Chitsanzo cha Mafunso Okambirana za Chemical Kinetics
Chemical kinetics ndi nthambi ya chemistry yomwe imaphunzira kuchuluka kwa zochita za mankhwala ndi zinthu zomwe zimawakhudza. Kumvetsetsa bwino za kinetics za mankhwala ndikofunikira kuti asayansi ndi mainjiniya a mankhwala apange njira zogwirira ntchito bwino zamafakitale ndikumvetsetsa machitidwe osiyanasiyana a biochemical omwe amapezeka m'zamoyo. Nkhaniyi ikambirana zitsanzo zingapo za mavuto okhudzana ndi kinetics za mankhwala ndi mayankho awo kuti timvetsetse bwino nkhaniyi.
Chitsanzo Funso 1: Kutsimikiza kwa Dongosolo la Kuyankha
Funso:
Chiyankho chili ndi equation yotsatirayi ya kuchuluka kwa chiŵerengero:
\[ R = k[A]^m[B]^n \]
Kumene:
– \( R \) ndi kuchuluka kwa zomwe zimachitika,
– \( k \) ndi nthawi zonse ya mlingo,
– \([A] \) ndi \([B]\) ndi kuchuluka kwa ma reactants A ndi B,
– \( m \) ndi \( n \) ndi ma reaction orders okhudzana ndi A ndi B.
Amadziwika kuti kuyeseraku kunachitika ndi mitundu yotsatirayi ya ndende:
| Kuyesera | \([A]\) (mol/L) | \([B]\) (mol/L) | Kuchuluka kwa zochita (mol/(Ls)) |
|————–|——————-|——————–|———————|
| 1 | 0,10 | 0,20 | 0,030 |
| 2 | 0,10 | 0,40 | 0,060 |
| 3 | 0,20 | 0,20 | 0,120 |
Dziwani dongosolo la reaction poyerekeza ndi A ndi B ndi mtengo wa rate constant \( k \).
Kukambirana:
Kuti tidziwe dongosolo la momwe zinthu zimachitikira poyerekeza ndi A ndi B, tiyenera kuyerekeza kuchuluka kwa momwe zinthu zimachitikira ndi kusiyana kosiyanasiyana kwa kuchuluka kwa zinthu.
Choyamba, timadziwa dongosolo la momwe zinthu zimachitikira poyerekeza ndi B poyerekeza zoyeserera 1 ndi 2:
\[ \frac{\text{R2}}{\text{R1}} = \frac{k[A]^m [B_2]^n}{k[A]^m [B_1]^n} \]
\[ \frac{0,060}{0,030} = \frac{[0,10]^m [0,40]^n}{[0,10]^m [0,20]^n} \]
\[ 2 = \kumanzere(\frac{0,40}{0,20}\kumanja)^n \]
\[ 2 = 2^n \]
\[ n = 1 \]
Dongosolo la mayankho okhudzana ndi B ndi 1.
Kenako, timapeza dongosolo la momwe zinthu zimachitikira poyerekeza ndi A poyerekezera zoyeserera 1 ndi 3:
\[ \frac{\text{R3}}{\text{R1}} = \frac{k[A_3]^m [B]^n}{k[A_1]^m [B]^n} \]
\[ \frac{0,120}{0,030} = \frac{[0,20]^m [0,20]^n}{[0,10]^m [0,20]^n} \]
\[ 4 = \kumanzere(\frac{0,20}{0,10}\kumanja)^m \]
\[4 = 2^m \]
\[m = 2 \]
Dongosolo la mayankho poyerekeza ndi A ndi 2.
Motero, equation ya reaction rate ndi:
\[ R = k[A]^2[B] \]
Tsopano tikupeza mtengo wa nthawi zonse wa mlingo \( k \). Gwiritsani ntchito deta yochokera ku kuyesa 1:
\[ 0,030 = k[0,10]^2[0,20] \]
\[ 0,030 = k \nthawi 0,01 \nthawi 0,20 \]
\[ 0,030 = k \nthawi 0,002 \]
\[ k = \frac{0,030}{0,002} \]
\[ k = 15 \ \malemba{L}^2/(\malemba{mol}^2 \cdot \malemba{s}) \]
Kotero, mlingo wokhazikika \( k \) ndi 15 L²/(mol²·s).
Chitsanzo Funso 2: Hafu ya Moyo wa Kuyankha kwa Gulu Lachiwiri
Funso:
Popeza yankho lachiwiri ndi equation ya rate:
\[ R = k[A]^2 \]
Mlingo wokhazikika (\( k \)) wa reaction ndi 0,5 L/(mol·s). Ngati kuchuluka koyambirira kwa reactant \( [A]_0 \) ndi 1 mol/L, pezani theka la moyo wa reaction.
Kukambirana:
Pazochita zachiwiri, theka la moyo (\( t_{1/2} \)) likhoza kuwerengedwa pogwiritsa ntchito equation:
\[t_{1/2} = \frac{1}{k[A]_0} \]
M'malo mwa mfundo zodziwika bwino:
\[t_{1/2} = \frac{1}{0,5 \times 1} \]
\[t_{1/2} = \frac{1}{0,5} \]
\[t_{1/2} = 2 \ \malemba{s} \]
Motero, theka la moyo wa reaction yachiwiri yokhala ndi rate constant ya 0,5 L/(mol·s) ndi concentration yoyamba ya reactant ya 1 mol/L ndi masekondi awiri.
Chitsanzo Funso 3: Mphamvu Yoyambitsa Kudzera mu Arrhenius Equation
Funso:
Kachitidwe kali ndi ma rate constants awiri osiyana pa kutentha kosiyana:
– Pa 300 K, nthawi yokhazikika ya mlingo (\( k_1 \)) ndi 0,2 L/(mol·s)
– Pa 350 K, nthawi yokhazikika ya mlingo (\( k_2 \)) ndi 0,4 L/(mol·s)
Dziwani mphamvu yoyambitsa (\( E_a \)) ya reaction pogwiritsa ntchito Arrhenius equation:
\[ k = A e^{-E_a/(RT)} \]
Kukambirana:
Equation ya Arrhenius ikhoza kulembedwa mu mawonekedwe a logarithmic motere:
\[ \ln k = \ln A – \frac{E_a}{RT} \]
Tingagwiritse ntchito deta yokhazikika ya liwiro ziwiri pa kutentha kosiyana kuti tidziwe \( E_a \):
Tiyeni tilembe ma equation awiri a zinthu ziwirizi:
\[ \ln k_1 = \ln A – \frac{E_a}{R \cdot T_1} \]
\[ \ln k_2 = \ln A – \frac{E_a}{R \cdot T_2} \]
Pochotsa ma equation awiriwa:
\[ \ln k_2 – \ln k_1 = \left(\ln A – \frac{E_a}{R \cdot T_2}\right) – \left(\ln A – \frac{E_a}{R \cdot T_1}\right) \]
\[ \ln \left(\frac{k_2}{k_1}\right) = -\frac{E_a}{R} \left(\frac{1}{T_2} – \frac{1}{T_1}\right) \]
Sinthani ma values a \( k_1 \), \( k_2 \), \( T_1 \), ndi \( T_2 \):
\[ \ln \left(\frac{0,4}{0,2}\right) = -\frac{E_a}{8,314} \left(\frac{1}{350} – \frac{1}{300}\right) \]
\[ \ln (2) = -\frac{E_a}{8,314} \left(\frac{1}{350} – \frac{1}{300}\right) \]
\[ 0,693 = -\frac{E_a}{8,314} \left(\frac{300 – 350}{350 \cdot 300}\right) \]
\[ 0,693 = -\frac{E_a}{8,314} \left(\frac{-50}{105000}\right) \]
\[ 0,693 = \frac{E_a}{8,314} \left(\frac{1}{2100}\right) \]
\[ 0,693 = \frac{E_a}{17462850/2100} \]
\[ 0,693 = \frac{E_a}{8314} \]
\[ E_a = 0,693 \nthawi 8314 \]
\[ E_a = 5761,842 \ \malemba{J/mol} \]
Motero, mphamvu yoyambitsa (\( E_a \)) ya reaction ndi pafupifupi 5761,842 J/mol kapena pafupifupi 5,76 kJ/mol.
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Kudziwa za kayendedwe ka mankhwala ndi kumvetsetsa bwino za mavuto ngati awa ndikofunikira kwambiri m'magawo osiyanasiyana, makamaka makampani opanga mankhwala ndi kafukufuku wa sayansi. Chitsanzo cha vutoli chimapereka kumvetsetsa njira zodziwira dongosolo la reaction, theka la moyo, ndi mphamvu yoyambitsa, zomwe ndizofunikira kwambiri pakukula kwaukadaulo komanso kumvetsetsa bwino njira zochitira reaction za mankhwala.
