How To Find Formula for The Half-Life First Order Reaction
May 28th, 2008
We can get general formula for the half-life of a first order reaction that erived from the integrated rate law for the general reaction:
aA -> products
The rate law is
Rate = k[A]
and the integrated fisrt order rate law is
ln[A] = -kt + ln [A]o
the important thing of this equation is that this is the y = mx + c where plot of y versus x is a straight line with the slope is m and the intercept c. Where y is ln[A], x is t, m= -k, and the c = ln[A]o. The plot of ln[A] versus t is the straight line it means that the reaction is first order when the plot is not a straight line the reaction is not first order. This is how we can test whether a reaction is the first order reaction or not.
or we can be expressed in term of a ratio as:
when t1/2 we have the concentration of [A] = 1/2 [A]o then the integrated formula becomes
ln { [A]o / (1/2 [A]o) } = k.t1/2
ln(2) = k.t1/2
because ln (2) is 0.693 then substituting this value to the equation above gives
the equation above is the formula to find half life of first order reaction. Just remember that for the fisrt order reaction the half life does not depend on the concentration
Entry Filed under: Chemical Kinetics
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