2.10: Reaction Chemistry Chapter Review

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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	$\text{[math]}$ Linear form: \[<span style="font-size: 16px">ln(k_{r})=-\frac{E_{a}}{R}×\frac{1}{T}+ln(A)\] 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 $k_{e1},k_{e2}>>k_{r1},k_{r2}$: \[\frac{[P_{1}]}{[P_{2}]}=\frac{k_{e1}}{k_{e2}}\]

Terms to Know:

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