Home > Chemistry > Detail
search_icon
Question

If you start out with a 136 gram sample of Plutonium that has a half life of 8, how much will be left after 32 days?

Answer

In order to tackle this particular question, it is essential that we have a grasp of the rate law concept. As a result, we can conclude that 8.242g will remain after a period of 32 days. Plutonium decay is governed by first order kinetics, and we must determine the expression for rate law in this scenario. Differential rate law and integrated rate law are the two types of rate law used in chemical kinetics. In first order kinetics, the rate law is K=(2.303/T)×log(a/a-x) and half life=0.693/K, where k represents the rate constant, t represents the time period during which the sample has been held, a represents the initial amount of reactant, and a-x represents the amount left after the decay process. To solve this problem, we utilized the fact that K=0.693/half life, which is equivalent to K=0.693/8=0.086. We could then solve for a-x by substituting this value into the expression: 0.086=(2.303/32)×log(136/a-x). Simplifying this expression further, we obtain 0.086=0.07×log(136/a-x), and upon applying logarithmic rules, we obtain 1.22=log(136/a-x). Thus, we can deduce that 136/a-x=16.5, and that a-x=8.242g. Consequently, after 32 days, only 8.242g of the initial reactant will be remaining. If you would like to learn more about the rate law for first order kinetics, please visit this website: brainly.com/question/12593974 #SPJ1.