Question

Starting from the integrated rate law of zeroth order reaction r to p show that the half life time of reaction is directly proportional to the initial molar concentration of reactant

Answer 1

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Answer 2

Explanation:

For the given reaction: $R\rightarrow P$

$rate=k[R]^0$    (1)

$rate=-\frac{d[R]}{dt}$    (2)

equating (1) and (2)

$k=-\frac{d[R]}{dt}$       $([R]^0=1)$

$kdt=-{d[R]}$

Integrating both sides and putting the limits for time as t=0 to t=t and for concentration from from $[R]=[a_0]$ to [R]=[a]

Rate law expression for zero order kinetics is given by:

where, t = time taken for decomposition

k = rate constant

$a_o$ = initial concentration

a = concentration left after time t

$t=t_\frac{1}{2}$  $[a]=\frac{[a_0]}{2}$

$t_\frac{1}{2}=\frac{[a_0]-\frac{[a_0]}{2}}{k}$

$t_\frac{1}{2}=\frac{[a_0]}{2k}$

Learn more about zero order kinetics:

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