ercise 13.13, the reaction of sucrose with water was In Practice Ex order with r
ID: 229828 • Letter: E
Question
ercise 13.13, the reaction of sucrose with water was In Practice Ex order with respect to sucrose. The rate constant under the conditions of the experiments was 6.17 × 10-4 s-1. Calculate the value of t1/2 for this reaction in minutes. How many minutes would it take for three-quarters of the sucrose to react? (Hint: What fraction of the sucrose remains?) From the answer to Practice Exercise 13.15, determine the half-life of an active ingredient that has a shelf life of 2.00 years. The radioactive isotope, phosphorus-32, has a half-life of 14.26 days. What percent of phosphorus-32 will remain after 60 days?Explanation / Answer
Rate constant k = 6.17 * 10^-4 s^-1
we have the formula t1/2 = 0.693/k
t1/2 = 0.693/(6.17*10^-4) = 1123.18 sec
k = 2.303/t log(a/a-x)
t = time for the reaction
a = initial concentration
a-x = final concentration after time t
6.17 * 10^-4 = 2.303/t*log(1/(1-3/4))
t = 2247.235 Sec
t = 2247.235/60 = 37.454 min
t1/2 of P-32 = 14.26 days
t1/2 = 0.693/k
14.26 = 0.693/k
k = 4.856*10^-2
k = 2.303/tlog(a/a-x)
4.856 * 10^-2 = 2.303/60*log(a/a-x)
(a/a-x) = 18.412
let us consider a = 100 then
a-x = remaining concentration of P-32 = 100/18.412 = 5.4312
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