isn't half-life a PC game? just kidding.. LOL
the equation
ln([A]1/[A0]) = -kt
Objectivist had given the reaction profile for a first-order reaction, not a 2nd order one.
the rate law is given by:
- dA/dt = k[A]
2-[A]
-2 dA/dt = k
integrating both sides with respect to t,
[A]
-1 = kt + C (integration constant)
using initial conditions when t = 0, [A] = [Ao] => C = [Ao]
-1hence, the reaction profile is given by:
[A]
-1 - [Ao]
-1 = kt
When [A]0 is .250 M, the reaction is 30.0% complete in 50.0 minutes.
when t = 50min, [Ao] = .250M, [A] = 70.0% x [Ao] = 0.175
0.175
-1 - 0.250
-1 = k(50)
k = 0.0343 dm
3mol
-1min
-1to find the half-life of the reaction, ie. when the reactants are 50% are used up, just plug in all the necessary values into the reaction profile equation, given you know k, [Ao], [A] ( = 50% x [Ao])