Example Help (First Order)

[Gabriel Ordonez 2K]

Can someone walk through a first order reaction problem step by step? Please include side information, conceptual knowledge, and graphical representations?

[sarahsalama2E]

A first order reaction is when the rate of the reaction depends in a linear manner on one reactant's concentration. We can see this linear relationship by plotting the equation which we utilize for first order reactions. The equation we use for first order reactions is ln[A]= -kt+ln[A0]; this is called the integrated rate law.
For some background knowledge, we get this equation by integrating both sides of d[A]/[A]= -kdt. When we plot ln[A] vs time for a first order reaction we get a straight line with a slope of -k. We can determine if the reaction truly is first order if it is linear.
Additionally, it is important to note that reactions are sometimes described by the time taken for reactant concentration to decrease to half of its original concentration. The half life for a first order reaction t1/2= .693/k.
We get this equation from manipulating the integrated rate law.
--> At t=1/2, [A]=1/2[A0], ln 1/2[A0]=-kt1/2+ln[A]0.