Pehea e hoʻoholo ai i ka helu o Avogadro
ʻO ka helu ʻo Avogadro kekahi o nā manaʻo koʻikoʻi loa i ka kemika a me ka physics hou no ka mea he hana ia ma ke ʻano he alahaka ma waena o ke ao microscopic (nā ʻātoma, nā molekala, nā ion) a me ke ao macroscopic (grams, liters, a me nā mea hiki iā mākou ke kaupaona). ʻO ka hoʻomaopopo ʻana i ke ʻano o ka hoʻoholo ʻana i ka helu ʻo Avogadro e maʻalahi ai ka hoʻomaopopo ʻana i ke kumumanaʻo o nā moles, e helu i ka helu o nā ʻāpana i loko o kahi mea, a e hoʻoponopono i nā pilikia stoichiometry like ʻole. Kūkākūkā kēia ʻatikala i ka wehewehe ʻana o ka helu ʻo Avogadro, kona kumu kumumanaʻo, a me kekahi mau ʻano hana no ka hoʻoholo ʻana i ka helu ʻo Avogadro i hoʻohana ʻia i ka ʻepekema.
Ke hoʻomaopopo nei i ka helu o Avogadro
ʻO ka helu ʻo Avogadro (i hōʻike ʻia e \(N_A\)) ka helu o nā ʻāpana (nā ʻātoma, nā molekala, a i ʻole nā mea ʻē aʻe) i loko o 1 mole o kahi mea. ʻO ka waiwai i ʻae ʻia i kēia manawa o ka helu ʻo Avogadro:
\[
N_A = 6{,}02214076 \times 10^{23}\ \text{mol}^{-1}
\]
He nui loa kēia helu no ka mea he liʻiliʻi loa nā ʻāpana e hana ana i nā mea. No ka laʻana, aia i loko o 1 mole o ka wai ma kahi o \(6{,}02 \times 10^{23}\) mau mole wai. ʻAʻole wale ka helu o Avogadro he helu "hoʻopaʻanaʻau", akā, ʻo ia ka hopena o nā ana a me nā wehewehe i hoʻokumu ʻia ma o nā hoʻokolohua lōʻihi ma o ka mōʻaukala o ka ʻepekema.
ʻO ka pilina ma waena o ka helu o Avogadro a me ke kumumanaʻo o nā moles
Ua wehewehe ʻia ke kumumanaʻo o ka mole ma ke ʻano he anakahi o ka nui o kahi mea. Ma nā huaʻōlelo maʻalahi:
– 1 mole o kahi mea = \(N_A\) mau ʻāpana o kēlā mea.
– Ua like ke kaumaha o 1 mole o kahi mea (ma nā grama) me kona kaumaha molar.
Eia kekahi laʻana, ʻo ka nuipa molar o ke kalapona-12 he 12 g/mol. ʻO ke ʻano kēia he 12 grams o ke kalapona-12 aia nā ʻātoma kalapona-12 \(6{,}022 \times 10^{23}\) o ke kalapona. ʻAe kēia pilina iā mākou e helu i ka helu o nā ʻāpana mai kahi nuipa e hiki ke kaupaona ʻia i loko o ka hale hana.
No ke aha e pono ai e "hoʻoholo ʻia" ka helu o Avogadro?
I ka mōʻaukala, ʻaʻole i ʻike pololei ʻia ka waiwai o ka helu o Avogadro. Pono nā kānaka ʻepekema e ʻimi i kahi ala e hoʻopili ai i nā ana macroscopic (ka nuipa, ka nui, ka hoʻouka uila) i ka helu o nā ʻāpana. No laila, ua hoʻoholo ʻia ka helu o Avogadro ma o nā ʻano hana hoʻokolohua like ʻole a me nā ʻano hana kumumanaʻo.
I kēia lā, ua wehewehe pono ʻia ka helu o Avogadro. Mai ka wehewehe hou ʻana o SI i ka makahiki 2019, ua wehewehe pono ʻia ka waiwai o \(N_A\) e like me \(6{,}02214076 \times 10^{23}\). Eia nō naʻe, no nā kumu hoʻonaʻauao, he mea nui ka hoʻomaopopo ʻana pehea e hoʻoholo ʻia ai ka helu o Avogadro, no ka mea, kōkua ia iā mākou e hoʻomaopopo i kahi i loaʻa ai ka helu a pehea e ana ai ka ʻepekema.
Hana 1: Ke Ala Mai ka Atomic Mass (Carbon-12)
ʻO kekahi o nā ala kumu loa e hoʻomaopopo ai i ka helu o Avogadro ma o ke kūlana kalapona-12. Ua wehewehe mua ʻia ka mole ʻo ia ka helu o nā ʻātoma i loko o 12 grams o ke kalapona-12. Inā ʻike mākou i ka nui o hoʻokahi ʻātoma kalapona-12, a laila hiki ke helu ʻia ka helu o Avogadro:
\[
N_A = \frac{\text{nuipa o 1 mole}}{\text{nuipa o 1 ʻātoma}}
\]
ʻOiai ʻo ke kaumaha o 1 mole o ke kalapona-12 he 12 grams, a laila:
\[
N_A = \frac{12\ \text{g}}{m_{\text{ʻātoma C-12}}}
\]
ʻO ka pilikia, he liʻiliʻi loa ka nuipa o kahi ʻātoma hoʻokahi a ʻaʻole hiki ke ana maʻalahi ʻia me ke kaulike maʻamau. Eia nō naʻe, me ka hoʻomohala ʻana o nā ʻenehana e like me ka spectrometry mass a me nā ʻenehana ana ʻana o ka atomic-scale, hiki ke hoʻoholo ʻia ka nuipa atomic ma ke ʻano ʻole. Hāʻawi kēia ʻano hana i kahi kumu manaʻo ikaika no ke ʻano o ka pilina o ka helu Avogadro me ka nuipa atomic.
Hana 2: Hana Electrolysis (Kānāwai o Faraday)
ʻO kekahi ʻano hana kaulana no ka hoʻoholo ʻana i ka helu ʻo Avogadro e hoʻohana ana i ka electrolysis, ke kaʻina hana o ka hoʻohaumia ʻana i kahi mea me ka hoʻohana ʻana i ke au uila. ʻŌlelo ke kānāwai o Faraday ʻo ka nui o ka mea e pane ana i ka electrolysis ua like ia me ka nui o ka hoʻouku uila e kahe ana.
ʻO ka manaʻo nui o kēia ʻano hana, ʻo ia ka hoʻohui ʻana:
– ʻO ka huina o ka uku o 1 mole o nā electrons (i kapa ʻia ʻo Faraday's constant, \(F\))
– Hoʻouka ʻia o hoʻokahi uila (\(e\))
Inā ʻike mākou i ke kūpaʻa o Faraday a me ka uku o kahi electron, hiki ke helu ʻia ka helu o Avogadro penei:
\[
N_A = \frac{F}{e}
\]
ʻO ke kūpaʻa o Faraday ma kahi o:
\[
F \approx 96485\ \text{C/mol}
\]
Ka hoʻopiʻi uila:
\[
e \approx 1{,}602 \times 10^{-19}\ \text{C}
\]
No laila ma ke ʻano he:
\[
N_A \approx \frac{96485}{1{,}602 \times 10^{-19}} \approx 6{,}02 \times 10^{23}
\]
He ala nani loa kēia no ka mea e pili ana i nā hanana kemika (nā hopena redox) i nā kumu paʻa o ka physics (ka hoʻopiʻi electron).
Hana 3: Hana ʻAno Crystal Silicon (Hana Density Crystal X-ray)
I ke metrology hou, ʻo kekahi o nā ʻano hana pololei loa no ka hoʻoholo ʻana i ka helu ʻo Avogadro ʻo ia ka hoʻohana ʻana i nā kristal silicon maʻemaʻe loa. Hoʻohana kēia ʻano hana i ka ʻoiaʻiʻo he hoʻonohonoho atomika maʻamau nā kristal, a hiki ke ana ʻia nā mamao ma waena o nā ʻātoma me ka hoʻohana ʻana i ka diffraction X-ray.
ʻIke laulā:
1. E lawe i kahi poepoe silicon me ka maʻemaʻe kiʻekiʻe a me ke ʻano kokoke i ka hemolele.
2. E ana i ka nui o ka pōpō me ka pololei loa.
3. E ana i ke kaumaha o ka pōpō e ʻike i kona nuipaʻa.
4. E hoʻohana i ka ʻikepili hoʻonohonoho kristal silicon e ʻike ai i ka nui o nā ʻātoma i loko o kēlā me kēia anakahi leo.
Ma ka ʻike ʻana i ka helu o nā ʻātoma i loko o kahi leo i hāʻawi ʻia a me ka hoʻopili ʻana iā ia i ka nuipa holoʻokoʻa, hiki i nā kānaka ʻepekema ke helu i ka nui o nā ʻātoma i loko o 1 mole, ʻo ia ka helu ʻo Avogadro. He pou koʻikoʻi kēia ʻano hana i ka hoʻokumu ʻana i nā kūpaʻa SI.
Hana 4: Ke Ala Kinoea Kūpono (Manaʻo Mōʻaukala)
I ka mōʻaukala, ua hoʻomaka ka manaʻo o Avogadro me nā kinoea: "Ma ka mahana like a me ke kaomi like, loaʻa i nā nui like o nā kinoea ka nui like o nā ʻāpana." ʻOiai ʻaʻole hāʻawi pololei kēia ʻano i ka waiwai o \(N_A\), ua hoʻomākaukau ia i ke ala no ka hoʻopili ʻana i ka nui o ke kinoea, ka helu o nā mole, a me ka helu o nā ʻāpana.
No ka laʻana, ma STP (wehewehe kahiko: 0°C a me 1 atm), noho ka 1 mole o ke kinoea kūpono i kahi nui o 22,4 L. Inā i kekahi lā ua hiki iā mākou ke helu i ka helu o nā ʻāpana i loko o kēlā nui ma o nā hoʻokolohua microscopic, a laila hiki ke loaʻa ka helu ʻo Avogadro. I ka hana maoli, ʻoi aku ka kūpono o ke ʻano kinoea kūpono ma ke ʻano he kumu manaʻo ma ka pae kula, no ka mea, ʻo ka hoʻoholo pololei ʻana o \(N_A\) e koi ana i nā ʻano pololei e like me ka electrolysis a me nā kristal silicon.
Pehea e hoʻohana ai i ka helu o Avogadro i nā helu
ʻOiai ʻo ka hoʻoholo pololei ʻana o ka helu ʻo Avogadro e hana ʻia e nā kānaka ʻepekema me nā lako paʻakikī, ʻo nā haumāna a me nā haumāna kulanui pinepine e "hoʻoholo" i ka helu o nā ʻāpana me ka hoʻohana ʻana i ka waiwai \(N_A\). ʻO ke ʻano hana i hoʻohana pinepine ʻia:
1. Ka helu o nā mole mai ka nuipa:
\[
n = \frac{m}{M}
\]
me \(m\) = nuipaʻa (g) a me \(M\) = nuipaʻa molar (g/mol).
2. Helu o nā ʻāpana:
\[
N = n \times N_A
\]
Laʻana wikiwiki: Ehia mau molekala i loko o 18 grams o ka wai (\(H_2O\))?
– Ka nuipa molar o ka wai = 18 g/mol
– Nā mole o ka wai = \(18/18 = 1\) mole
– Helu o nā molekala = \(1 \times 6{,}02 \times 10^{23} = 6{,}02 \times 10^{23}\)
Ka hopena
Hiki ke hoʻomaopopo ʻia ke ʻano hana no ka hoʻoholo ʻana i ka helu o Avogadro ma o kekahi mau ʻano hana nui: ka pilina ma waena o nā nui atomika (kalapona-12), electrolysis ma o ke kānāwai o Faraday, ke ʻano kristal silicon me ka diffraction X-ray, a me ke ʻano hana manaʻo o nā kinoea kūpono. Mai kēia mau ʻano hana like ʻole, ua maopopo ʻaʻole he helu "random" ka helu o Avogadro, akā ʻo ka hopena o nā ana ʻepekema e hoʻopili ana i ka unahi atomika me nā unahi hiki iā mākou ke ana i ke ola o kēlā me kēia lā. Ma ka hoʻomaopopo ʻana i ke kaʻina hana o ka hoʻoholo ʻana, ʻaʻole mākou e hoʻopaʻanaʻau wale i kona waiwai akā hoʻomaopopo pū i ke ʻano ʻepekema ma hope o ke kumumanaʻo o ka mole a me nā helu kemika ma ke ʻano holoʻokoʻa.
