If 3.0 g of substance A decomposes for 36 minutes the mass of unreacted A remaining is found to be 0.375 g. What is the half life of this reaction if it is first order?

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Explanation: 

For this solve for k from the integral rate law equation ;

[A]t / [A]o = e−kt

k=−ln[A]t / [A]o / t

ln 0.375g/3g / 36 min = 0.0578 min−1

t1/2=ln2 / k

     = 0.693 / 0.058 = 12 min.693.693 .693

t1/2=ln2k

k=ln[A]t[A]ot

 

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Answer: 

12 min