Ethyl chloride vapor decomposes by the first-order reaction: C₂H₅Cl → C₂H₄ + HCl The activation energy is 249 kJ/mol, and the frequency factor is 1.6⨉10¹⁴ s^-1. Find the value of the rate constant at 710 K.

Video transcript

Hello everyone. So in this question we're being told to consider the following first order action. That's given right over here if the reaction has an activation energy of kg joules per mole and are erogenous constant of 2.1 times 10 to the 13th power as two negative one, calculate the rate constant of the reaction at 650 kelvin's. So let's recall what the Arrhenius equation is. So this is equal to K. equaling two capital a. E. Race apart of negative E. A over R. T. What this case stands for here is the rate constant with this E. Of a value is the activation energy usually in the units of joules per mole. Then we have this capital R. This is the ideal gas constant and that's 8.314 joules per mole times Calvin's. We'll just write this in later. T here, right next to the R. Is going to be temperatures and it's in the units of kelvin's. And then of course are a here is the Arrhenius constant or the frequency factor In our case we're given the Arrhenius constant. Let's go ahead and solve for E. Of A. So the E. Of a. Is to go to 100 and three killer jewels per mole. We want to go ahead and convert this killer jewel unit into jewels. So do a direct conversion here for every jewels. We have one killer jewel, this gives me a of a value to be 103000 units being jewels per mole. Now for my cake constant here is equal to 2. times 10 to the 13 seconds. Raised to negative 101 over seconds times E raised the power of negative 30 00. You forgot the units here. This is jules per month divided by Our our value. That's 8.314 joules per mole times kelvin multiplied by T. And that is our temperature and that is 650 Calvin's. Alright, so here we're just solving for K. The rate constant of the reaction. So we're simplifying this values here. So we'll just keep 2.1 times 10 to the 13 S. Race to power negative one as constant. Then we have e raised to power now of negative 19.5960 to 89. Alright, so we find this further. We get that K. Is equal to 2.1 times 10 to the 13 as raising power of negative one, multiplied by 5.27861 times to the negative nine. Alright, let's put this all into our calculators. We finally get the rate constant of this reaction is equal to 1.6 times 10 to the fifth. Power. S per seconds raised to a negative one. Or just one over seconds. So this race constant Here is going to be my final answer for this problem