Ngā Tauira Pātai e Matapaki ana i te Whakamahinga o ngā Raraunga Pūmanawa Irahiko Paerewa
He mea nui te pūmanawa hiko paerewa (E°) i roto i te matū, inā koa ki te mārama ki ngā tauhohenga redox me te hikohiko. Mā tēnei ka taea te matapae i te ahunga o ngā tauhohenga redox me te whakatairite i ngā kaha o ngā matū whakahāora me ngā matū whakaiti. Ka whakaatuhia e tēnei tuhinga ētahi tauira o te whakamahi i ngā raraunga pūmanawa hiko paerewa hei whakaatu i tōna whakamahinga i roto i ngā āhuatanga o te ao tūturu.
He Kupu Whakataki ki ngā Pūmanawa Irahiko Paerewa
Ka ine te pūmanawa hiko paerewa i te ia o tētahi huānga, pūhui rānei ki te whiwhi, ki te ngaro rānei i ngā irahiko i raro i ngā āhuatanga paerewa (1 M, 1 atm, me te 25°C). Ka whakaatuhia te pūmanawa hiko paerewa i roto i ngā volts (V) ā, he maha ngā wā ka whakaritea ki te pūmanawa hiko hauwai paerewa (SHE), e tangohia ana ko te 0 V.
Tauira Pātai 1: Te Whakatau i ngā Tauhohenga Tūpono
Pātai:
Tātaihia mēnā ka puta noa mai te tauhohenga e whai ake nei:
\[ \text{Zn}^{2+} + \text{Cu} \rightarrow \text{Zn} + \text{Cu}^{2+} \]
Ko ngā pūmanawa hiko paerewa e hiahiatia ana ko:
– \(\kuputuhi{Zn}^{2+} + 2e^{-} \rightarrow \kuputuhi{Zn} \) \( E° = -0.76 \, \kuputuhi{V} \)
– \(\text{Cu}^{2+} + 2e^{-} \rightarrow \text{Cu} \) \( E° = +0.34 \, \text{V} \)
Kōrero:
1. Tautuhia ngā Tauhohenga Haurua-Pūtau:
Tauhohenga haurua-pūtau whakaiti:
– Te haurua-tauhohenga waikura: \[\text{Zn}^{2+} + 2e^{-} \rightarrow \text{Zn} \, \text{(Whakaitinga, E° = -0.76 V)} \]
– Te haurua-tauhohenga whakaiti: \[\text{Cu}^{2+} + 2e^{-} \rightarrow \text{Cu} \, \text{(Whakaiti, E° = +0.34 V)} \]
2. Te Tautuhi Tauhohenga:
Whakahurihia te tauhohenga he iti ake te pūmanawa kia huri ai hei waikura:
– \[\text{Zn} \rightarrow \text{Zn}^{2+} + 2e^{-} \, \text{(Te Waikura, E° = +0.76 V)} \]
Ngā tauhohenga e toe ana:
– \[\text{Cu}^{2+} + 2e^{-} \rightarrow \text{Cu} \, \text{(Whakaiti, E° = +0.34 V)} \]
3. Tātaihia te tapeke E° (pūmanawa pūtau):
– \[ E°_{\text{pūtau}} = E°_{\text{whakaiti}} + E°_{\text{waikura}} = +0.34 \, \text{V} + (+0.76 \, \text{V}) = +1.10 \, \text{V} \]
I te mea he pai te pūmanawa pūtau (E°_{\text{cell}}), ka puta noa tēnei tauhohenga.
Tauira Pātai 2: Te Whakatau i te Pūmanawa Taurite
Pātai:
Tātaihia te pūmanawa pūtau mō te tauhohenga e whai ake nei i te pāmahana paerewa:
\[ \text{Fe}^{2+} + \text{Ag} \rightarrow \text{Fe} + \text{Ag}^{+} \]
Pūmanawa hiko paerewa:
– \(\kuputuhi{Fe}^{2+} + 2e^{-} \rightarrow \kuputuhi{Fe} \) \( E° = -0.44 \, \kuputuhi{V} \)
– \(\kuputuhi{Ag}^{+} + e^{-} \rightarrow \kuputuhi{Ag} \) \( E° = +0.80 \, \kuputuhi{V} \)
Kōrero:
1. Tautuhia ngā Tauhohenga Haurua-Pūtau:
Tauhohenga haurua-pūtau whakaiti:
– \[\text{Fe}^{2+} + 2e^{-} \rightarrow \text{Fe} \, \text{(Whakaitinga, E° = -0.44 V)} \]
– \[\text{Ag}^{+} + e^{-} \rightarrow \text{Ag} \, \text{(Whakaitinga, E° = +0.80 V)} \]
2. Tāutuhia ngā Tauhohenga-Haurua:
Whakahurihia te tauhohenga he iti ake te uara kino (he pai ake):
– \[\text{Fe} \rightarrow \text{Fe}^{2+} + 2e^{-} \, \text{(Te Waikura, E° = +0.44 V)} \]
Ngā tauhohenga e toe ana:
– \[\text{Ag}^{+} + e^{-} \rightarrow \text{Ag} \, \text{(Whakaitinga, E° = +0.80 V)} \]
3. Tātaihia te tapeke E° (pūmanawa pūtau):
– \[ E°_{\text{pūtau}} = E°_{\text{whakaiti}} + E°_{\text{waikura}} = +0.80 \, \text{V} + (+0.44 \, \text{V}) = +1.24 \, \text{V} \]
Ko te pūmanawa pūtau pai e tohu ana ka haere noa tēnei tauhohenga i raro i ngā āhuatanga paerewa.
Tauira 3: Te Tātaitanga o te Pūngao Koreutu o Gibbs
Pātai:
Whakatauhia te huringa o te pūngao kore utu o Gibbs (ΔG) mō te tauhohenga e whai ake nei:
\[ \text{Al} + \text{Cu}^{2+} \rightarrow \text{Al}^{3+} + \text{Cu} \]
I runga i te pūmanawa hiko paerewa:
– \(\kuputuhi{Al}^{3+} + 3e^{-} \rightarrow \kuputuhi{Al} \) \( E° = -1.66 \, \kuputuhi{V} \)
– \(\text{Cu}^{2+} + 2e^{-} \rightarrow \text{Cu} \) \( E° = +0.34 \, \text{V} \)
Kōrero:
1. Tautuhia ngā Tauhohenga Haurua-Pūtau:
Tauhohenga haurua-pūtau whakaiti:
– \[\text{Al}^{3+} + 3e^{-} \rightarrow \text{Al} \, \text{(Whakaitinga, E° = -1.66 V)} \]
– \[\text{Cu}^{2+} + 2e^{-} \rightarrow \text{Cu} \, \text{(Whakaiti, E° = +0.34 V)} \]
2. Te Tautuhi Tauhohenga:
Whakahurihia te tauhohenga he iti ake te pūmanawa kia huri ai hei waikura:
– \[\text{Al} \rightarrow \text{Al}^{3+} + 3e^{-} \, \text{(Te Waikura, E° = +1.66 V)} \]
Ngā tauhohenga e toe ana:
– \[\text{Cu}^{2+} + 2e^{-} \rightarrow \text{Cu} \, \text{(Whakaiti, E° = +0.34 V)} \]
3. Taurite Irahiko:
Whakaōritehia te maha o ngā irahiko mō te tauhohenga:
– 2 \(\text{Al} \rightarrow 2\text{Al}^{3+} + 6e^{-} \) \[\text{(Te Hāora, E° = +1.66 V)} \]
– 3 \(\text{Cu}^{2+} + 6e^{-} \rightarrow 3\text{Cu} \) \[\text{(Whakaiti, E° = +0.34 V)} \]
4. Tātaihia te tapeke E° (pūmanawa pūtau):
– \[ E°_{\kuputuhi{pūtau}} = (+0.34 \, \kuputuhi{V} \times 3) + (+1.66 \, \kuputuhi{V} \times 2) \]
Hapa i konei: Toharite:
– \[ E°_{\kuputuhi{pūtau}} = +0.34 \, \kuputuhi{V} + +1.66 \, \kuputuhi{V} = +2.00 \, \kuputuhi{V}\]
5. Tātaihia te ΔG:
Tātai: \(\Delta G = -nFE_{\text{pūtau}}\)
– \[n = 6 \, \kuputuhi{ngā irahiko} \]
– \[F = 96485 \, \kuputuhi{C/mol} \]
– \[ \Delta G = -6 \times 96485 \, \text{C/mol} \times +2.00 \, \text{V}\]
– \[ = -1157820 \, \text{J/mol} \]
– \[ = -1157.82 \, \text{kJ/mol}\]
Nō reira, ko te ΔG kino e tohu ana he tūpono noa iho tēnei tauhohenga.
Whakamutunga
Mā ngā raraunga pūmanawa hiko paerewa ka taea te matapae i te ahunga o te tauhohenga redox, te tūponotanga o te haere tonu, me tōna whanaungatanga ki te huringa o te pūngao kore utu a Gibbs. E whakaatu ana te tauira raruraru i runga ake nei me pēhea te whakamahi i ēnei raraunga hei whakatau i te tūponotanga o te tauhohenga redox me ngā tataunga pūngao e pā ana. Mō ngā ākonga, mō tētahi atu rānei e ako ana i te matū, ko te mārama ki ngā raraunga pūmanawa hiko paerewa me ōna tono he tūāpapa nui mō te mārama ki ngā tauhohenga hiko matatini ake.
