## Order of reaction

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## Order of reaction – Experimental determination-

### 1) Graphical method-

#### This method is used when there is only one reactant . This method involves the following steps-

*a) The concentration of the reactants are measured by some suitable method.*

*b) A graph is plotted between concentration and time.*

*c) The instantaneous rates of the reaction at different times are calculated by finding out the slopes of the tangents corresponding to different times.*

*d) The rate of reaction Vs concentration is plotted.*

*i) If rate of reaction remains constant in graph potted rate Vs concentration . Then it is concluded that rate is independent of the concentration of reactants.*

*Rate = K [A] ^{0} = K*

*Hence reaction is zero order.*

**ii) If a straight line is obtained in rate Vs concentration graph . Then it is concluded that rate is directly proportional to the concentration of reactant.**

*Rate = K [A]*

*Hence reaction is first order.*

**iii) If a straight line is obtained in rate Vs (conc.) ^{2} graph . Then it is concluded that rate is directly proportional to the square of the concentration of reactant.**

*Rate = K [A] ^{2}*

*Hence reaction is second order.*

**iv) If a straight line is obtained in rate Vs (conc.) ^{3} graph . Then it is concluded that rate is directly proportional to the cube of the concentration of reactant.**

*Rate = K [A] ^{3}*

*Hence reaction is third order.*

source : askIITians

### 2) Method of integration ( Hit and Trial method)-

*It is simplest method . In this method a, x and t are determined and substituted in the kinetic equations of different orders. The equation gives the constant value of rate constant for different time intervals . In this way order of reaction is determined.*

*For first order reaction,*

*K = 2.303/t [log(a / a-x)*

*For second order reaction,*

*K = 1/t [( 1/a-x) – (1/a)]*

*For third order reaction,*

*K = 1/2t [(1/a-x ) ^{2} – (1/a^{2})*

### 3) Half life method-

*t1/2 ∝ 1 / an-1*

*n is the order of reaction.*

*Suppose , initial conc. = a _{1} and a_{2}*

*half lives = (t _{1/2})_{1} and (t_{1/2})_{2}*

*(t _{1/2})_{1} ∝ 1 / a_{1}^{n-1} eq 1*

*(t _{1/2})2 ∝ 1 / a2^{n-1} eq 2*

*divide eq 1 by eq 2*

*(t _{1/2})_{1} / (t_{1/2})_{2} = (a_{2} / a_{1} )^{n-1}*

*Taking log of both sides,*

*log [(t _{1/2})_{1} / (t_{1/2})_{2]} = log [ (a_{2} / a_{1} )^{n-1}]*

*log [(t _{1/2})_{1} – (t_{1/2})_{2]} = (n-1 ) [log a_{2} – log a_{1} ]*

*(n-1) = log [(t _{1/2})_{1} – (t_{1/2})_{2]} / [log a_{2} – log a_{1} ]*

*n= 1 +[ log [(t*_{1/2})_{1} – (t_{1/2})_{2]} / (log a_{2} – log a_{1} )]

_{1/2})

_{1}– (t

_{1/2})

_{2]}/ (log a

_{2}– log a

_{1})]

*This formula is used to determine order of reaction.*

### 4) Vant Hoff differential method-

*‘n’ is order of reaction, A _{1} and A_{2} are different initial concentrations.*

*-dx _{1} /dt = KA_{1}^{n} ——-eq.1*

*-dx _{2} /dt = KA_{2}^{n} ———eq.2*

*taking log of both equations,*

*log [-dx _{1} /dt] = log KA_{1}^{n}*

*log [-dx _{1} /dt] = log K + n log A_{1} ———eq .3*

*log [-dx _{2} /dt] = log KA_{2}^{n}*

*log [-dx _{2} /dt] = log K + n log A_{2} ———-eq.4*

*Subtracting both equations,*

*log [-dx _{1} /dt] – log [-dx_{2} /dt] = log K +n log A_{1} – log K – n log A_{2}*

*= n ( log A _{1} – log A_{2})*

*n = log [-dx _{1} /dt] – log [-dx_{2} /dt] / [( log A_{1} – log A_{2})]*

*– dx _{1}/dt and -dx_{2}/dt are determined from graph conc. Vs time. So value of ‘n’ can be calculated.*