1. Rate/velocity of Chemical Reaction:

$Rate = \frac{ΔC}{Δt} = \frac{\frac{mole}{lit}}{time} = mole lit^{- 1} {time}^{- 1} = mole {dm}^{- 3} {time}^{- 1}$ .

2. Types of Rates of Chemical Reaction:

For a reaction $R ⟶ P$

Average rate $= \frac{T o t a l c h a n g e i n c o n c e n t r a t i o n}{T o t a l t i m e t a k e n}$

$R_{instantaneous} = \lim_{t \to 0} [\frac{Δc}{Δt}] = \frac{dc}{dt} = - \frac{d [R]}{dt} = \frac{d [P]}{dt}$

3. Rate Law (dependence of rate on concentration of reactants):

Rate $= k {(c o n c .)}^{o r d e r} \to$ differential rate equation for rate expression.

Where $k =$ Rate constant $=$ specific reaction rate $=$ rate of reaction when concentration is unity.

$u n i t o f k = (c o n c)^{1 - o r d e r} {t i m e}^{- 1}$

4. Order of Reaction:

$m_{1} A + m_{2} B ⟶ p r o d u c t s .$

$R \propto {[A]}^{p} {[B]}^{q}$

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.

5. Molecularity of a Reaction:

It is defined as the number of molecules colliding with each other in an elementary reaction. For example: $A \to B$ reaction has molecularity $= 1$

For an elementary reaction, Molecularity $=$ Order.

For a complex reaction, Molecularity has no meaning. However, Molecularity of Rate determining step (RDS) can be approximately used to determine the overall rate of reaction.

6. Integrated Rate Laws:

$C_{0}$ or $' a^{'}$ is initial concentration and $C_{t}$ or $a - x$ is concentration at time $' t^{'}$

(i) For Zero Order Reaction:

$R a t e = k [c o n c .]^{0} = c o n s t a n t$

$R a t e = k = \frac{C_{0} - C_{t}}{t^{}} o r C_{t} = C_{0} - k t$

$U n i t o f k = m o l {l i t}^{- 1} {s e c}^{- 1},$ Time for completion of reaction $= \frac{C_{0}}{k}$

$a t Half life time (t_{\frac{1}{2}}), C_{t} = \frac{C_{0}}{2}, s o k t_{\frac{1}{2}} = \frac{C_{0}}{2}$

$\Rightarrow t_{\frac{1}{2}} = \frac{C_{0}}{2 k} ∴ t_{\frac{1}{2}} \propto C_{0}$

(ii) For First Order Reaction:

For a $1^{s t}$ order reaction is $A ⟶$ Products.

$t = \frac{2.303}{k} \log \frac{a}{a - x} o r k = \frac{2.303}{t} \log \frac{C_{0}}{C_{t}}$

$⟹ t_{\frac{1}{2}} = \frac{l n 2}{k} = \frac{0.693}{k} =$ Independent of initial concentration.

$t_{A v g .} = \frac{1}{k} = 1.44 t_{\frac{1}{2}}$

Graphical representation:

$t = - \frac{2.303}{k} \log C_{t} + \frac{2.303}{k} \log C_{0}$

(iii) Second Order Reaction:

2^nd order Reactions are of two types

$A + A ⟶ p r o d u c t s$

$a a 0$

$(a - x) (a - x) x$

$∴ \frac{d x}{d t} = k (a - x)^{2}$

$\Rightarrow \frac{1}{(a - x)} - \frac{1}{a} = k t$

$A + B ⟶ p r o d u c t s .$

$a b 0$

$(a - x) (b - x) x$

$\frac{d x}{d t} = k (a - x) (b - x)$

$k = \frac{2.303}{(a - b)} \log \frac{b (a - x)}{a (b - x)}$

(iv) Pseudo first order reaction:

$∴$ For $A + B ⟶ Products [Rate = K {[A]}^{1} {[B]}^{1}]$

$k = \frac{2.303}{t (a - b)} \log \frac{b (a - x)}{a (b - x)}$

Now if $' B^{'}$ is taken in large excess $b > > a$

$\Rightarrow k = \frac{2.303}{b t} \log \frac{a}{a - x}$

$' b^{'}$ is very large can be taken as constant.

$\Rightarrow k b = \frac{2.303}{t} l o g \frac{a}{a - x} \Rightarrow k^{'} = \frac{2.303}{t} \log \frac{a}{a - x}$

$k^{'} = k b$ is pseudo first order rate constant.

7. Methods to determine Order of a Reaction:

(i) Initial rate method:

$r = k {[A]}^{a} {[B]}^{b} {[C]}^{c}$

if $[b] =$ constant and $[c] =$ constant

then for two different initial concentrations of $A$ we have

$r_{0_{1}} = k {[A_{0}]}_{1}^{a}, r_{0_{2}} = k {[A_{0}]}_{2}^{a} \Rightarrow \frac{r_{0_{1}}}{r_{0_{2}}} = {(\frac{{[A_{0}]}_{1}}{{[A_{0}]}_{2}})}^{a}$

(ii) Using integrated rate law: It is a method of trial and error.

(iii) Method of half-lives:

For $n^{t h}$ order reaction $t_{\frac{1}{2}} \propto \frac{1}{{[R_{0}]}^{n - 1}}$

(iv) Ostwald Isolation Method:

rate $= k {[A]}^{a} {[B]}^{b} {[C]}^{c} = k_{0} {[A]}^{a}$

If $B$ and $C$ is taken in excess.

8. Methods to monitor the Progress of the First Order Reaction:

(i) 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.

$A_{n} \overset{Δ}{\to} n A$

$∴ k = \frac{2.303}{t} l o g \frac{P_{0} (n - 1)}{n P_{0} - P_{t}}$ {Formula is not applicable when $n = 1$ , the value of n can be fractional also}.

Here, $P_{o}$ and $P_{t}$ represent the total pressure exerted by the system of gas at the starting of the reaction and at the reference time respectively.

(ii) By titration method:

$H_{2} O_{2} (l) \overset{}{\to} H_{2} O (l) + O_{2} (g)$

$\begin{matrix} a & 0 & 0 \\ a - x & x & \frac{x}{2} \end{matrix}$

$∴ a \propto V_{0} a - x \propto V_{t}$

$\Rightarrow k = \frac{2.303}{t} \log \frac{V_{0}}{V_{t}}$

(iii) Study of acid hydrolysis of an ester:

$R C O O R^{'} (l) + H_{2} O (l) \overset{H^{+} (a q .)}{\to} R C O O H + R^{'} O H$

$V_{\infty} =$ Volume of $NaOH$ used at $t = \infty$ .

$V_{t} =$ Volume of $NaOH$ used at reference time.

$V_{0} =$ Volume of $NaOH$ used at $t = 0$

$k = \frac{2.303}{t} \log \frac{V_{\infty} - V_{0}}{V_{\infty} - V_{t}}$

(iv) By measuring optical rotation produced by the reaction mixture:

$R C O O R^{'} (l) + H_{2} O (l) \overset{H^{+} (a q .)}{\to} R C O O H + R^{'} O H$

$θ_{\infty} =$ Optical rotation produced by the mixture at time $t = \infty .$

$θ_{0} =$ Optical rotation produced by the mixture at $t = 0 .$

$θ_{t} =$ Optical rotation produced by the mixture at reference time.

$k = \frac{2.303}{t} \log (\frac{θ_{0} - θ_{\infty}}{θ_{t} - θ_{\infty}})$

9. Effect of Temperature on Rate of Reaction:

$T . C . = \frac{K_{t} + 10}{K_{t}} = 2 t o 3$ (for most of the reactions)

Arrhenius theory of reaction rate:

${Σ H}_{R} =$ Summation of enthalpies of reactants.

${Σ H}_{P} =$ Summation of enthalpies of products.

$Δ H =$ Enthalpy change during the reaction.

$E_{a_{1}} =$ Energy of activation of the forward reaction.

$E_{a_{2}} =$ Energy of activation of the backward reaction.

${Σ H}_{P} > {Σ H}_{R} \to$ endothermic.

${Σ H}_{P} < {Σ H}_{R} \to$ exothermic.

$Δ H = ({Σ H}_{P} - {Σ H}_{R}) =$ enthalpy change:

$Δ H = {Σ H}_{P} - {Σ H}_{R}$

$E_{t h r e s h o l d} = E_{a_{1}} + {Σ H}_{R} = E_{a_{2}} + {Σ H}_{P}$

Arrhenius equation:

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

$r = k {[conc .]}^{n}$

$\frac{d l n k}{d T} = \frac{E_{a}}{{R T}^{2}}$

$\log k = (- \frac{E a}{2.303 R}) \frac{1}{T} + \log A$

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:

$\log \frac{k_{2}}{k_{1}} = \frac{E_{a}}{2.303 R} (\frac{1}{T_{1}} - \frac{1}{T_{2}})$

$In k = \ln A - \frac{E_{a}}{R T}$

$T \to \infty, K \to A$

10. Reversible Reactions:

$k_{f} = A_{f} e^{- \frac{E_{a}}{R T}}$

$k_{b} = A_{b} e^{- \frac{E_{b}}{R T}}$

$K_{e q} = \frac{k_{f}}{k_{b}} = (\frac{A_{f}}{A_{b}}) e^{- \frac{(E_{a} - E_{b})}{R T}}$

In $K_{e q} = - \frac{Δ H}{R T} + l n (\frac{A_{f}}{A_{b}})$

Parallel $1^{s t}$ Order Reaction:

$\frac{[B]}{[C]} = \frac{k_{1}}{k_{2}} \Rightarrow E_{a} = \frac{E_{a_{1}} k_{1} + E_{a_{2}} k_{2}}{k_{1} + k_{2}}$ .

$x = \frac{k_{f} a}{k_{f} + k_{b}} (1 - e^{- (k_{f} + k_{b}) t})$

REVERSIBLE 1^ST ORDER REACTION: $A \overset{k_{f}}{\underset{k_{b}}{⇌}} B$

$k_{f} + k_{b} = \frac{1}{t} \ln (\frac{x_{e q .}}{x_{e q} - x})$

SEQUENTIAL $1^{S T}$ ORDER REACTION: $A \overset{k_{1}}{\to} B \overset{k_{2}}{\to} C$

${[A]}_{t} = {[A]}_{o} e^{- k_{1} t}$

${[B]}_{t} = \frac{k_{1} a}{k_{2} - k_{1}} \{e^{- k_{1} t} - e^{- k_{2} t}\} t_{B (m a x)} = \frac{1}{(k_{1} - k_{2})} \ln \frac{k_{1}}{k_{2}}$

$t_{B (m ax)} =$ Time taken by $B$ to reach the maximum concentration

CASE-I:

$k_{1} ≫ k_{2}$

CASE-II:

$k_{2} ≫ k_{1}$

NO2 required for a reaction is produced by the decomposition of N2O5 in CCl4 as per the equation, 2N2O5g→4NO2g+O2g. The initial concentration of N2O5 is 3.00 mol L-1 and it is 2.75 mol L-1 after 30 minutes. The rate of formation of NO2 is:

Important Questions on Chemical Kinetics

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