipu = (893 mole) x (32 karamu/mol) = 28576 karamu = 28,576 kg
Tauira pātai 4:
Kei roto i tētahi tāke e 4 rita o te hau hāora (O2). Ko te pāmahana o te hau hāora = 20 oC me te pēhanga ine = 20 x 105 N / m2. Tātaihia te papatipu o te hau hāora (papatipu ngota o te hāora = 32 kg/kmol = 32 karamu/mol)
Kōrero
TE TURE HAUREHU TINO PAI (I roto i te maha o ngā ngota)
Ki te kore e whakaatuhia te rahi o tētahi matū mā te papatipu (m), engari mā te maha o ngā ira (n), ka pā te pūmau hau whānui (R) ki ngā hau katoa. Nā Amedeo Avogadro (1776‐1856), he kaipūtaiao Itari, tēnei i kitea tuatahitia.
I kī a Avogadro, ina ōrite te rōrahi, te pēhanga me te pāmahana o ia hau, ka ōrite te maha o ngā ngota ngota o ia hau.
Ko te rerenga kōrero i roto i ngā reta whakarara matotoru e kiia ana ko te whakapae a Avogadro. Ko te whakapae, ko te whakapae rānei a Avogadro, e hangai ana ki te meka he rite te pūmau R mō ngā hau katoa. Anei ētahi taunakitanga:
Tuatahi, ki te whakaotihia te raruraru mā te whakamahi i te whārite ture hau pai (PV = nRT), ka kitea e tātou ina rite te maha o ngā ira (n), ka rite anō hoki te pēhanga me te pāmahana, kātahi ka rite te rōrahi o ngā hau katoa, ki te whakamahia e tātou te pūmau hau whānui (R = 8,315 J/mol.K). I te STP, ko ia hau he rite te maha o ngā ira (n) ka rite te rōrahi. Ko te rōrahi o te 1 ira o te hau i te STP = 22,4 rita. Ko te rōrahi o te 2 ira o te hau = 44,8 rita. Ko te rōrahi o te 3 ira o te hau = 67,2 rita. Ā, pērā tonu… e pā ana tēnei ki ngā hau katoa.
Tuarua, he rite tonu te maha o ngā ngota i roto i te 1 mole mō ngā hau katoa. Ko te maha o ngā ngota i roto i te 1 mole = te maha o ngā ngota mō ia mole = te tau a Avogadro (NANō reira, he rite tonu te tau a Avogadro mō ngā hau katoa.
Ka whiwhihia te rahi o te tau a Avogadro mā roto i ngā inenga:
NA = 6,02 x 1023 ngā ngota/mol
Hei whiwhi i te tapeke o ngā ngota (N), ka taea e tātou te whakarea i te maha o ngā ngota mō ia ira (NA) ki te maha o ngā ira (n).
Koinei te whārite ture hau tino pai e pā ana ki te maha o ngā ngota.
Ngā Mōhiohio:
P = Pēhanga
V = Rōrahi
N = Te tapeke o ngā ngota ngota
k = te pūmau a Boltzmann (k = 1,38 x 10-23 (J/K)
T = Te pāmahana
rōrahi
1 rita (L) = 1000 miririta (mL) = 1000 henimita pūtoru (cm3)
1 rita (L) = 1 tekimita kūpiko (dm)3) = 1 x 10-3 m3
Tekana
1 N / m2 = 1 Pa
1 atm = 1.013 x 105 N / m2 = 1,013x105 Pā = 1,013 x 102 kPa = 101,3 kPa (ko te tikanga he 101 kPa te whakamahinga)
Pa = pascal
te hau = te āhuarangi
Pūngao ā-roto o te hau pai
Pūngao ā-roto o te hau pai monoatomic
Ko te pūngao ā-roto o te hau pai monoatomic ko te tapeke o te pūngao nekeneke whakawhiti o ngā ngota o te hau pai monoatomic. Ko te tapeke o te pūngao nekeneke whakawhiti o ngā ngota o te hau pai = te hua o te pūngao nekeneke whakawhiti toharite o ia ngota mā te maha o ngā ngota (N). Mā te pāngarau:
Ngā Mōhiohio:
U = Pūngao ā-roto o te hau pai monoatomic (J)
N = Te maha o ngā ngota ngota
k = te pūmau a Boltzmann (k = 1,38 x 10 -23 (J/K)
T = Te pāmahana tino (K)
n = Te maha o ngā mole (mol)
R = Pūmau hau whānui (R = 8,315 J/mol.K = 8315 kJ/kmol.K)
Pūngao i roto i te hau pai rua-atomic
Ko te pūngao ā-roto o te hau pai rua-atomika ko te tapeke o te pūngao nekeneke whakawhiti, te pūngao nekeneke hurihuri, me te pūngao nekeneke wiri o ngā ngota o te hau pai rua-atomika. E ai ki te mātāpono o te wehewehenga pūngao ōrite, ko te pūngao ā-roto o te hau pai rua-atomika ko:
U = 5/2 n RT
Pūngao i roto i te hau pai polyatomic
Ko te pūngao ā-roto o te hau pai maha-atomika ko te tapeke o te pūngao nekeneke whakawhiti, te pūngao nekeneke hurihuri, me te pūngao nekeneke wiri o ngā ngota o te hau pai maha-atomika. E ai ki te mātāpono o te wehewehenga pūngao ōrite, ko te pūngao ā-roto o te hau pai maha-atomika ko:
U = 7/2 n RT
Pūngao i roto i te hau tūturu
Ko te pūngao o te hau tūturu e whakawhirinaki ana ki te pāmahana. Ina teitei te pēhanga o te hau tūturu (he iti te rōrahi o te hau tūturu), ka tīmata te hau tūturu ki te whakaatu i te whanonga rerekē. Nō reira, ka taea te kī ko te pūngao o te hau tūturu e whakawhirinaki ana ki te pēhanga me te rōrahi.
