Trans-cycloheptene 1C7H122, a strained cyclic hydrocarbon, converts to cis-cycloheptene at low temperatures. This molecular rearrangement is a second-order process with a rate constant of 0.030 M-1 s-1 at 60 °C. If the initial concentration of trans-cycloheptene is 0.035 M: (c) What is the half-life of trans-cycloheptene at an initial concentration of 0.075 M?

Video transcript

Hey everyone in this example, we have a reaction of the hypothetical compound A. B. Which occurs in second order kinetics were told that at a certain temperature the reaction has a rate constant of 3.54 times 10 to the negative third power inverse polarity times inverse seconds. We need to determine the half life of the reaction when the initial concentration of 2.50 moller is the concentration of our react in a. B. So what we need to do is recall our formula for calculating half life for a second order reaction. And we would recall that we would find the half life by taking one divided by K times our initial concentration of a react in A B. So plugging in what we know from the prompt, we can say that our half life is equal to one divided by our rate constant K. Which from the prompt is given to us as 3.54 times 10 to the negative third power inverse polarity times inverse seconds. And then we are going to multiply this by our initial concentration of our react in A. B. And sorry, Which is given in the prompt as 0.250 moller. So we would be able to now cancel out our units of inverse polarity with polarity here. And we're left with inverse seconds as our final unit. So what we're going to get for our half life is a value equal to 1.13 times 10 to the third power seconds now. And so this would be our final answer for our half life of our reaction when the initial concentration of a B is 100.2 50 moller. So I hope that everything I explained is clear. If you have any questions, just leave them down below and I will see everyone in the next practice video.