A decomposition reaction has a half life of 578 years. (a) What is the rate constant for this reaction? (b) How many years does it take for the reactant concentration to reach 12.5% of its original value? Report your answer to 3 significant figures.

is the rate constant for this reaction.

It will take to concentration to reach 12.5% of its original value.

Explanation:

A decomposition reaction follows first order kinetics:

Half life of the reaction =

Rate constant of the reaction = k

For first order reaction, half life and rate constant are linked with an expression :

is the rate constant for this reaction.

Initial concentration of reactant = =  x

Final concentration of reactant after time t = =  12.5% of x = 0.125x

The integrated law of first order reaction :

t = 1,734.31 years =

It will take to concentration to reach 12.5% of its original value.