(i) Each step of a complex reaction is called an elementary step.
(ii) Rate of reaction is the change in concentration of any one of the reactants or products per unit time.

\([A]=[A]_0 \mathrm{e}^{-k t}\) where [A]0 is initial concentration.[A] is concentration time t and k is rate constant.

\(\text {Rate }=\left(\frac{d x}{d t}\right)=k[A]^0[B]^0=\mathrm{k} \text { (rate const.) }\)

(i) Order = 2, Dimensions of k \(=\frac { Rate }{ { \left[ NO \right] }^{ 2 } } =\frac { mol \ { L }^{ -1 } \ { s }^{ -1 } }{ { \left( mol \ { L }^{ -1 } \right) }^{ 2 } } =L \ { mol }^{ -1 }{ s }^{ -1 }\)
(ii) Order = 2, Dimensions of k = same as in (i)
(iii) Order = \(\frac { 3 }{ 2 } \), Dimensions of k\(=\frac { Rate }{ { \left[ { CH }_{ 3 }CHO \right] }^{ { 3 }/{ 2 } } } =\frac { mol \ { L }^{ -1 } \ { s }^{ -1 } }{ { \left( mol \ { L }^{ -1 } \right) }^{ { 3 }/{ 2 } } } ={ L }^{ { 1 }/{ 2 } }{ mol }^{ -{ 1 }/{ 2 } }{ s }^{ -1 }\)
(iv) Order = 1, Dimensions of k\(=\frac { Rate }{ { \left[ { C }_{ 2 }{ H }_{ 5 }Cl \right] } } =\frac { mol \ { L }^{ -1 } \ { s }^{ -1 } }{ mol \ { L }^{ -1 } } ={ s }^{ -1 }\)

Activated complex is intermediate compound between reactants and products as shown above. It is highly unstable as it has highest energy. It readily charges into product. Those molecules which can form activated complex can lead to formation of products, e.g

\({ t }_{ { 1 }/{ 2 } }=\frac { 0.693 }{ k } \)
\(=\frac { 0.693 }{ 5.5\times { 10 }^{ -14 }{ s }^{ -1 } }\)
\(=1.26\times { 10 }^{ 13 }s\)

(a) (i) Order of a reaction. The sum of the exponents (powers) of the concentration of reactants in the rate law is termed as order of the reaction. It can be in fraction. It can be zero also.
(ii) Molecularity: Total number of atoms, ions or molecules of the reactants involved in the reaction is termed as its molecularity. It is always in whole number. It is never more than three. It cannot be zero.
(b)
\(\log { \frac { { k }_{ 2 } }{ { k }_{ 1 } } } =\frac { { E }_{ a } }{ 2.303R } \left( \frac { 1 }{ { T }_{ 1 } } -\frac { 1 }{ { T }_{ 2 } } \right)\)
\(\log { 4 } =\frac { { E }_{ a } }{ 2.303\times 8.314 } \left( \frac { 1 }{ 300 } -\frac { 1 }{ 320 } \right) \)
\({ E }_{ a }=\frac { 19.147\times 0.6021\times 300\times 320 }{ 20 }\)
\(=55.336\quad kJ\ { mol }^{ -1 }\)

(a) (i) It is sum of powers to which cone. terms are raised in rate law or rate equation.
(ii) Each step of complex reaction (which takes place in more than one step) is called elementary, step in a reaction.
\((b) \ k=0.00510 \ { min }^{ -1 }\)
\(t=\frac { 2.303 }{ k } \log { \frac { { \left[ R \right] }_{ 0 } }{ \left[ R \right] } }\)
\(3\times 60\times 60=\frac { 2.303 }{ 0.00510 } \log { \frac { 0.1 }{ \left[ R \right] } }\)
\(\log { \frac { 0.1 }{ \left[ R \right] } } =\frac { 10800\times 0.00510 }{ 2.303 } \)
\(=23.94\)
\(\frac { 0.1 }{ \left[ R \right] } =Antilog \ 23.94\)
\(\frac { 0.1 }{ \left[ R \right] } =8.71\times { 10 }^{ 23 }\)
\(\left[ R \right] =\frac { 0.1 }{ 8.71\times { 10 }^{ 23 } }\)
\(\left[ R \right] =0.1148\times { 10 }^{ -24 }\)
\(\left[ R \right] =1.148\times { 10 }^{ -25 }M\)

(b) : log [A] vs times is linear for 1st order reactions, 1/[A] vs time is linear for 2nd  order reactions ; 1/[A]² vs time is linear for 3rd order reactions.

(c) : 75% of reaction is completed in two half-lived  i.e., 2 \(\times\) t ₁₂ = 32 min or t _1/2 = 16 min

(c) : On the basis of given units of k, the reactions of 3 rd order.

(a) : \(k = \frac {0.693}{t/2}= \frac {0.693}{34.65}s^{-1} = 2 \times 10^{-2}\)s^-1

(a) Rate = \(\frac {dx}{dt} = k[A_o]^{o} = k \) or \(k = \frac {dx}{dt} = \frac {conc}{Time} =\frac {mol L^{-1}}{s}\)mol L^-1 s^-1.

(a) : The rate of constant of a reaction depends only on temperature and does not depend upon concentrations of the reactants.

(c) : (i) r = k \(a ^ { \alpha}\) (ii) 2 r = k (4 a) ^\(\alpha\)  dividing (ii) by (i), 4 ^\(\alpha\)= 2 or 2 \(\alpha\)= 1/2

(d) : Rate = k ab. When volume is reduced to 1/4 th, Concentrations will become = 4 times

New rate = k (4 a) (4 b) = 16 k ab = 16 times.