Calculate the fraction of atoms in a sample of argon gas at 400 K that has an energy of 10.0 kJ or greater.

Video transcript

Hi everyone for this problem it reads calculate the fraction of Xenon atoms having an energy of 6.40 kg per mole or greater at a temperature of 150°C. Okay, so our goal here is to calculate the fraction. Okay, and the fraction of an atom having specified energy is given by the equation fraction is equal to e raise to negative activation energy over R times T. Okay, so just based off of what we're given in the problem, we know that our activation energy is equal to 6.40 killer jewels. Permal, we know R is a constant and that constant is 8.314 jewels over mole times Kelvin and our temperature is equal to 150°. So we know that based off of what was given in the problem, we need to make sure our units match here. So looking at our our constant, we can see that our energy is and jewels and our temperature is in kelvin. So we need to convert our activation energy to jewels and our temperature to Calvin. So in one killer jewel There's 1000 jewels. Okay, so our killer jewels cancel and our activation energy and jules is 6400 jewels per mole. Now for our temperature to go from C to Kelvin we add 273.15. So this gives us a new temperature and Kelvin to be 423.15 Kelvin. So now we have everything we need to plug into our equation and all of our units match. So let's go ahead and plug in. So our fraction is going to equal e raise to negative jewels per mole over R times T. So 8.314 jewels over mole times kelvin times 423.15 kelvin. Okay, So we get our fraction is equal to E raised to the negative 1.82. Okay, so once we plug this into our calculator, we'll get our fraction is equal to 0.162. And that is our final answer. That's it for this problem. I hope this was helpful.