Assume that you have developed a tracer with first-order kinetics and k = 0.1 s − 1 . for any given mass, how long will it take the tracer concentration to drop by (a) 50% and (b) by 75%?

It will take 6.93 sec for tracer concentration to drop by 50% and 13.9 sec for tracer concentration to drop by 75%

Explanation:

Expression for rate law for first order kinetics is given by:

where,

k = rate constant  =

t = age of sample  

a = let initial amount of the reactant  = 100 g

a - x = amount left after decay process  

a) for tracer concentration to drop by 50%

a - x = amount left after decay process   = 50

It will take 6.93 sec for tracer concentration to drop by 50%

b) for  tracer concentration to drop by 75 %

a - x = amount left after decay process   = 25

It will take 13.9 sec for tracer concentration to drop by 75%.

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