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QUESTION

# 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.