Tauira o ngā Pātai e Matapaki ana i te Tere Tauhohenga
He ariā taketake te tere tauhohenga i roto i te matū, ā, he mea nui tēnei i roto i ngā tukanga maha, i roto i ngā mahi ahumahi me ngā mahi o ia rā. I roto i tēnei tuhinga, ka whakamāramahia e mātou te ariā o te tere tauhohenga me te whakarato tauira me ngā kōrero taipitopito kia mārama pai ai ngā kaipānui.
Te Mārama ki te Tere Tauhohenga
Ko te tere o te tauhohenga e tautuhia ana ko te huringa o te kukū o tētahi matū tauhohenga, hua rānei mō ia wā. I roto i tētahi whārite māmā, ka taea te tuhi i te tere o te tauhohenga penei:
\[ \text{Te Auau Tauhohenga} = \frac{\Delta \text{[Te Kukū]}}{\Delta t} \]
Ko te tikanga ka inehia te kukū i roto i ngā mole ia rita (M) ā, ko te wā i roto i ngā hēkona (s). Nō reira, ko ngā waeine o te tere tauhohenga he M/s.
Ngā Take e Pā Ana ki te Tere o te Tauhohenga
Anei ētahi āhuatanga e pā ana ki te tere o te tauhohenga:
1. Te Kukū o ngā Tauhohenga: Mā te whakanui ake i te kukū o ngā tauhohenga ka piki ake te tere o te tauhohenga.
2. Mahana: Ko te whakanui ake i te pāmahana ka tere ake te tere o te tauhohenga.
3. Horahanga Mata: Ka nui ake te horahanga mata e wātea ana, ka tere ake te tere o te tauhohenga.
4. Kaiwhakaoho: Ka whakatereterehia e ngā kaiwhakaoho te tere o te tauhohenga me te kore e pāngia e ngā huringa tuturu.
5. Pēhanga: Mō ngā tauhohenga e uru ana ngā hau, ko te whakanui ake i te pēhanga ka whakanui ake i te tere o te tauhohenga.
Ngā Pātai Tauira me te Kōrero
Tauira Pātai 1
Ko te tauhohenga i waenga i te konutai thiosulfate (Na2S2O3) me te waikawa hauwaiora (HCl) penei:
\[ \text{Na}_2\text{S}_2\text{O}_3 + 2 \text{HCl} \rightarrow 2 \text{NaCl} + \text{S} + \text{SO}_2 + \text{H}_2\text{O} \]
I roto i tētahi whakamātautau, ka rerekē te kukū o te konutai thiosulfate mai i te 0,10 M ki te 0,05 M i roto i te 30 hēkona. Tātaihia te tere tauhohenga toharite!
Kōrero
Ka taea te tatau i te tere tauhohenga toharite mā te whakamahi i te tātai:
\[ \text{Te Tere Tauhohenga} = -\frac{\Delta \text{[Na}_2\text{S}_2\text{O}_3\text{]}}{\Delta t} \]
Whakakapia ngā uara kua hoatu ki roto i te tātai:
\[ \Delta \text{[Na}_2\text{S}_2\text{O}_3\text{]} = 0,05 \text{ M} – 0,10 \text{ M} = -0,05 \text{ M} \]
\[ \Delta t = 30 \text{ s} \]
Nō reira,
\[ \text{Te Tere Tauhohenga} = -\left(\frac{-0,05 \text{ M}}{30 \text{ s}}\right) = \frac{0,05 \text{ M}}{30 \text{ s}} = 0,00167 \text{ M/s} \]
Nō reira, ko te tere tauhohenga toharite ko 0,00167 M/s.
Tauira Pātai 2
I roto i tētahi tauhohenga, ka hoatu te tere tauhohenga e te whārite tere:
\[ \text{Reiti} = k [A]^m [B]^n \]
Mai i te whakamātautau, i riro mai ngā raraunga e whai ake nei:
| Whakamātautau | [A] (M) | [B] (M) | Tere Tauhohenga (M/s) |
|—————–|————|——————-|
| 1 | 0.10 | 0.10 | 2.0 × 10^-3 |
| 2 | 0.20 | 0.10 | 8.0 × 10^-3 |
| 3 | 0.10 | 0.20 | 2.0 × 10^-3 |
Tātaihia ngā raupapa tauhohenga m me n, ka tatau i te uara o te pūmau tere, k.
Kōrero
Te Whakatau i te Raupapa Tauhohenga \( m \) me \( n \):
1. Mai i ngā Whakamātautau 1 me te 2:
\[ \frac{\text{Reiti}_2}{\text{Reiti}_1} = \frac{k [A]_2^m [B]_2^n}{k [A]_1^m [B]_1^n} \]
\[ \frac{8.0 \times 10^{-3}}{2.0 \times 10^{-3}} = \frac{(0.20)^m (0.10)^n}{(0.10)^m (0.10)^n} \]
\[ 4 = (2)^m \]
Nō reira, \( m = 2 \).
2. Mai i ngā Whakamātautau 1 me te 3:
\[ \frac{\text{Reiti}_3}{\text{Reiti}_1} = \frac{k [A]_3^m [B]_3^n}{k [A]_1^m [B]_1^n} \]
\[ \frac{2.0 \times 10^{-3}}{2.0 \times 10^{-3}} = \frac{(0.10)^m (0.20)^n}{(0.10)^m (0.10)^n} \]
\[ 1 = (2)^n \]
Nō reira, \( n = 0 \).
Nō reira, ko te raupapa tauhohenga e pā ana ki a A ko te 2, ā, ko te raupapa tauhohenga e pā ana ki a B ko te 0.
Te Tātai i te Uara Pūmau Tere \( k \):
Mā te whakamahi i ngā raraunga mai i te whakamātautau 1:
\[ \text{Reiti} = k [A]^m [B]^n \]
\[ 2.0 \times 10^{-3} = k (0.10)^2 (0.10)^0 \]
\[ 2.0 \times 10^{-3} = k (0.01) \]
\[ k = \frac{2.0 \times 10^{-3}}{0.01} \]
\[ k = 0.20 \]
Nō reira, ko te pūmau tere \( k \) he 0.20 M^{-1} s^{-1}.
Tauira Pātai 3
Ka whai te tauhohenga matū i te tikanga e whai ake nei:
\[ \text{Tauhohenga 1: } \text{A} \rightarrow \text{B} \quad (k_1 = 1.0 \, \text{s}^{-1}) \]
\[ \text{Tauhohenga 2: } \text{B} \rightarrow \text{C} \quad (k_2 = 0.1 \, \text{s}^{-1}) \]
Mena i te tīmatanga ko te kukū o A he 1 M, ā, ko B he 0, tātaihia te kukū o A me B i muri i te 5 hēkona.
Kōrero
Mā te whakamahi i te ture tere tauhohenga, kei a tātou:
Tauhohenga 1: A ki B
\[ [A] = [A]_0 e^{-k_1 t} \]
\[ [A] = 1 \text{ M} \times e^{-1.0 \text{ s}^{-1} \times 5 \text{ s}} \]
\[ [A] = e^{-5} \text{ M} \]
Tauhohenga 2: B ki C
\[ \frac{d[B]}{dt} = k_1 [A] – k_2 [B] \]
\[ \frac{d[B]}{dt} = 1.0 \text{ s}^{-1} \times [A] – 0.1 \text{ s}^{-1} \times [B] \]
Mā te whakamahi i tētahi otinga tātari, tau rānei o tēnei whārite rerekētanga (ko te tikanga Euler, ko Runge-Kutta rānei te tikanga):
\[ [B] \tata ki te 0.316 \kuputuhi{ M} \]
Nō reira, i muri i te 5 hēkona, ko te kukū o A kei te tata ki te \( e^{-5} \text{ M} \) ā, ko te kukū o B kei te tata ki te 0.316 M.
Whakamutunga
He kaupapa nui te tere o te tauhohenga i roto i te matū, e whakaata ana i te tere o te hurihanga o ngā kukū o ngā matū tauhohenga ki ngā hua. I roto i ngā tauira raruraru i runga ake nei, kua matapakihia e tātou te huarahi ki te tatau i te tere tauhohenga toharite, te whakatau i te raupapa tauhohenga, me te tatau i te pūmau tere tauhohenga. Mā te mārama ki ēnei ariā ka taea e tātou te whakamahi i ēnei i roto i ngā āhuatanga mahi maha, i roto i te taiwhanga me ngā tukanga ahumahi.
