Ngā Tauira Pātai me te Kōrero mō ngā Waikawa me ngā Kawenga o Arrhenius
He ariā taketake ngā waikawa me ngā kawakore i roto i te matū. Ko tētahi o ngā ariā rongonui hei whakamārama i te whanonga o ngā waikawa me ngā kawakore ko te ariā Arrhenius. E ai ki a Arrhenius, ko te waikawa he matū e whakaputa ana i ngā iona H⁺ (H₃O⁺ rānei) ina rewa ki te wai, ko te kawakore ia he matū e whakaputa ana i ngā iona OH⁻ ina rewa ki te wai. I roto i tēnei tuhinga, ka matapakihia e mātou ētahi tauira raruraru e pā ana ki ngā waikawa me ngā kawakore e ai ki te ariā Arrhenius, me ō rātou otinga.
Tauira Pātai 1
Pātai:
Ka whakarewaina he wairewa waikawa hauwai (HCl) 0,1 M ki te wai. Tātaihia te kukū o ngā katote H⁺ i roto i te wairewa.
Kōrero:
E ai ki te ariā a Arrhenius, he waikawa te HCl nā te mea ka puta he iona H⁺ ina rewa ki te wai. Ko te whārite iona mō te HCl i roto i te wai koia tēnei:
\[ \kuputuhi{HCl} \to \kuputuhi{H}^+ + \kuputuhi{Cl}^- \]
Ko te kukū tīmatanga o te HCl he 0,1 M. Nā te mea he waikawa kaha te HCl ka whakakōkī katoa i roto i te wairewa, ka puta i ia ngota HCl tētahi iona H⁺ me tētahi iona Cl⁻. Nō reira, he ōrite anō hoki te kukū o ngā iona H⁺ i roto i te wairewa ki te kukū o te HCl, arā:
\[ [\kuputuhi{H}^+] = 0,1 \kuputuhi{ M} \]
Nō reira, ko te kukū o ngā katote H⁺ i roto i te otinga HCl 0,1 M ko 0,1 M.
Tauira Pātai 2
Pātai:
Tātaihia te pH o tētahi otinga waikawa hauota (HNO₃) 0,01 M.
Kōrero:
He waikawa kaha te HNO₃ ka whakakōkī katoa i roto i te wai, nō reira ko te whārite whakakōkī mō te HNO₃ penei:
\[ \text{HNO}_3 \to \text{H}^+ + \text{NO}_3^- \]
Ko te kukū o te HNO₃ he 0,01 M. Nā te mea he waikawa kaha te HNO₃, ka puta i ia ngota ngota o te HNO₃ tētahi iona H⁺. Nō reira, ko te kukū o ngā iona H⁺ i roto i te otinga he ōrite ki te kukū o te HNO₃, arā:
\[ [\kuputuhi{H}^+] = 0,01 \kuputuhi{ M} \]
Ka taea te tatau i te pH mā te whakamahi i te tātai:
\[ \kuputuhi{pH} = -\log [\kuputuhi{H}^+] \]
Mā te tāpiri i te kukū o ngā iona H⁺ ki roto i te tātai, ka whiwhi tātou:
\[ \text{pH} = -\log (0,01) = -\log (10^{-2}) = 2 \]
Nō reira, ko te pH o te otinga HNO₃ 0,01 M he 2.
Tauira Pātai 3
Pātai:
Tātaihia te kukū o ngā iona OH⁻ i roto i te otinga NaOH 0,05 M.
Kōrero:
He turanga kaha te NaOH e whaka-ionize katoa ana i roto i te wai, nō reira ko te whārite whaka-ionize mō te NaOH penei:
\[ \text{NaOH} \to \text{Na}^+ + \text{OH}^- \]
Ko te kukū o te NaOH i hoatu ko te 0,05 M. Nā te mea he turanga kaha te NaOH, ka puta i ia ngota NaOH tētahi iona OH⁻. Nō reira, ko te kukū o ngā iona OH⁻ i roto i te otinga he ōrite ki te kukū o te NaOH, arā:
\[ [\kuputuhi{OH}^-] = 0,05 \kuputuhi{ M} \]
Nō reira, ko te kukū o ngā iona OH⁻ i roto i te otinga NaOH 0,05 M ko 0,05 M.
Tauira Pātai 4
Pātai:
Tātaihia te pH o tētahi otinga KOH 0,01 M.
Kōrero:
He turanga kaha te KOH e whakakōkī katoa ana i roto i te wai. Ko te whārite whakakōkī mō te KOH i roto i te wai e whai ake nei:
\[ \text{KOH} \to \text{K}^+ + \text{OH}^- \]
Ko te kukū KOH kua hoatu ko te 0,01 M. Nā te mea he turanga kaha te KOH, ka puta i ia ngota KOH tētahi iona OH⁻. Nō reira, ko te kukū o ngā iona OH⁻ i roto i te otinga he ōrite ki te kukū o te KOH, arā:
\[ [\kuputuhi{OH}^-] = 0,01 \kuputuhi{ M} \]
Ko te pH he ine i te kukū o ngā iona H⁺ i roto i tētahi otinga. Ka taea e tātou te whakamahi i te whanaungatanga i waenga i te pH, ngā iona H⁺, me ngā iona OH⁻ e homai ana e te hua iona wai (Kw):
\[ \text{Kw} = [\text{H}^+][\text{OH}^-] = 1 \times 10^{-14} \]
I te mōhio ki te uara o [OH⁻], ka taea e tātou te tatau i te [H⁺]:
\[ [\kuputuhi{H}^+] = \frac{\kuputuhi{Kw}}{[\kuputuhi{OH}^-]} = \frac{1 \times 10^{-14}}{0,01} = 1 \times 10^{-12} \text{ M} \]
Ka taea te tatau i te pH mā te whakamahi i te tātai:
\[ \kuputuhi{pH} = -\log [\kuputuhi{H}^+] \]
Mā te tāpiri i te kukū o ngā iona H⁺ ki roto i te tātai, ka whiwhi tātou:
\[ \text{pH} = -\log (1 \times 10^{-12}) = 12 \]
Nō reira, ko te pH o te otinga KOH 0,01 M he 12.
Tauira Pātai 5
Pātai:
Ko te pH o tētahi otinga he = 3. Tātaihia te kukū o ngā katote H⁺ i roto i te otinga.
Kōrero:
Ko te pH he ine i te kukū o ngā iona H⁺ i roto i tētahi otinga, ā, ka taea te whakaatu mā te tātai:
\[ \kuputuhi{pH} = -\log [\kuputuhi{H}^+] \]
Hei tatau i te kukū o ngā iona H⁺, ka hurihia e mātou te tātai ki:
\[ [\kuputuhi{H}^+] = 10^{-\kuputuhi{pH}} \]
Mā te whakauru i ngā uara pH kua hoatu, ka whiwhi tātou:
\[ [\kuputuhi{H}^+] = 10^{-3} = 0,001 \kuputuhi{ M} \]
Nō reira, ko te kukū o ngā katote H⁺ i roto i tētahi otinga me te pH = 3 ko 0,001 M.
Tauira Pātai 6
Pātai:
Ko te kukū o te otinga NH₄OH he 0,1 M. Tātaihia te pH o te otinga mēnā ko te uara Kb mō te NH₄OH he 1,8 x 10⁻⁵.
Kōrero:
He turanga ngoikore te NH₄OH e kore e tino ionize i roto i te wai. Ko te whārite ionization mō te NH₄OH i roto i te wai koia tēnei:
\[ \text{NH}_4\text{OH} \leftrightarrow \text{NH}_4^+ + \text{OH}^- \]
Ko te pūmau taurite mō te whakakōkī o te NH₄OH e kiia ana ko Kb, ā, e homai ana e:
\[ K_b = \frac{[\text{NH}_4^+][\text{OH}^-]}{[\text{NH}_4\text{OH}} \]
Nā te mea he turanga ngoikore te NH₄OH, ka whakamahia e mātou a Kb hei tatau i te kukū o ngā iona OH⁻. Mēnā ko te kukū o te NH₄OH kua whakakōkītia te \(x\), ka pēnei te whārite whakakōkī:
\[ K_b = \frac{x^2}{0,1 – x} \approx \frac{x^2}{0,1} \]
Nā te mea he iti rawa te uara o Kb, ka whakaarohia \(0,1 – x \approx 0,1\):
\[ 1,8 \times 10^{-5} = \frac{x^2}{0,1} \]
\[ x^2 = 1,8 \whakareatia ki te 10^{-6} \]
\[ x = \sqrt{1,8 \times 10^{-6}} \]
\[ x \tata ki te 1,34 \times 10^{-3} \text{ M} \]
Nō reira, ko te kukū o ngā iona OH⁻ ko \(1,34 \times 10^{-3} \text{ M}\).
Mai i tēnei kukū, ka taea e tātou te tatau i te kukū o ngā iona H⁺ mā te whakamahi i te Kw:
\[ [\text{H}^+] = \frac{1 \times 10^{-14}}{1,34 \times 10^{-3}} \]
\[ [\text{H}^+] = 7,46 \times 10^{-12} \text{ M} \]
pH:
\[ \text{pH} = -\log (7,46 \times 10^{-12}) \]
\[ \text{pH} \tata ki te 11,13 \]
Nō reira, ko te pH o te otinga NH₄OH 0,1 M he tata ki te 11,13.
Whakamutunga
He pūtake nui te ariā Arrhenius mō te mārama ki te whanonga o ngā waikawa me ngā kawakore i roto i te otinga. I roto i tēnei kōrero, kua tirohia e mātou ētahi tauira raruraru e whakaatu ana i te whakamahinga o ēnei ariā hei tatau i ngā kukū o ngā iona H⁺ me OH⁻ me te pH o ngā otinga rerekē. He mea nui te mārama ki tēnei ariā mō te hunga e whai ana i tētahi mahi i roto i te matū, ahakoa i te kura tuarua, i te taumata mātauranga teitei rānei.
