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Homework Help: General Chemistry questions and kinetics

  1. Sep 26, 2007 #1
    1. The problem statement, all variables and given/known data
    The initial concentration of reactant in a first-order reaction is 0.75M. The rate constant for the reaction is 2.75/s. What is the concentration (mol/L) of reactant after 6.5s?


    2. Relevant equations

    -kt=[A]initial/[A]anytime



    3. The attempt at a solution

    -(2.75/s)(6.5s)=[0.75M]/[A]@6.5seconds

    -17.875/1=0.75M/x; x= -4.20x10^-2; The answer to this problem is not right, but I do not have any idea how to go about it another way.

    Problem 2.

    The usefulness of radiocarbon dating is limited to 50,000 years. Show mathematically why this is true. (Hint: Remember half life follows first order kinetics. The half life of C-14 is 5.73 x 10^3 years).

    Half life formula : t1/2= 0.693/k
    Common integrate rate law for first order reactions: ln[A]=-kt + ln[A@ initial]
    5.73x10^3 = 0.693/k, k = 1.21x10^-4/s

    How would I use k in my integrated formula to prove that the half life is limited to 50,000 years?
     
  2. jcsd
  3. Sep 27, 2007 #2

    Gokul43201

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    Staff Emeritus
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    Gold Member

    #1. You have the wrong rate equation for a first-order reaction. Look at the rate equation you've used in #2. That's the one you need to use here.

    #2. What is (roughly) the relative abundance of C-14 (w.r. to C-12) in the atmosphere? Assume you have a sample that has about 1kg of C. How much of that would have been C-14, when the organism was alive? How much of that C-14 will be present in the sample today (use the rate equation to find this)?
     
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