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# If first order reaction x tend to y 40% of given sample of compound remain unreacted in 45min.Calculate rate constant of reaction?

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 :

##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##.