Me pēhea te whakatau i te Tau o Avogadro
Ko te tau a Avogadro tētahi o ngā ariā tino nui i roto i te matū me te ahupūngao o ēnei rā, nā te mea he piriti i waenganui i te ao moroiti (ngota, ngota, katote) me te ao makroskopi (karamu, rita, me ngā mea ka taea e tātou te pauna). Mā te mārama ki te whakatau i te tau a Avogadro ka māmā ake te mārama ki te ariā o ngā mole, te tatau i te maha o ngā matūriki i roto i tētahi matū, me te whakaoti rapanga stoichiometry. Ka matapakihia e tēnei tuhinga te whakamāramatanga o te tau a Avogadro, tōna pūtake ariā, me ētahi tikanga mō te whakatau i te tau a Avogadro e whakamahia ana i roto i te pūtaiao.
Te Mārama ki te Tau a Avogadro
Ko te tau a Avogadro (e tohuhia ana e \(N_A\)) ko te maha o ngā matūriki (ngota, ngota, ētahi atu hinonga rānei) kei roto i te 1 mole o tētahi matū. Ko te uara e whakaaetia ana i tēnei wā o te tau a Avogadro ko:
\[
N_A = 6{,}02214076 \times 10^{23}\ \text{mol}^{-1}
\]
He nui rawa tēnei tau nā te mea he iti rawa ngā matūriki e hanga ana i te matū. Hei tauira, kei roto i te 1 mole wai te tata ki te \(6{,}02 \times 10^{23}\) ngā ngota wai. Ehara te tau a Avogadro i te tau "kua maumaharatia" noa iho, engari he hua o ngā inenga me ngā whakamāramatanga i whakatūria mā roto i ngā whakamātautau roa puta noa i te hītori o te pūtaiao.
Te Hononga i waenga i te Tau a Avogadro me te Ariā o ngā Mole
Ko te ariā o te mole e whakamāramahia ana ko te waeine o te rahinga o tētahi matū. I roto i ngā kupu māmā:
– 1 mole o tētahi matū = \(N_A\) ngā matūriki o taua matū.
– Ko te papatipu o te 1 mole o tētahi matū (i roto i te karamu) he ōrite ki papatipu molar.
Hei tauira, ko te papatipu molar o te waro-12 he 12 karamu/mol. Ko te tikanga o tēnei, kei roto i te 12 karamu o te waro-12 he \(6{,}022 \times 10^{23}\) ngā ngota waro-12. Mā tēnei whanaungatanga ka taea e tātou te tatau i te maha o ngā matūriki mai i tētahi papatipu ka taea te pauna i roto i te taiwhanga.
He aha i hiahia ai kia "Whakatauhia" te Tau a Avogadro?
I ngā wā o mua, kāore i te mōhiotia tika te uara o te tau a Avogadro. Me kimi e ngā kaipūtaiao he huarahi hei hono i ngā inenga makaro (papatipu, rōrahi, utu hiko) ki te maha o ngā matūriki. Nō reira, i whakatauhia te tau a Avogadro mā roto i ngā tikanga whakamātautau me ngā huarahi ariā.
I ēnei rā, kua tino tika te tautuhi i te tau a Avogadro. Mai i te tautuhi anō i te tau SI 2019, kua tino tautuhia te uara o \(N_A\) ko \(6{,}02214076 \times 10^{23}\). Heoi, mō ngā kaupapa mātauranga, he mea nui tonu te mārama ki te whakatau i te tau a Avogadro, nā te mea ka āwhina i a tātou ki te mārama ki te pūtake mai o te tau me te ine a te pūtaiao.
Tikanga 1: Te Huarahi mai i te Papatipu Atomika (Waro-12)
Ko tētahi o ngā huarahi tino taketake ki te mārama ki te tau o Avogadro ko te whakamahi i te paerewa waro-12. I mua ko te mole te maha o ngā ngota i roto i te 12 karamu o te waro-12. Mēnā e mōhio ana tātou ki te papatipu o tētahi ngota waro-12, ka taea te tatau i te tau o Avogadro:
\[
N_A = \frac{\text{papatipu o te 1 mole}}{\text{papatipu o te 1 ngota}}
\]
Nā te mea ko te taumaha o te 1 mole o te waro-12 he 12 karamu, kāti:
\[
N_A = \frac{12\ \text{g}}{m_{\text{C-12 atom}}}
\]
Ko te raruraru, he tino iti te papatipu o tētahi ngota kotahi, ā, kāore e taea te ine tika mā te pauna tikanga. Heoi, nā te whanaketanga o ngā hangarau pēnei i te ine papatipu me ngā tikanga ine tauine ngota, ka taea te whakatau ā-kore i te papatipu ngota. Mā tēnei tikanga ka whakaratohia he pūtake ariā pakari mō te hononga o te tau Avogadro ki te papatipu ngota.
Tikanga 2: Tikanga Hikohiko (Ture a Faraday)
Ko tētahi atu tikanga rongonui mō te whakatau i te tau a Avogadro ko te electrolysis, te tukanga o te wetewete i tētahi matū mā te whakamahi i te iahiko. E ai ki te ture a Faraday, ko te nui o te matū e tauhohe ana i roto i te electrolysis he rite ki te nui o te utu hiko e rere ana.
Ko te whakaaro matua o tēnei tikanga ko te hono atu:
– Te utunga katoa o te 1 mole o ngā irahiko (e kiia nei ko te pūmau o Faraday, \(F\))
– Te utu o te irahiko kotahi (\(e\))
Mena e mōhio ana tātou ki te pūmau o Faraday me te utu o te irahiko, ka taea te tatau i te tau o Avogadro penei:
\[
N_A = \frac{F}{e}
\]
Ko te pūmau o Faraday he tata ki:
\[
F \tata ki te 96485\ \kuputuhi{C/mol}
\]
Utu irahiko:
\[
e \tata ki te 1{,}602 \times 10^{-19}\ \text{C}
\]
Nā reira, tata ki:
\[
Kāore i te mōhiotia \approx \frac{96485}{1{,}602 \times 10^{-19}} \approx 6{,}02 \times 10^{23}
\]
He huarahi tino huatau tēnei nā te mea e hono ana i ngā āhuatanga matū ( ngā tauhohenga redox ) ki ngā pūmau taketake o te ahupūngao (te utu irahiko).
Tikanga 3: Tikanga Tioata Hiraka (Tikanga Matotoru Tioata Hiko-X)
I roto i te ine ine hou, ko tētahi o ngā tikanga tino tika mō te whakatau i te tau Avogadro ko te whakamahi i ngā tioata silicon tino parakore. Ka whakamahia e tēnei tikanga te meka he rite tonu te whakaritenga ngota o ngā tioata, ā, ka taea te ine i ngā tawhiti i waenga i ngā ngota mā te whakamahi i te X-ray diffraction.
Tirohanga whānui:
1. Tangohia he porowhita silicon he tino parakore, ā, tata tino pai te āhua.
2. Inehia te rōrahi o te pōro me te tino tika.
3. Inehia te papatipu o te pōro kia kitea ai tōna mātotoru.
4. Whakamahia ngā raraunga te hanganga tioata silicon hei kimi i te maha o ngā ngota kei roto i ia rōrahi.
Mā te mōhio ki te maha o ngā ngota i roto i tētahi rōrahi kua whakaritea, me te hono atu ki te papatipu katoa, ka taea e ngā kaipūtaiao te tatau i te maha o ngā ngota i roto i te 1 mole , koinei te tau a Avogadro. He pou matua tēnei tikanga ki te whakatū i ngā pūmau SI.
Tikanga 4: Huarahi Hau Pai (Ariā Hītori)
I ngā wā o mua, i tīmata te whakaaro o Avogadro me ngā hau: "I te pāmahana me te pēhanga ōrite, he ōrite te maha o ngā matūriki kei roto i ngā rahinga ōrite o ngā hau." Ahakoa kāore tēnei huarahi e whakarato tika i te uara o (N_A), i whakatakoto i te ara mō te hononga i te rōrahi o te hau , te maha o ngā ira, me te maha o ngā matūriki.
Hei tauira, i te STP (whakamāramatanga tawhito: 0°C me te 1 atm), ka noho te 1 mole o te hau pai ki te rōrahi o te 22,4 L. Mēnā i tētahi rā ka taea e tātou te tatau i te maha o ngā matūriki i roto i taua rōrahi mā roto i ngā whakamātautau moroiti, ka taea te whiwhi i te tau a Avogadro. I roto i te mahi, he pai ake te tikanga hau pai hei tūāpapa ariā i te taumata kura, nā te mea ko te whakatau tika o \(N_A\) me whai tikanga tika ake pērā i te electrolysis me ngā tioata silicon.
Me pēhea te whakamahi i te Tau a Avogadro i roto i ngā Tātaitanga
Ahakoa e mahia ana te whakatau tika o te tau a Avogadro e ngā kaipūtaiao me ngā taputapu matatau, ko te nuinga o ngā ākonga me ngā tauira whare wānanga ka "whakatau" i te maha o ngā matūriki mā te whakamahi i te uara \(N_A\). Ko te tātai e whakamahia whānuitia ana ko:
1. Te maha o ngā mole mai i te papatipu:
\[
n = \frac{m}{M}
\]
ko \(m\) = papatipu (g) me \(M\) = papatipu molar (g/mol).
2. Te maha o ngā matūriki:
\[
N = n \whakanuia te N_A
\]
Tauira tere: E hia ngā ngota i roto i te 18 karamu o te wai (\(H_2O\))?
– Papatipu molar o te wai = 18 karamu/mol
– Ngā ira wai = \(18/18 = 1\) ngā ira
– Te maha o ngā ngota = \(1 \times 6{,}02 \times 10^{23} = 6{,}02 \times 10^{23}\)
Whakamutunga
Ka taea te mārama ki te tikanga mō te whakatau i te tau o Avogadro mā roto i ētahi huarahi matua: te whanaungatanga i waenga i ngā papatipu ngota (waro-12), te hikohiko mā te ture a Faraday, te tikanga karaihe silicon me te diffraction hihi-X, me te huarahi ariā o ngā hau pai. Mai i ēnei tikanga maha, e mārama ana ehara te tau o Avogadro i te tau "matapōkere", engari he hua o ngā inenga pūtaiao e hono ana i te tauine ngota ki ngā tauine ka taea e tātou te ine i ia rā. Mā te mārama ki te tukanga whakatau, ehara i te mea ka maumahara noa tātou ki tōna uara engari ka mārama hoki ki te tikanga pūtaiao kei muri i te ariā o te ira me ngā tataunga matū katoa.
