The reaction x → y follows second order kinetics.
herefore, the rate equation for this reaction will be:
Rate = k[X]² (1)
Let [X] = a mol L⁻¹, then equation (1) can be written as:
Rate₁ = k .(a)²
= ka²
If the concentration of X is increased to three times, then [X] = 3a mol L⁻¹
Now, the rate equation will be:
Rate = k (3a)²

Complex reaction proceeds through several elementary reactions.  Molecularity of each elementary reaction may be different, therefore, molecularity of complex reaction can't be determined.  Order of complex reaction is determined by slowest step in mechanism (involving elementary reactions).

Rate law  is expression which gives relationship between rate of a reaction and conc. of reactants, e.g.
\(\frac { dx }{ dt } =k{ \left[ A \right] }^{ x }{ \left[ B \right] }^{ y }\)
Rate constant is equal to rate of reaction when conc. of reactants is equal to unity.'k' is rate constant in above expression.
(i) Zero order    
(ii) Second order.

\({ T }_{ 1 }=295K, \ { T }_{ 2 }=305K, \ { k }_{ 2 }=2{ k }_{ 1 } \ (given)\)
\(\log { \frac { { k }_{ 2 } }{ { k }_{ 1 } } } =\frac { { E }_{ a } }{ 2.303R } \left( \frac { { T }_{ 2 }-{ T }_{ 1 } }{ { T }_{ 1 }{ T }_{ 2 } } \right) \)
\(\log { 2 } = \ \frac { { E }_{ a } }{ 2.303\times 8.314 } \left( \frac { 305-295 }{ 305\times 295 } \right) \)
\({ E }_{ a } \ = \ \frac { 19.147\times 305\times 295\times 0.3010 }{ 10 } \)
\( { E }_{ a } \ = \ 51854.8 \ J \ { mol }^{ -1 }\)
\(=51.85 \ KJ \ { mol }^{ -1 }\)

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

(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.

(c) : Dividing throught by 3, we get -\(\frac {d[A]}{dt}\) = \(-\frac {1}{3} \frac {d[B]}{dt}= + \frac {1}{2}\frac {d[C]}{dt}\)

This is so for the reaction A + 3B \(\longrightarrow\) 2 C

(d) \(\frac{1}{3} \frac { d[{ Br }_{ 2 }] }{ dt } =-\frac { 1 }{ 5 } \frac { d[{ Br }^{ - }] }{ dt } \) or \(\frac { d[{ Br }_{ 2 }] }{ dt } =-\frac {3 }{ 5 } \frac { d[{ Br }^{ - }] }{ dt } \)