Consider the endothermic reactions in Exercise 3-32. Assume that indepedent expe
ID: 3022897 • Letter: C
Question
Consider the endothermic reactions in Exercise 3-32. Assume that indepedent experiments are conducted.
(a) What is the probability that the first reaction to result in a final temperature less than 272K is the tenth reaction?
(b) What is the mean number of reactions until the first final temperature is less than 272K?
(c)What is the probability that the first reaction to result in a final temperature less than 272K occurs within 3 or fewer reactions?
(d) What is the mean number of reactions until two reactions result in final temperatures less than 272K?
3-32. The data from 200 endothermic reactions involving sodium bicarbonate are summarized as follows: Final Temperature Conditions 266 K 271 K 274 K Number of Reactions 48 60 92Explanation / Answer
the probability that the reaction to result in a final temperature less than 272K is
=0.24+0.3 = 0.54
the probability that the first reaction to result in a final temperature less than 272K is the tenth reaction is
(1-0.54)^9 * 0.54 = 0.000498
mean number of reactions until the first final temperature is less than 272K = q/p = (1-0.54)/0.54 = 0.8518
the probability that the first reaction to result in a final temperature less than 272K occurs within 3 or fewer reactions is =0.54 [(1-0.54)^0 + (1-0.54)^1 +(1-0.54)^2 +(1-0.54)^3] = 0.955
(d) mean number of reactions until two reactions result in final temperatures less than 272K is
2/0.54 = 3.7 = 4 trails needed
Final temperature conditions Number of reactions P(x) 266K 48 0.24 271K 60 0.3 274K 92 0.46 200