Part B

A certain second$-$order reaction $($B$->$products

$)$ has a rate constant of $1\mathrm{.}40\backslash$times $103$ M$1$s$1$

at $27$C

and an initial half$-$life of $300$ s

$.$ What is the concentration of the reactant B

after one half$-$life?

Express your answer with the appropriate units.The half$-$life of a reaction, t$1/2$

$,$ is the time it takes for the reactant concentration $[$A$]$

to decrease by half. For example, after one half$-$life the concentration falls from the initial concentration $[$A$]0$

to $[$A$]0/2$

$,$ after a second half$-$life to $[$A$]0/4$

$,$ after a third half$-$life to $[$A$]0/8$

$,$ and so on$.$ on$.$

For a first$-$order reaction, the half$-$life is constant. It depends only on the rate constant k

and not on the reactant concentration. It is expressed as

t$1/2=0\mathrm{.}693$k

For a second$-$order reaction, the half$-$life depends on the rate constant and the concentration of the reactant and so is expressed as

t$1/2=1$k$[$A$]0$

Part A

A certain first$-$order reaction $($A$->$products

$)$ has a rate constant of $5\mathrm{.}40\backslash$times $103$ s$1$

at $45$C

$.$ How many minutes does it take for the concentration of the reactant, $[$A$]$

$,$ to drop to $6\mathrm{.}25\%$

of the original concentration?

Express your answer with the appropriate units.