Focus Exercise 7.27

[Stella Nguyen 1J]

Hi everyone!

I was wondering if you guys could explain how you guys approached this problem, and how we should approach problems like these in the future? Would we start off by finding the rate constant from the first-order half-life equation using the 4.5 hours? What would we do after that?

7.27: To prepare a dog of mass 1.5 kg for surgery, 150 mg of the anesthetic phenobarbitol is administered intravenously. The reaction in which the anesthetic is metabolized (decomposed in the body) is first order in phenobarbitol and has a half-life of 4.5 h. After about 2 h, the drug begins to lose its effect. However, the surgical procedure requires more time than had been anticipated. What mass of phenobarbitol must be re-injected to restore the original level of the anesthetic in the dog?

Thank you!

[Jasmine Ho 3I]

Hi! First, I plugged the 4.5 into the 1st order half-life equation to find the value of k. Then you can find the value of [A]naught by dividing mass of phenobarbitol by the mass of the dog. Plug these values into the equation for a 1st order reaction to find ln [A] for time=2hrs.
Use stoichiometry to find out the mass of phenobarbitol that is still present and then subtract this value from 150.

[Varsha Ravi 3E]

I started off by using the half-life equation to solve for the value of k. Then I used ln[A] = -kt + ln[A](initial) to solve for [A] 2 hours later and subtracted that from the initial amount to figure out how much they had to administer. You could divide by the mass of the dog for the technical [A] value but I ended up using ln[150] and since I was going straight to the mg of the drug itself it worked out.