(a) The activation energy for the isomerization of methyl isonitrile (Figure 14.6) is 160 kJ>mol. Calculate the fraction of methyl isonitrile molecules that has an energy equal to or greater than the activation energy at 500 K. (b) Calculate this fraction for a temperature of 520 K. What is the ratio of the fraction at 520 K to that at 500 K?

Video transcript

Hi everyone for this problem it reads is operation of n butane to ice. A butane is a bit difficult to accomplish because it requires breaking carbon carbon bonds. The activation barrier for the transformation is 120 kg joules per mole. What fraction of N butane molecules with an energy equal to or greater than the activation barrier exists at Calvin and 575 kelvin. Also determine the ratio of the two fractions at 575 Calvin to 455 kelvin. Okay, so we have two parts to this question. We want to find the fraction At Kelvin and 555 575 Kelvin. And then I want to find the ratio between the two. Okay, so the fraction of an atom having specified energy is given by the equation. The fraction is equal to e raise to negative activation energy over r times T. So we need to calculate it at both temperatures. So let's start off with at 455 kelvin. Let's just write out what were given in the problem. So we know our activation energy is equal to 120 kg joules per mole. We know r is a constant, we should have memorized and that's 8.314 jewels over mole times kelvin. And we know the temperature is 455 kelvin. So making sure all of our units match. We can see here that in our our constant our unit is in jewels but our activation energy was given in units of killer jewels. So we need to first convert this from kilo jewels, two jewels. So in one killer jewel There's 1000 jewels. So our killer is canceled And we're going to have a activation energy in jewels to be 120,000 Jules Permal okay, so now we can just plug in to solve for our fraction at Kelvin. So we get our fraction is equal to e raised to negative activation energy over are times T Okay, 455 Kelvin. So we get our fraction is equal to e raise to negative 31.7. So when we solve this, we're going to get Our fraction at 455 Kelvin is equal to 1.71 times 10 to the -14. So that is one of our answers. So we're gonna go ahead and do the same thing, calculate our fraction but we're going to calculate it at 575 Kelvin. Okay, so our activation energy, we already said it's going to be the same. So it's going to be 120,000 jules per mole r is the same. The only thing that's going to change is our temperature, so 8.14 jewels over, multi times Calvin. And our temperature is equal to 575 Kelvin now. So let's go ahead and plug in. So we're going to get our fraction is equal to e raise to -120000 jewels over mold over Our 8.314 jewels over mole Times Kelvin. Not only our temperature changes here. So this is going to be times 575 Kelvin. So we get f is equal to E raised to negative 25.1. Okay, so when we saw for this At Kelvin, our fraction is going to equal 1.26 times 10 to the -11, which is our second answer. And lastly it asked us for the ratio of the fraction. So we're just going to divide this by each other. So our ratio Is going to equal 1.26 times 10 to the -11 over 1. times 10 to the -14. And this is going to equal 737. So this is going to be the ratio of our fraction. So those are our three answers. That's the end of the problem. I hope this was helpful