Tauira o ngā Pātai Kōrero mō te Ariā Tukinga
Pendahuluan
Ko te ariā tukinga he ariā taketake i roto i te matū e whakamārama ana i te āhua me te take o ngā tauhohenga matū. I tuatahitia tēnei e Max Trautz rāua ko William Lewis i te tīmatanga o te rautau 20. E ai ki tēnei ariā, ka puta ngā tauhohenga matū ina tukinga ngā matūriki tauhohenga tetahi ki tetahi me te nui o te kaha me te whakatakotoranga tika.
Ka matapakihia e tēnei tuhinga ētahi tauira raruraru e pā ana ki te ariā tukinga me ā rātou otinga hei whakarato i tētahi māramatanga hōhonu ake mō tēnei ariā. Kia tae ki te mutunga o te tuhinga, me mārama ngā kaipānui ki ngā tikanga taketake o te ariā tukinga me pēhea te whakamahi i tēnei ki ngā āhuatanga raruraru matū.
Ariā Tukinga Taketake
E kī ana te ariā tukinga e rua ngā āhuatanga matua e whakatau ana mēnā ka puta he tauhohenga matū i tētahi tukinga:
1. Pūngao Whakahohe (Ea): Ko te pūngao iti rawa e hiahiatia ana mō ngā tukinga i waenga i ngā ngota matū tauhohe hei whakaputa hua.
2. Te whakatakotoranga o ngā ngota: He mea tino nui anō hoki te tūranga o ngā ngota ina tukinga. Ka puta he tauhohenga i te tukinga mēnā ka tika te whakatakotoranga o ngā ngota.
Ngā Take e Pā Ana ki te Ariā Tukinga
1. Te Kukū: Ka nui ake te kukū o ngā matū tauhohe, ka nui ake te tūponotanga ka tukinga ngā ngota matū tauhohe.
2. Pāmahana: Mā te pikinga o te pāmahana ka nui ake te pūngao nekeneke o ngā ngota, ka nui ake pea ngā tukinga he nui ake ō rātou pūngao i te pūngao whakahohe.
3. Kaiwhakaoho: Ko te mahi a te kaiwhakaoho he whakaiti i te pūngao whakahohe kia angitu ai ngā tukinga maha atu.
Ngā Tauira Pātai me ngā Kōrerorero
Tauira Pātai 1: Te Pānga o te Arotahi
Pātai:
Ki te takiruahia te kukū o te ngota A i roto i te tauhohenga `A + B -> C`, ka pēhea te rerekētanga o te tere o te tauhohenga e ai ki te ariā tukinga?
Kōrero:
E ai ki te ariā tukinga, ko te tere o te tauhohenga e whakawhirinaki ana ki te auau o ngā tukinga i waenga i ngā matūriki A me B. Mēnā ka takiruahia te kukū o A, ka piki ake anō hoki te maha o ngā tukinga i waenga i ngā ngota A me B. I te nuinga o te wā, ka taea e tātou te kī ka takiruahia te tere o te tauhohenga.
Heoi, i roto i te nuinga o ngā wā, he uaua ake te raupapa o ngā tauhohenga. Mō te tauhohenga raupapa tuatahi e pā ana ki a A, mā te whakarea rua i te kukū o A ka whakarea rua te tere o te tauhohenga:
\[ r = k[A][B] \rightarrow r' = k[2A][B] = 2r \]
Tauira Pātai 2: Te Pānga o te Pāmahana
Pātai:
Ko te pūngao whakahohe o tētahi tauhohenga he 50 kJ/mol. Mēnā ka whakanuia te pāmahana mai i te 300 K ki te 310 K, ka pēhea te rerekētanga o te tere tauhohenga e ai ki te ariā tukinga me te tauwehenga Arrhenius?
Kōrero:
Mā te pikinga o te pāmahana ka piki ake te kaha nekeneke o ngā ngota, ka hua ake he nui ake ngā ngota he kaha nui ake, he rite rānei ki te kaha whakahohe. Ko te tikanga o tēnei ka whakaahuahia e te whārite Arrhenius:
\[
k = Ae^{-\frac{Ea}{RT}}
\]
Dimana:
– Ko te pūmau tere o te tauhohenga te \( k \)
– Ko te \( A \) he tauwehenga mua-pūtau
– Ko te pūngao whakahohenga te \( Ea \)
– Ko te pūmau hau te \( R \) (8.314 J/mol·K)
– Ko te pāmahana i roto i te Kelvin te \( T \)
Ka taea e tātou te tango i te logarithm tūturu o te whārite Arrhenius:
\[
\ln k = \ln A – \frac{Ea}{RT}
\]
Hei tatau i te huringa o te tere tauhohenga, ka tangohia e tātou te ōwehenga o ngā pūmau tere i ngā pāmahana rerekē e rua:
\[
\frac{k_2}{k_1} = \frac{Ae^{-\frac{Ea}{R \cdot T2}}}{Ae^{-\frac{Ea}{R \cdot T1}}} = e^{\left(-\frac{Ea}{R}\left(\frac{1}{T2} – \frac{1}{T1}\right)\right)}
\]
Te whakauru i ngā uara kua hoatu:
\[
k_1 = Ae^{-\frac{50000}{8.314 \times 300}}
\]
\[
k_2 = Ae^{-\frac{50000}{8.314 \times 310}}
\]
Te tatau i te huringa:
\[
\frac{k_2}{k_1} = e^{\left(-\frac{50000}{8.314}\left(\frac{1}{310} – \frac{1}{300}\right)\right)}
\]
\[
= e^{\maui(-6012.9 \times (-0.00010753)\matau)}
\]
\[
= e^{0.646}
\]
\[
tata ki te 1.91
\]
Nō reira, mā te whakanui ake i te pāmahana mai i te 300 K ki te 310 K ka tata rua te tere o te tauhohenga, mā te 91% pea.
Tauira Pātai 3: Te Pānga o ngā Whakakōkī
Pātai:
I roto i tētahi tauhohenga, mā te tāpiri i tētahi whakakorikori ka tere ake te tauhohenga mā te whakaheke i te pūngao whakahohe mai i te 75 kJ/mol ki te 50 kJ/mol i te 298 K. Tātaihia te ōwehenga o ngā tere tauhohenga me te whakakorikori, me te kore hoki.
Kōrero:
Whakamahia te whārite Arrhenius hei tatau i ngā pūmau tere e rua:
\[
k_{uncat} = Ae^{-\frac{75000}{8.314 \times 298}}
\]
\[
k_{ngeru} = Ae^{-\frac{50000}{8.314 \times 298}}
\]
Kātahi, ko te ōwehenga i waenga i ēnei tere tauhohenga e rua ko:
\[
\frac{k_{cat}}{k_{uncat}} = \frac{e^{-\frac{50000}{8.314 \times 298}}}{e^{-\frac{75000}{8.314 \times 298}}}
\]
\[
= e^{\maui(\frac{75000 – 50000}{8.314 \times 298}\matau)}
\]
\[
= e^{10.075}
\]
\[
tata ki te 23685
\]
E whakaatu ana tēnei ōwehenga mā te tāpiri i tētahi whakakorikori, ka taea te piki ake o te tere tauhohenga ki ngā mano whakarea, he mea tino nui tēnā.
Whakamutunga
Mā roto i ngā tauira i runga ake nei, ka taea e tātou te mārama ake ki te whakamārama a te ariā tukinga i ngā pānga o te kukū, te pāmahana, me ngā whakakorikori ki te tere o ngā tauhohenga matū. He pānga motuhake, he pānga nui hoki tō ia o ēnei āhuatanga ki te auau me te kaha o ngā tukinga, ā, ko ēnei ka pā ki te tere o te puta o tētahi tauhohenga matū. Mā te whakamahi i te ariā tukinga, ka taea e tātou te hoahoa i ngā whakamātautau me ngā tukanga ahumahi matū whai hua ake.
