The desorption (leaving of the surface) of a single molecular layer of n-butane from a single crystal of aluminum oxide is found to be first order with a rate constant of 0.128/s at 150 K. b. If the surface is initially completely covered with n-butane at 150 K, how long will it take for 25% of the molecules to desorb (leave the surface)? For 50% to desorb?

Video transcript

Hey everyone in this example we have the hydraulics sis of the anticancer drugs CISplatin occurring with first order kinetics with the following rate constant at 310.15 Kelvin. We're assuming that we start with 100% CISplatin. We need to determine the time that it will take for 35% of the CISplatin to react. And then we need to figure out how much time it will take for 50% of the CISplatin to react. So because the prompt mentions were following first order kinetics for reaction. We want to recall that for the first order kinetics are half life is going to equal Ln of two divided by our rate constant K. And we should recall that our first order rate law is the L. N. Of the concentration of our reactant at a given time. Equal to the negative value of our rate constant times time plus the Ln of the initial value of our rate or sorry, of our reactant. Sorry that would be the initial concentration of our reactant. So if we know that we will first be determining the Time of our CISplatin reacting at 35% of the CISplatin reacting. We would take 100 Total of our CISplatin -35%. And this would leave us with 65% of our CISplatin left Because again 35% of it reacts. So for the amount of time we would take the Ln of 65 setting that equal to the negative value of our rate constant given in the prompt as 5.33 times 10 to the negative third power in verse minutes. And then this is multiplied by tea time and then added to The Ln of 100% of our CISplatin that we originally have. And this is going to give us a value for time equal to 80.8 minutes. Next we want to go ahead and calculate for our half life where we have again the natural log Of two divided by our rate constant. Where From the prompt? Were given that as a value of five 0. Times 10 to the negative 3rd power inverse minutes. We're now going to be able to get our half life at 50% of the CISplatin reacting equal to a value of 130 minutes. And so for our final answers, we have our half life When we have 35% of the CISplatin reacting. Which gave us an amount of time being 80.8 minutes. And then when we have 50% of the CISplatin reacting, we have a half life of 130 minutes. So what we have highlighted here, our final answers. If you have any questions, please leave them down below. And I will see everyone in the next practice video