Te ture hau pai (Te whārite o te āhua o te hau pai)

He tuhinga mō te ture hau pai (te whārite o te āhua o te hau pai)

Kāore ngā ture hau, tae atu ki te ture a Boyle, te ture a Charles, me te ture a Gay-Lussac , e pā ki ngā āhuatanga hau katoa, ā, ka uaua ake tā mātou tātari. Hei whakahaere i te tātari, ka hangaia he tauira o te hau pai. Kāore he hau pai i te ao o ia rā; he āhua tino tika noa iho ēnei 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 → Ōwehenga 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:

P ₁ = te pēhanga tīmatanga (Pa, N/m ^{2 rānei} )

P ₂ = te pēhanga whakamutunga (Pa, N/m ^{2 rānei} )

V ₁ = rōrahi tīmatanga (m ³ )

V ₂ = te rōrahi whakamutunga (m ³ )

T ₁ = pāmahana tīmatanga (K)

T ₂ = te pāmahana whakamutunga (K)

(Pa = pascal, N = Newton, m2 ⁼ mita tapawha, 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, ko te papatipu ngota o te hau Hāora (O ₂ ) = 16 u + 16 u = 32 u (e rua ngā ngota Hāora kei roto i ia ngota Hāora, ā, ko te papatipu o ia ngota Hāora he 16 u). Nō reira, ko te papatipu o te 1 mole o te O ₂ he 32 karamu. Ko te papatipu ngota rānei o te O ₂ = 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 (CO ₂ ) = [12 u + (2 x 16 u)] = [12 u + 32 u] = 44 u (kei roto i ia ngota waro hauhā 1 te ngota waro (C) me te 2 ngā ngota hāora (O). Te papatipu o te ngota waro 1 = 12 u me te papatipu o te ngota hāora 1 = 16 u). Nō reira, ko te papatipu o te 1 mole o te CO ₂ he 44 karamu. Ko te papatipu ngota rānei o te CO ₂ = 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 o 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

Papatipu 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 = te 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 te tikanga mō te Paerewa me te Pēhanga.

Pāmahana paerewa (T) = 0 ^° C = 273 K

Pēhanga paerewa (P) = 1 atm = 1,013 x 105 ^N /m2 ⁼ 1,013 x 102 ^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 hauhautanga (101 kPa), ko te pāmahana o te hau waro hauhā = 20 ^o C, ā, ko tōna rōrahi = 2 rita. Mēnā ka whakarerekētia te pēhanga ki te 201 kPa, ā, ka whakanuia te pāmahana ki te 40 ^o C, tatauhia te rōrahi whakamutunga o te hau waro hauhā.

Kōrero

E mōhiotia ana:

P ₁ = 101 kPa

P ₂ = 201 kPa

T ₁ = 20 ^° C + 273 K = 293 K

T ₂ = 40 ^° C + 273 K = 313 K

V ₁ = 2 rita

I pātaihia: V ₂

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:

Ko te rōrahi o te hau hāora i te STP = 20 m³ ^. He 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:

E 4 rita o te hau hāora (O2) kei roto i tētahi tāke _. Ko te pāmahana o te hau hāora he 20 ^° C, ā, ko te pēhanga ine he 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 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 o Avogadro (NA ₎ . Nō reira, he rite te tau o Avogadro mō ngā hau katoa.

Ka whiwhihia te rahi o te tau a Avogadro mā roto i ngā inenga:

NA = 6,02 x 1023 ^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 = Pūmau Boltzmann (k = 1,38 x 10 ^‐23 J/K)

T = Te pāmahana

rōrahi

1 rita (L) = 1000 miririta (mL) = 1000 henimita kūpiko (cm ³ )

1 rita (L) = 1 tekimita kūpiko (dm ³ ) = 1 x 10 ^‐3 m ³

Tekana

1 N/m2 ⁼ 1 Pa

1 atm = 1,013 x 105 ^N /m2 ⁼ 1,013 x 105 ^Pa = 101,3 x 102 ^kPa = 101.3 kPa (101 kPa te tikanga e whakamahia ana)

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 = Pūmau 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.