# All Formulas of Chemical Kinetics Class 12 | JEE | NEET

Here is the list of All Formulas of Chemical Kinetics Class 12. These are very important formulas and to be covered at time of exam. In this list you will find formulas of Chemical Kinetics and Radioactivity.

## List of All Formulas of Chemical Kinetics Class 12

• RATE/VELOCITY OF CHEMICAL REACTION:
Rate $=\frac{\Delta c }{\Delta t }$ $=\frac{ mol / lit .}{ sec }$ $= mol lit ^{-1} time ^{-1}$ $= mol dm ^{-3} time ^{-1}$
• Types of Rates of chemical reaction:
For a reaction R→P
• RATE LAW (DEPENDENCE OF RATE ON CONCENTRATION OF REACTANTS) :
Rate $=K$ (conc.) $^{\text {order }}-$ differential rate equation or rate expression
Where $K =$ Rate constant $=$ specific reaction rate $=$ rate of reaction when concentration is unity unit of $K =( conc )^{1-\text { order }} time ^{-1}$
• Order of reaction:
$m _{1} A + m _{2} B \longrightarrow$ products.
$R \propto[ A ]^{ P }[ B ]^{ q }$
Where $p$ may or may not be equal to $m_{1} \&$ similarly q may or may not be equal to $m_{2}$.
$p$ is order of reaction with respect to reactant $A$ and $q$ is order of reaction with respect to reactant $B$ and $(p+q)$ is overall order of the reaction.
• INTEGRATED RATE LAWS :
$C _{0}$ or ‘a’ is initial concentration and $C _{ t }$ or $a – x$ is concentration at time ‘t’

• Zero order reactions :
Rate $= k [ conc .]^{\circ}= constant$
Rate $= k =\frac{ C _{0}- C _{ t }}{ t ^{\prime}} \quad$ or $\quad C _{ t }= C _{0}- kt$
Unit of $K = mol lit ^{-1} sec ^{-1},$ Time for completion $=\frac{ C _{0}}{ k }$
at $t_{1 / 2}, C_{t}=\frac{C_{0}}{2},$ so $k t_{1 / 2}=\frac{C_{0}}{2}$
$\Rightarrow \quad t _{1 / 2}=\frac{C_{0}}{2 k}$
$\therefore t _{1 / 2} \propto C _{0}$
• First Order Reactions :
Let a $1^{\text {st }}$ order reaction is, $A \longrightarrow$ Products
$t=\frac{2.303}{ k } \log \frac{ a }{ a – x }$ or $k =\frac{2.303}{ t } \log \frac{ C _{0}}{ C _{ t }}$
$\Rightarrow \quad t _{1 / 2}=\frac{\ell n 2}{ k }=\frac{0.693}{ k }=$ Independent of initial concentration.
$t_{\text {Avg. }}=\frac{1}{k}=1.44 t _{1 / 2}$

Graphical Representation:
$t =-\frac{2.303}{ k } \log C _{ t }+\frac{2.303}{ R } \log C _{0}$

• Second order reaction :
 Type 1 Type 2
• Psuedo first order reaction :
$\therefore$ For $A + B \longrightarrow$ Products [Rate $\left.= K [ A ]^{1}[ B ]^{1}\right]$
$k=\frac{2.303}{t(a-b)} \log \frac{b(a-x)}{a(b-x)}$
Now if ‘B’ is taken in large excess $b>>$ a.
$\Rightarrow \quad k =\frac{2.303}{ bt } \log \frac{ a }{ a – x }$
‘b’ is very large can be taken as constant
$\Rightarrow kb =\frac{2.303}{ t } \log \frac{ a }{ a – x }$
$\Rightarrow \quad k^{\prime}=\frac{2.303}{t} \log \frac{a}{a-x}$
$k ^{\prime}$ is psuedo first order rate constant
• METHODS TO DETERMINE ORDER OF A REACTION
• Initial rate method :
$r=k[A]^{a}[B]^{b}[C]^{c}$
If $[ B ]= constant$ & $[ C ]= constant$ then for two different initial concentrations of A we have
$r_{0_{1}}=k\left[A_{0}\right]_{1}^{a}, \quad r_{0_{2}}=k\left[A_{0}\right]_{2}^{a}$
$\Rightarrow \quad \frac{r_{0_{1}}}{r_{0_{2}}}=\left(\frac{\left[A_{0}\right]_{1}}{\left[A_{0}\right]_{2}}\right)^{a}$
• Using integrated rate law : It is method of trial and error.
• Method of half lives:
for $n^{\text {th }}$ order reaction: $t _{1 / 2} \propto \frac{1}{\left[ R _{0}\right]^{ n -1}}$
• Ostwald Isolation Method:
rate $= k [ A ]^{ a }[ B ]^{ b }[ C ]^{ c }= k _{0}[ A ]^{ a }$
• METHODS TO MONITOR THE PROGRESS OF THE REACTION:
• Progress of gaseous reaction can be monitored by measuring total pressure at a fixed volume & temperature or by measuring total volume of mixture under constant pressure and temperature.
$\therefore k =\frac{2.303}{ t } \log$ $\frac{P_{0}(n-1)}{n P_{0}-P_{t}}$
$\{$ Formula is not applicable when $n =1,$ the value of $n$ can be fractional also. $.\}$
• By titration method:
• $\therefore a \propto V_{0}$
$a-x \propto V_{t}$
$\Rightarrow \quad k=\frac{2.303}{t} \log \frac{V_{0}}{V_{t}}$
• Study of acid hydrolysis of an easter
$k =\frac{2.303}{ t } \log \frac{ V _{\infty}- V _{0}}{ V _{\infty}- V _{ t }}$
• By measuring optical rotation produced by the reaction mixture:
$k =\frac{2.303}{ t } \log \left(\frac{\theta_{0}-\theta_{\infty}}{\theta_{ t }-\theta_{\infty}}\right)$
• EFFECT OF TEMPERATURE ON RATE OF REACTION
T.C. $=\frac{ K _{ t }+10}{ K _{ t }} \approx 2$ to 3 ( for most of the reactions)

• Arhenius theroy of reaction rate

Here,
$SH _{ R }=$ Summation of enthalpies of reactants
$SH _{ p }=$ Summation of enthalpies of reactants
$DH =$ Enthalpy change during the reaction
$Ea _{1}=$ Energy of activation of the forward reaction
$Ea _{2}=$ Energy of activation of the backward reaction
$E _{ p }> E _{ r } \rightarrow$ endothermic
$E _{ p }< E _{ r } \quad \rightarrow$ exothermic
$\Delta H =\left( E _{ p }- E _{ r }\right)=$ enthalpy change
$\Delta H = E _{ af }- E _{ ab }$
$E_{\text {threshold }}=E_{\text {af }}+E_{r}=E_{b}+E_{p}$
• Arhenius equation
$k = Ae ^{- E _{ a } RT }$
$r=k[\text { conc. }]^{\text {order }}$
$\frac{ d \ln k }{ d T }=\frac{ E _{ a }}{ RT ^{2}}$
$\log k =\left(-\frac{ Ea }{2.303 R }\right) \frac{1}{ T }+\log A$
If $k _{1}$ and $k _{2}$ be the rate constant of a reaction at two different temperature $T _{1}$ and $T _{2}$ respectively, then we have
$\log \frac{ k _{2}}{ k _{1}}=\frac{ E _{ a }}{2.303 R } \cdot\left(\frac{1}{ T _{1}}-\frac{1}{ T _{2}}\right)$

$\operatorname{Ink}=\ln A-\frac{E_{a}}{R T}$
$T \rightarrow \infty, K \rightarrow A$
• REVERSIBLE REACTIONS
$k _{ f }= A _{ f } e ^{- E _{ af } / RT }$
$k _{ b }= A _{ b } e ^{- E _{ ab } / RT }$
$K _{ eq }=\frac{ K _{ f }}{ K _{ b }}=\left(\frac{ A _{ f }}{ A _{ b }}\right) e ^{-\left( E _{ af }- E _{ ab }\right) / RT }$
In $K _{ eq }=-\frac{\Delta H }{ RT }+\ln \left(\frac{ A _{ f }}{ A _{ b }}\right)$

$\frac{[ B ]}{[ C ]}=\frac{ K _{1}}{ K _{2}} \quad \Rightarrow \quad E _{ a }=\frac{ E _{ a _{1}} k _{1}+ E _{ a _{2}} k _{2}}{ k _{1}+ k _{2}}$
• REVERSIBLE $1^{\text {ST }}$ ORDER REACATION ( both forward and backward)
$x=\frac{K_{f} a}{K_{f}+K_{b}}\left(1-e^{-\left(k_{f}+k_{b}\right) t}\right)$
$K_{ f }+ K _{ b }=\frac{1}{ t } \ln \left(\frac{ x _{ eq .}}{ x _{ eq }- x }\right)$
• SEQUENTIAL1 $^{\text {ST }}$ ORDER REACTION
$[ A ]=[ A ] e ^{- k _{1} t }$
$x = a \left(1- e ^{- k _{1} t }\right)$
$y =\frac{ K _{1} a }{ K _{2}- K _{1}}\left\{ e ^{- k _{1} t }- e ^{- k _{2} t }\right\}$
$t_{B(\max .)}=\frac{1}{\left(K_{1}-K_{2}\right)} \ln \frac{K_{1}}{K_{2}}$Case 1: $K _{1}>> k _{2}$

Case 2: $K _{2}>> k _{1}$

This was the list of All Formulas of Chemical Kinetics Class 12.

## Class 12 Chemistry Formulas

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