Muenzaniso weMibvunzo yeKukurukurirana yeChemical Kinetics
Chemical kinetics ibazi rekemikari rinoongorora mwero wemaitiro emakemikari nezvinhu zvinoakanganisa. Kunzwisisa kwakakwana kwemakemikari kinetics kwakakosha kuti masayendisiti emakemikari nemainjiniya vagadzire maitiro anoshanda eindasitiri uye vanzwisise maitiro akasiyana-siyana emakemikari anoitika muzvinhu zvipenyu. Chinyorwa chino chichakurukura mienzaniso yakati wandei yematambudziko ane chekuita nemakemikari kinetics nemhinduro dzawo kuti tinzwisise zvakadzama nyaya iyi.
Muenzaniso Mubvunzo 1: Kusarudzwa kweKurongeka kweKuita
Mubvunzo:
Mhinduro ine chiyero chehuwandu hwehuwandu hunotevera:
\[ R = k[A]^m[B]^n \]
Di mana:
– \( R \) ndiyo chiyero chemhinduro,
– \( k \) ndiyo chiyero chinoramba chiripo,
– \([A] \) uye \([B]\) ndiwo huwandu hwezvinhu zvinokonzeresa A naB,
– \( m \) uye \( n \) ndiwo maerekitiro ekuita maererano naA naB.
Zvinozivikanwa kuti kuyedza uku kwakaitwa nekuchinja kwehuwandu hunotevera:
| Kuedza | \([A]\) (mol/L) | \([B]\) (mol/L) | Chiyero chemhinduro (mol/(Ls)) |
|————–|——————-|——————–|———————|
| 1 | 0,10 | 0,20 | 0,030 |
| 2 | 0,10 | 0,40 | 0,060 |
| 3 | 0,20 | 0,20 | 0,120 |
Sarudza kurongeka kwekuita maererano naA naB uye kukosha kwehuwandu hwechigarire \( k \).
Kukurukurirana:
Kuti tizive kurongeka kwekuita maererano naA naB, tinofanira kuenzanisa mwero wekuita nekusiyana kwakasiyana kwehuwandu.
Kutanga, tinowana kurongeka kwekuita maererano neB nekuenzanisa kuedza 1 ne2:
\[ \frac{\text{R2}}{\text{R1}} = \frac{k[A]^m [B_2]^n}{k[A]^m [B_1]^n} \]
\[ \frac{0,060}{0,030} = \frac{[0,10]^m [0,40]^n}{[0,10]^m [0,20]^n} \]
\[ 2 = \kuruboshwe(\frac{0,40}{0,20}\kurudyi)^n \]
\[ 2 = 2^n \]
\[ n = 1 \]
Kurongeka kwemhinduro maererano naB i1.
Tevere, tinosarudza kurongeka kwekuita maererano neA nekuenzanisa kuyedza 1 ne3:
\[ \frac{\text{R3}}{\text{R1}} = \frac{k[A_3]^m [B]^n}{k[A_1]^m [B]^n} \]
\[ \frac{0,120}{0,030} = \frac{[0,20]^m [0,20]^n}{[0,10]^m [0,20]^n} \]
\[ 4 = \kuruboshwe(\frac{0,20}{0,10}\kurudyi)^m \]
\[ 4 = 2^m \]
\[ m = 2 \]
Kurongeka kwemhinduro maererano naA i2.
Saka, reaction rate equation ndeiyi:
\[ R = k[A]^2[B] \]
Iye zvino tawana kukosha kwechiyero chisingachinji \( k \). Shandisa data kubva mukuyedza 1:
\[ 0,030 = k[0,10]^2[0,20] \]
\[ 0,030 = k \nguva 0,01 \nguva 0,20 \]
\[ 0,030 = k \nguva 0,002 \]
\[ k = \frac{0,030}{0,002} \]
\[ k = 15 \ \text{L}^2/(\text{mol}^2 \cdot \text{s}) \]
Saka, chiyero chisingachinji \( k \) i15 L²/(mol²·s).
Muenzaniso Mubvunzo 2: Hafu yeHupenyu hweReaction yeSecond-Order
Mubvunzo:
Kupiwa maitiro echipiri ekutevera ne equation yemutengo:
\[ R = k[A]^2 \]
Chiyero chinoramba chiripo (\( k \)) chemhinduro i0,5 L/(mol·s). Kana huwandu hwekutanga hwe reactant \( [A]_0 \) huri 1 mol/L, tsvaga hafu yehupenyu hwemhinduro.
Kukurukurirana:
Pakuita kwechipiri, hafu yehupenyu (\( t_{1/2} \)) inogona kuverengerwa uchishandisa equation:
\[t_{1/2} = \frac{1}{k[A]_0} \]
Tsiva tsika dzinozivikanwa:
\[t_{1/2} = \frac{1}{0,5 \kawa 1} \]
\[t_{1/2} = \frac{1}{0,5} \]
\[t_{1/2} = 2 \ \mashoko{s} \]
Saka, hafu yehupenyu hwe reaction yechipiri ine rate constant ye0,5 L/(mol·s) uye concentration yekutanga ye reactant ye1 mol/L imasekondi maviri.
Muenzaniso Mubvunzo 3: Simba reKushanda kuburikidza neArrhenius Equation
Mubvunzo:
Kuita kwemuviri kune ma "rate constants" maviri akasiyana patembiricha mbiri dzakasiyana:
– Pa 300 K, chiyero chisingachinji (\( k_1 \)) i 0,2 L/(mol·s)
– Pa 350 K, chiyero chisingachinji (\( k_2 \)) i 0,4 L/(mol·s)
Tsvaga simba rekuita (\( E_a \)) rekuita uchishandisa equation yeArrhenius:
\[ k = A e^{-E_a/(RT)} \]
Kukurukurirana:
Equation yeArrhenius inogona kunyorwa muchimiro che logarithmic seinotevera:
\[ \ln k = \ln A – \frac{E_a}{RT} \]
Tinogona kushandisa data rema rate constant maviri patembiricha mbiri dzakasiyana kuti tione \( E_a \):
Ngatinyorei maequation maviri emamiriro maviri aya:
\[ \ln k_1 = \ln A – \frac{E_a}{R \cdot T_1} \]
\[ \ln k_2 = \ln A – \frac{E_a}{R \cdot T_2} \]
Nekubvisa ma equation maviri aya:
\[ \ln k_2 – \ln k_1 = \left(\ln A – \frac{E_a}{R \cdot T_2}\right) – \left(\ln A – \frac{E_a}{R \cdot T_1}\right) \]
\[ \ln \left(\frac{k_2}{k_1}\right) = -\frac{E_a}{R} \left(\frac{1}{T_2} – \frac{1}{T_1}\right) \]
Tsiva kukosha kwe \( k_1 \), \( k_2 \), \( T_1 \), uye \( T_2 \):
\[ \ln \left(\frac{0,4}{0,2}\right) = -\frac{E_a}{8,314} \left(\frac{1}{350} – \frac{1}{300}\right) \]
\[ \ln (2) = -\frac{E_a}{8,314} \left(\frac{1}{350} – \frac{1}{300}\right) \]
\[ 0,693 = -\frac{E_a}{8,314} \left(\frac{300 – 350}{350 \cdot 300}\right) \]
\[ 0,693 = -\frac{E_a}{8,314} \left(\frac{-50}{105000}\right) \]
\[ 0,693 = \frac{E_a}{8,314} \left(\frac{1}{2100}\right) \]
\[ 0,693 = \frac{E_a}{17462850/2100} \]
\[ 0,693 = \frac{E_a}{8314} \]
\[ E_a = 0,693 \kawa 8314 \]
\[ E_a = 5761,842 \ \chinyorwa{J/mol} \]
Saka, simba rekuita kuti chinhu chishande (\( E_a \)) rekuita kwechinhu ichi rinenge 5761,842 J/mol kana kuti rinenge 5,76 kJ/mol.
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Ruzivo rwemakemikari emuchina uye kunzwisisa hurukuro yezvinetso zvakaita seizvi zvakakosha muminda yakasiyana-siyana, kunyanya muindasitiri yemakemikari nekutsvagisa kwesainzi. Muenzaniso wedambudziko riri pamusoro apa unopa kunzwisisa nzira dzekuziva kurongeka kwekuita, hafu yehupenyu, uye simba rekuita kuti zvinhu zvishande, izvo zvakakosha pakukura kwetekinoroji uye kunzwisisa kwakadzama kwemaitiro ekuita kwemakemikari.
