A certain first-order reaction has a rate constant of 1.0 * 10-3 s-1 at 25 °C. (b) What is the Ea (in kJ/mol) if the same temperature change causes the rate to triple?

Video transcript

Hello everyone today. We have the following problem at 40 degrees Celsius. The rate constant of particular. First order reaction is 2.6 times 10 to the negative fourth seconds to the negative one, calculate the activation energy in joules per mole. If the rate of the reaction quadruples when the temperatures increased to degrees. So what we need to do is we need to find the two point form of the Iranians equation. And that is that the natural log of our second constant divided by our first constant is equal to the negative activation energy, divided by a gas constant times One over our initial temperature -1 over our final temperature. So it was said that the rate quadruples. So that means that the rate of our second or second rate is going to be four times our initial rate or first rate. So for our first temperature was going to be from 40 degrees Celsius. We need to convert that to kelvin and to do that, we're just going to add it to 73.15 to get 13.15 kelvin. And then for our final temperature we're going to get 70 degrees Celsius, we're going to add it to 73.15 to give us 343.15 degrees kelvin. So from that we're simply going to plug that into our equation. So we're gonna have the natural log, we're going to have our four, we're gonna substitute our case of to our second constant with four case of one and then divide that by a constant one. We're going to equal that too. We're gonna have our activation energy. There are gas constant 8.314 jewels per mole kelvin. And then we're gonna multiply by the differences with our temperature. So we're gonna have one over our 3 43.15 kelvin minus 1/3 13.15 kelvin. And it's actually going to be our final temperature minus our initial temperature. And so when we solve for our activation energy, we're going to get negative Or 40,040, 1,283.9 jewels per mole. However, we need this in terms of killing jules, we're going to use the conversion factor that one. Killer jewels equal to 10 to the third jewels. And when our units of jewels canceled out, we were left with relatively or close to 41 killer jules Permal as our final answer. And so without. We've answered the question overall, I hope this helped. And until next time