Question #45035

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Answer 1 · 2017-04-12T18:30:51

We can understand it through the derivation of half life for 1st order reaction.

Equation for 1st order reaction is:

$k = 2.303/t × log_10(["A"_0]/["A"])$

Where,
$k$ = rate constant
$["A"]$ = concentration after time $t$
$["A"_0]$ = initial concentration

For half life, $["A"]$ = $["A"_0]/2$

Therefore,
$k = 2.303/"t"_½ × log_10( ["A"_0]/(["A"_0]/2))$

$k = 2.303/"t"_½× log_10(2)$

$k = 2.303/"t"_½ × 0.301$

$k = 0.693/"t"_½$

Therefore, the equation for half life of first order reaction is independent of concentration and thus independent of stoichiometric ratio.