For the decomposition reaction PCl₅(g) ⇌ PCl₃(g) + Cl₂(g), K_p = 381 at 600 K and K_c = 46.9 at 700 K. (a) Is the reaction endothermic or exothermic? Explain. Does your answer agree with what you would predict based on bond energies?

Video transcript

Hi everyone. This problem reads, consider the following hypothetical reaction, determine whether the reaction is endo thermic or eggs. A thermic, given that K P is equal to 0.580 at temperature equals 900 kelvin and K C is equal to 0.158 at temperature equals 1000 kelvin. And justify your answer. Is this the same as predicted? Using bond energies. Okay, so we want to answer the question of whether the reaction is endo thermic or eggs. A thermic. Okay. And let's go ahead and write what we're given. So let's start off by writing our reaction. So for our reaction we have the following. Okay, And we're told that the K. P. So the equilibrium constant based off partial pressure is equal to 0.580 At temperature is equal to 900 Kelvin and the equilibrium constant is 0.158 At temperature is equal to 1000 Kelvin. Okay. And so we want to essentially calculate or figure out what is the K P At 1000 Kelvin. Okay. And we can do that by using the equation that relates K P two, K C. And the equation that relates that is K P is equal to K C. Times gas constant, R times temperature raised to the change in moles. Okay, so for our change in moles, based off of our reaction, we have our change in moles, we're going from one. We have 1 -2. Okay, so our change in moles is -1. We know what the K C is at 1000 kelvin because that was given. We know what the gas constant R is this is the value we should have memorized and we know what the change in moles is. So we have everything we need to calculate K. P. So let's plug all of that in. So K P is equal to K C. R K C is given at 1000 kelvin. It's 0.158. And this is going to be multiplied by R times t raise the delta N. So R is 0.08206. And temperature in Kelvin is 1000. Okay, and this is raised to -1. So when we do the calculation, we're going to get K. P is equal to 1.9, 2 Times 10 to the -3. And this is at 1000 Kelvin. Okay, so when we compare we'll see that. Alright, this in a different color. When we compare we're going to see that K P At 900 Kelvin is greater than the K P. At 1000 kelvin. So this essentially leads to that being at a higher temperature. Okay, And the reaction was shift backwards. So if it shifts backwards, it's shifting left. Okay, so at higher temperature. Excuse me? At higher temperature, the reaction shifts left. And what that means is the reaction is eggs a thermic. All right. And another way that we can justify this is one bond brakes. So that is this bond to form two bonds, which means it's exotic thermic. So our answer for this problem is since the K. P at 900 is greater than the K. P. At 1001 bond breaks to form two bonds, the reaction is eggs a thermic, and the two predictions are the same. So this is going to be our final answer for this problem, along with the justification, that is it for this problem. I hope this was helpful.