20 Reaction Chemistry Chapter Review
Important Equations
| Reaction rate | [latex]r = \frac{1}{\nu}\frac{d[J]}{dt}[/latex] |
| Extent of reaction | [latex]d n_{j} = \nu_{j} d\xi[/latex] |
| Relating extent of reaction with reaction rate | [latex]r = \frac{1}{V} \frac{d\xi}{dt} = \frac{1}{\nu_{j}} \frac{1}{V} \frac{dn_{j}}{dt}[/latex] |
| Rate law (general form) |
[latex]r=k_{r}[A]^a[B]^b[/latex] [latex]r=k_{r}p_{A}^a p_{B}^b[/latex] |
| Zeroth-order rate law | [latex][A]-[A]_{0}=-k_{r}*t[/latex]
[latex][A]=[A]_{0}-k_{r}*t[/latex] |
| First-order rate law |
[latex]ln[A]-ln[A]_{0}=-k_{r}*t[/latex] [latex][A]=[A]_{0}e^{-k_{r}*t}[/latex] |
| Second-order rate law |
[latex]\frac{1}{[A]}-\frac{1}{[A]_{0}}=k_{r}*t[/latex] [latex][A]=\frac{[A]_{0}}{1+k_{r}*t*[A]_{0}}[/latex] |
| Equilibrium constant |
[latex]K\;\; or\;\; K_{eq}=\prod_{i} a_{i,eq}^{vi}[/latex] [latex]K=\frac{k_{r}}{k'_{r}} \;\;,c^\theta\text{is used for unit consistency}[/latex] [latex]k'_{r}[product]_{eq}^{p}=k_{r}[reactant]_{eq}^{r}[/latex] |
| Arrhenius equation |
[latex]ln(k_{r})=ln(A)-\frac{E_{a}}{RT}[/latex] [latex]k_{r}=Ae^{-\frac{E_{a}}{RT}}[/latex] Linear form: [latex]ln(k_{r}) = -\frac{E_{a}}{R} * \frac{1}{T} + ln(A)[/latex] Simplification for temperature dependency calculations: [latex]ln(\frac{k_{r2}}{k_{r1}})=\frac{E_{a}}{R}(\frac{1}{T_{1}}-\frac{1}{T_{2}})[/latex] |
| Unimolecular rate law | [latex]A→P:\;\;-\frac{d[A]}{dt}=k_{r}*[A][/latex] |
| Biomolecular rate law |
[latex]A+B→P:\;\;-\frac{d[A]}{dt}=k_{r}*[A]*[B][/latex] [latex]A+A→P:\;\;-\frac{d[A]}{dt}=k_{r}*[A]^2[/latex] |
| Kinetic control | If [latex]k_{e1},k_{e2}\text{<<}k_{r1},k_{r2}[/latex]:
[latex]\frac{[P_{1}]}{[P_{2}]}=\frac{k_{r1}}{k_{r2}}[/latex] |
| Thermodynamic control | If [latex]k_{e1},k_{e2}>>k_{r1},k_{r2}[/latex]:
[latex]\frac{[P_{1}]}{[P_{2}]}=\frac{k_{e1}}{k_{e2}}[/latex] |
Feedback/Errata