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Answer 1 · 2017-01-16T22:35:32

The rate constant #k# is #3.39**10^-4# #s^-1#.

We are given that the reaction is a first order reaction, meaning that it can be expressed through the first order reaction integrated rate law:

#ln[A]_t# = #-kt + ln[A]_0#

Let us assume a sample size of 1 M. Therefore, #[A]_0# = 1

40%, or .4 of the sample remains after 45 minutes. Therefore,
.4 = #ln[A]_t#

While we are given minutes, I prefer to use seconds for rate law calculations.
#45# m x #(60 s)/(1 m)# = 2700 seconds = #t#

Now, we can plug in the numbers to get this equation:

#ln[.4]# = -#k**2700# + #ln[1]#

Solving for #k# in a calculator gives a value of #3.39**10^-4#. Since this is a first order reaction, the units are #s^-1#.