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The Rate Law: Half life

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Wize University Chemistry Textbook > Kinetics

Half-lives for Various Orders

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Given a second order reaction, derive the expression for the half life:

The integrated rate law for the second order reaction is:

1[A]t=kt +1[A]0\frac{1}{\left[A\right]_t}=kt\ +\frac{1}{\left[A\right]_0}


More Half-lives for Various Orders Questions:
The Rate Law: Half Life
What is the half‐life of a reaction that has k = 0.254 M/s and [A]0 of 0.254 M.
A reaction, A →\rightarrow is performed in a lab and the concentration of the reactant A is plotted as a function of time.
What is the half life?
A first order gas phase reaction N2O4 → 2 NO2 was carried out isothermally and the activation barrier was found to be 23.5 kJ/mol. Initially p(N2O4) = 2.6 atm and p(NO2) = 0. After 1 hour p(NO2) = 2.0 atm and p(N2O4) =1.6 atm. Assume that both NO2 and N2O4 are ideal gases.
Determine the first order rate constant k, and the half life t1/2.
The above reaction was performed at 220oC. Calculate the pre-exponential factor.
Practice: Using Integrated Rate Laws
Americium-241 is a synthetic isotope made in nuclear reactors around the world. Chances are you have been in close proximity to this radioactive isotope thousands of times in your life because it is used in household smoke detectors. 241Am is an alpha emitter whose decay obeys a first order rate-law (as do all nuclear decays) with a half-life of 432.6 years.