20 Reaction Chemistry Chapter Review

$r=k_{r}[A]^a[B]^b$

$r=k_{r}p_{A}^a p_{B}^b$

$[A]=[A]_{0}-k_{r}*t$

$ln[A]-ln[A]_{0}=-k_{r}*t$

$[A]=[A]_{0}e^{-k_{r}*t}$

$\frac{1}{[A]}-\frac{1}{[A]_{0}}=k_{r}*t$

$[A]=\frac{[A]_{0}}{1+k_{r}*t*[A]_{0}}$

$K\;\; or\;\; K_{eq}=\prod_{i} a_{i,eq}^{vi}$

$K=\frac{k_{r}}{k'_{r}} \;\;,c^\theta\text{is used for unit consistency}$

$k'_{r}[product]_{eq}^{p}=k_{r}[reactant]_{eq}^{r}$

$ln(k_{r})=ln(A)-\frac{E_{a}}{RT}$

$k_{r}=Ae^{-\frac{E_{a}}{RT}}$

Linear form:

$ln(k_{r}) = -\frac{E_{a}}{R} * \frac{1}{T} + ln(A)$

Simplification for temperature dependency calculations:

$ln(\frac{k_{r2}}{k_{r1}})=\frac{E_{a}}{R}(\frac{1}{T_{1}}-\frac{1}{T_{2}})$

$A+B→P:\;\;-\frac{d[A]}{dt}=k_{r}*[A]*[B]$

$A+A→P:\;\;-\frac{d[A]}{dt}=k_{r}*[A]^2$

$\frac{[P_{1}]}{[P_{2}]}=\frac{k_{r1}}{k_{r2}}$

$\frac{[P_{1}]}{[P_{2}]}=\frac{k_{e1}}{k_{e2}}$