Laʻana o nā nīnau kūkākūkā Chemical Kinetics
ʻO ke kinetics kemika kahi lālā o ke kemika e aʻo ana i nā wikiwiki o nā hopena kemika a me nā mea e hoʻohuli iā lākou. He mea nui ka hoʻomaopopo piha ʻana i ke kinetics kemika no nā kānaka ʻepekema a me nā ʻenekinia kemika e hoʻomohala i nā kaʻina hana ʻoihana kūpono a hoʻomaopopo i nā ʻano hopena biochemical like ʻole e hana ʻia i loko o nā meaola ola. E kūkākūkā kēia ʻatikala i kekahi mau pilikia hoʻohālike e pili ana i ke kinetics kemika a me kā lākou mau hoʻonā e hāʻawi i kahi ʻike hohonu o kēia kumuhana.
Laʻana Nīnau 1: Hoʻoholo ʻana i ke Kauoha o ka Pane
Nīnau:
Loaʻa i kahi hopena ka hoʻohālikelike wikiwiki maʻamau:
\[ R = k[A]^m[B]^n \]
Ma hea:
– ʻo \( R \) ka wikiwiki o ka hopena,
– ʻo \( k \) ke ʻano paʻa o ka wikiwiki,
– ʻO \([A] \) a me \([B]\) nā ʻano o nā mea hana A a me B,
– ʻO \( m \) a me \( n \) nā kauoha pane e pili ana iā A a me B.
Ua ʻike ʻia ua hoʻokō ʻia ka hoʻokolohua me nā ʻano like ʻole o ka noʻonoʻo ʻana:
| Hoʻokolohua | \([A]\) (mol/L) | \([B]\) (mol/L) | Ka wikiwiki o ka pane (mol/(Ls)) |
|—————–|——————-|——————–|————————|
| 1 | 0,10 | 0,20 | 0,030 |
| 2 | 0,10 | 0,40 | 0,060 |
| 3 | 0,20 | 0,20 | 0,120 |
E hoʻoholo i ke kauoha o ka hopena e pili ana iā A a me B a me ka waiwai o ke kūpaʻa wikiwiki \( k \).
Kūkākūkā:
No ka hoʻoholo ʻana i ke kaʻina hana e pili ana iā A a me B, pono mākou e hoʻohālikelike i nā wikiwiki o ka hopena me nā ʻano like ʻole o ka noʻonoʻo ʻana.
ʻO ka mea mua, hoʻoholo mākou i ke kaʻina o ka hopena e pili ana iā B ma ka hoʻohālikelike ʻana i nā hoʻokolohua 1 a me 2:
\[ \frac{\text{R2}}{\text{R1}} = \frac{k[A]^m [B_2]^n}{k[A]^m [B_1]^n} \]
\[ \frac{0,060}{0,030} = \frac{[0,10]^m [0,40]^n}{[0,10]^m [0,20]^n} \]
\[ 2 = \left(\frac{0,40}{0,20}\right)^n \]
\[ 2 = 2^n \]
\[ n = 1 \]
ʻO ke kaʻina hana e pili ana iā B he 1.
A laila, hoʻoholo mākou i ke kaʻina hana e pili ana iā A ma ka hoʻohālikelike ʻana i nā hoʻokolohua 1 a me 3:
\[ \frac{\text{R3}}{\text{R1}} = \frac{k[A_3]^m [B]^n}{k[A_1]^m [B]^n} \]
\[ \frac{0,120}{0,030} = \frac{[0,20]^m [0,20]^n}{[0,10]^m [0,20]^n} \]
\[ 4 = \left(\frac{0,20}{0,10}\right)^m \]
\[ 4 = 2^m \]
\[ m = 2 \]
ʻO ke kaʻina hana e pili ana iā A he 2.
No laila, ʻo ke kaulike o ka wikiwiki o ka hopena:
\[ R = k[A]^2[B] \]
I kēia manawa, loaʻa iā mākou ka waiwai o ke kūpaʻa wikiwiki \( k \). E hoʻohana i ka ʻikepili mai ka hoʻokolohua 1:
\[ 0,030 = k[0,10]^2[0,20] \]
0,030 = k manawa 0,01 manawa 0,20
\[ 0,030 = k \times 0,002 \]
\[ k = \frac{0,030}{0,002} \]
\[ k = 15 \ \kikokikona{L}^2/(\kikokikona{mol}^2 \cdot \kikokikona{s}) \]
No laila, ʻo ke kūpaʻa o ka wikiwiki \( k \) he 15 L²/(mol²·s).
Laʻana Nīnau 2: Ka hapalua o ke ola o kahi hopena lua-kauoha
Nīnau:
Hāʻawi ʻia kahi hopena kauoha ʻelua me ka hoʻohālikelike wikiwiki:
\[ R = k[A]^2 \]
ʻO ke kūpaʻa o ka wikiwiki (\( k \)) o ka hopena he 0,5 L/(mol·s). Inā ʻo ka nui mua o ka mea hana \( [A]_0 \) he 1 mol/L, e ʻimi i ka hapalua ola o ka hopena.
Kūkākūkā:
No nā hopena kauoha lua, hiki ke helu ʻia ka hapalua ola (\( t_{1/2} \)) me ka hoʻohana ʻana i ka hoohalike:
\[ t_{1/2} = \frac{1}{k[A]_0} \]
E pani i nā waiwai i ʻike ʻia:
\[ t_{1/2} = \frac{1}{0,5 \times 1} \]
\[ t_{1/2} = \frac{1}{0,5} \]
\[ t_{1/2} = 2 \ \kikokikona{s} \]
No laila, ʻo ka hapalua ola o kahi hopena lua-kauoha me kahi paʻa o ka wikiwiki o 0,5 L/(mol·s) a me kahi hui mua o ka reactant o 1 mol/L he 2 kekona.
Laʻana Nīnau 3: Ikehu Hoʻāla ma o ka Hoʻohālikelike Arrhenius
Nīnau:
ʻElua mau kūpaʻa wikiwiki like ʻole o kahi hopena ma nā mahana like ʻole ʻelua:
– Ma 300 K, ʻo ke kūpaʻa o ka wikiwiki (\( k_1 \)) he 0,2 L/(mol·s)
– Ma 350 K, ʻo ke kūpaʻa o ka wikiwiki (\( k_2 \)) he 0,4 L/(mol·s)
E hoʻoholo i ka ikehu hoʻāla (\( E_a \)) o ka hopena me ka hoʻohana ʻana i ka hoʻohālikelike Arrhenius:
\[ k = A e^{-E_a/(RT)} \]
Kūkākūkā:
Hiki ke kākau ʻia ka hoʻohālikelike Arrhenius ma ke ʻano logarithmic penei:
\[ \ln k = \ln A – \frac{E_a}{RT} \]
Hiki iā mākou ke hoʻohana i ʻelua ʻikepili paʻa o ka wikiwiki ma nā mahana like ʻole ʻelua e hoʻoholo ai \( E_a \):
E kākau kākou i ʻelua mau kaulike no kēia mau kūlana ʻelua:
\[ \ln k_1 = \ln A – \frac{E_a}{R \cdot T_1} \]
\[ \ln k_2 = \ln A – \frac{E_a}{R \cdot T_2} \]
Ma ka unuhi ʻana i kēia mau kaulike ʻelua:
\[ \ln k_2 – \ln k_1 = \left(\ln A – \frac{E_a}{R \cdot T_2}\right) – \left(\ln A – \frac{E_a}{R \cdot T_1}\right) \]
\[ \ln \left(\frac{k_2}{k_1}\right) = -\frac{E_a}{R} \left(\frac{1}{T_2} – \frac{1}{T_1}\right) \]
E hoʻololi i nā waiwai o \( k_1 \), \( k_2 \), \( T_1 \), a me \( T_2 \):
\[ \ln \left(\frac{0,4}{0,2}\right) = -\frac{E_a}{8,314} \left(\frac{1}{350} – \frac{1}{300}\right) \]
\[ \ln (2) = -\frac{E_a}{8,314} \left(\frac{1}{350} – \frac{1}{300}\right) \]
\[ 0,693 = -\frac{E_a}{8,314} \left(\frac{300 – 350}{350 \cdot 300}\right) \]
\[ 0,693 = -\frac{E_a}{8,314} \left(\frac{-50}{105000}\right) \]
\[ 0,693 = \frac{E_a}{8,314} \left(\frac{1}{2100}\right) \]
\[ 0,693 = \frac{E_a}{17462850/2100} \]
\[ 0,693 = \frac{E_a}{8314} \]
\[ E_a = 0,693 \times 8314 \]
\[ E_a = 5761,842 \ \kikokikona{J/mol} \]
No laila, ʻo ka ikehu hoʻāla (\( E_a \)) no ka hopena ma kahi o 5761,842 J/mol a i ʻole ma kahi o 5,76 kJ/mol.
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He mea koʻikoʻi ka ʻike o ke kinetics kemika a me ka hoʻomaopopo ʻana i ke kūkākūkā ʻana i nā pilikia e like me kēia ma nā ʻano like ʻole, ʻoiai ka ʻoihana kemika a me ka noiʻi ʻepekema. Hāʻawi ka pilikia laʻana ma luna i kahi hoʻomaopopo ʻana i nā ʻano hana no ka hoʻoholo ʻana i ke kauoha pane, ka hapalua ola, a me ka ikehu hoʻāla, he mea koʻikoʻi ia no ka hoʻomohala ʻenehana a me ka hoʻomaopopo hohonu ʻana i nā ʻano hana pane kemika.
