Given the Arrhenius equation, k = Ae-Ea>RT, and the rela- tion between the equilibrium constant and the forward and reverse rate constants, Kc = kf>kr, explain why Kc for an exothermic reaction decreases with increasing temperature.

Video transcript

Hello everyone today. We are being given the falling problem based on the Iranians equation here. The relationship between the forward and reverse rate constant K. F. And K. R. And the equilibrium constant K. C provide an explanation as to why equilibrium constant of an endo thermic process increases as temperature rises. So for an endo thermic reaction for an endo thermic reaction, the activation energy of the forward is going to be greater than the activation energy of the reverse reaction. And so we can relate that to our K. C. Value. So our K. C. Value is going to essentially be the rate constant forward divided by the rate constant reverse or K. F. Over K. R. And so how are we gonna incorporate that with our radius equation? Well we can say that R K. F is equal to the following. We have the activation energy for F divided by R. T. R. Rate constant times the temperature. And then we're gonna divide that by the same for our reverse. And so how we're gonna we're gonna basically derive this equation at the end. So With this we're essentially going to combine the two. Es so this is going to transform into, we're gonna have our K. C. Value Equalling our a sub F over R a sub are times our E. Which is raised to our negative activation energy. It's going to be F. R. T. Plus energy for R. Over R. T. The plus came because when you subtract a negative number, you end up adding the two numbers. And so this is going to transform into, we're gonna have Casey is equal to a sub F over a sub. Are times E raised to the power of e activation energy, sub r minus the activation and energy sub F divided by our rate constant. So based on this derived equation here, this will be smaller as the temperature increases. And so we can say as our temperature increases, our Casey will decrease and this best is best represented by answer choice D. The derived equation is as follows, and the activation energy of the forward reaction is greater than the activation energy of the reverse reaction. Therefore the overall value K. C decreases as temperature rises. And with that we've answered the question overall, I hope this helps and until next time.