|
|||
Using the PSSH, develop a rate law for the rate of formation of HBr for the mechanism given by Equations (CD7-3), (CD7-4), and (CD7-6) through (CD7-8). |
|||
SolutionEach reaction is to be considered elementary. First we write down the net rate of formation of the product resulting from all the reaction steps: |
|||
|
|
(CDE7-2.1) (CDE7-2.2) |
|
|
|||
|
The intermediate species Br |
||
|
|||
|
|
(CDE7-2.3) (CDE7-2.4) |
|
|
|||
|
Adding Equations (CDE7-2.3) and (CDE7-2.4) gives |
||
|
|||
(Br |
|
(CDE7-2.5) | |
|
Subtracting Equation (CDE7-2.3) from (CDE7-2.2) gives |
||
rHBr= 2k3 (H |
(CDE7-2.6) | ||
To eliminate (H |
|||
|
(CDE7-2.7) | ||
and solve for (H |
|||
|
(CDE7-2.8) | ||
|
To eliminate (Br |
||
|
|||
(H |
|
||
|
Substituting Equation (CDE7-2.9) into Equation (CDE7-2.6), we see that |
||
|
(CDE7-2.10) | ||
We can rewrite Equation (CDE7-2.10) in the form |
|||
|
(CDE7-2.11) | ||
By comparing Equations (CDE7-2.6) and (CDE7-2.11) we again see that the mechanism produces a rate law consistent with experimental observation! |