# 20 Reaction Chemistry Chapter Review

## Important Equations

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