# (a) Define order of reaction. How does order of a reaction differ from molecularity for a complex reaction?(b) A first-order reaction is $\inline 50\; ^{o}/_{o}$ complete in 25 minutes. Calculate the time for $\inline 80\; ^{o}/_{o}$ completion of the reaction.

(a) Order of a Reaction: The sum of the power of the concentration of the reactants in the rate law expression is known as the order of the reaction

Consider the general reaction

$bA+bB\rightarrow cC+dD$

$Rate=K\left [ A \right ]^{x}\left [ B \right ]^{y}$

Where x is order w.r.t  A and Y is order w.r.t B

Overall order $=x+y$

 Order of  Reaction Molecularity (1) It is the sum of the concentration terms on which the rate of reaction actually depends.  (2) It can be fractional as well as zero. (1) It is the number of atom ions or molecules that must collide with one another simultaneously so as to result into a chemical reaction. (2) It is always a whole number. It cannot be zero or fractional.

(b) For a first-order reaction :

$t_{\frac{1}{2}}=\frac{0.693}{K}$

$K=\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{25}=0.028\; min^{-1}$

Now, using the first-order reaction,

$K=\frac{2.303}{t}\log \frac{\left [ R_{0} \right ]}{\left [ R \right ]}$

$t=\frac{2.303}{0.028}\log \frac{R_{o}}{0.2R_{o}}=\frac{2.303}{0.028}log\; 5$

$=82.25\times 0.6991=57.50\; min$

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