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siskhd · Feb 16, 2011, 08:46 AM

If it takes 81.1 min for the concentration of a reactant to drop to 20% of its initial value in a first-order reaction, what is the rate constant for the reaction in the units min-1?

jcaron2 · Feb 16, 2011, 05:22 PM

In a first-order equation, the concentration as a function of time can be written as

$A=A_0e^{-kt}$ ,

where $A$ is the concentration at time $t$ , the initial concentration is $A_0$ , and $k$ is the rate constant.

In this case, we know that after 81.1 min, the concentration $A$ is only 20% of it's initial value. Hence

$A=0.2\cdot A_0$ when $t=81.1$

So just plug in those values in the equation and solve for $k$ . That's it.

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