Reaction Chemistry Chapter Review

20 Reaction Chemistry Chapter Review

Reaction rate

r = \frac{1}{ν} \frac{d [J]}{d t}

Extent of reaction

d n_{j} = ν_{j} d ξ

Relating extent of reaction with reaction rate

r = \frac{1}{V} \frac{d ξ}{d t} = \frac{1}{ν_{j}} \frac{1}{V} \frac{d n_{j}}{d t}

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

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

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

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

$K o r K_{e q} = \prod_{i} a_{i, e q}^{v i}$

$K = \frac{k_{r}}{k_{r}^{'}}, c^{θ} is used for unit consistency$

$k_{r}^{'} [p r o d u c t]_{e q}^{p} = k_{r} [r e a c t a n t]_{e q}^{r}$

Arrhenius equation

$l n (k_{r}) = l n (A) - \frac{E_{a}}{R T}$

$k_{r} = A e^{- \frac{E_{a}}{R T}}$

Linear form:

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

Simplification for temperature dependency calculations:

$l n (\frac{k_{r 2}}{k_{r 1}}) = \frac{E_{a}}{R} (\frac{1}{T_{1}} - \frac{1}{T_{2}})$

Unimolecular rate law

A \to P : - \frac{d [A]}{d t} = k_{r} * [A]

Biomolecular rate law

$A + B \to P : - \frac{d [A]}{d t} = k_{r} * [A] * [B]$

$A + A \to P : - \frac{d [A]}{d t} = k_{r} * [A]^{2}$

Kinetic control

If

k_{e 1}, k_{e 2} << k_{r 1}, k_{r 2}

:

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

Thermodynamic control

If

k_{e 1}, k_{e 2} >> k_{r 1}, k_{r 2}

:

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

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