Homework Help Forum: Half-Life

Posted by Critical on Sunday, June 21, 2009 at 7:02pm.

Can someone please show me a detailed solution to this problem? Thanks. In a first order decompostion reaction, 42.6% of a compound decomposes in 18.5 minutes. How long, in minutes, will it take for only 25.0% of the compound to remain? The answer is: 46.2 (I just don't know how to get it).

• Half-Life - DrBob222, Sunday, June 21, 2009 at 7:12pm

  Use ln(No/N)=kt to determine the value of k. For example, start with 100 atoms/molecules/whatever in the reaction that is decomposing) so No = 100 and N = 100-42.6 = 57.4. t, or course, is 18.5 min. Then, knowing the value of k, use the same formula to calculate t. (No will be 100 and N will be 25). Post your work if you get stuck.

  
  

• Half-Life - Damon, Sunday, June 21, 2009 at 7:15pm

  A = Ao e^kt where A is amount REMAINING (1-.426) Ao = Ao e^18.5k ln .574 = 18.5 k -.555=18.5 k k = -.03 then .25 = e^-.03t ln .25 = -.03 t -1.386 = -.03 t t = 46.2 minutes sure enough

  
  

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