1. Imagine two competing first-order reactions with rate constants k1 >
k2. In other words, the first reaction is faster. Show mathematically that,
as you lower the temperature, the selectivity will normally increase. Hint:
Selectivity can be measured as the ratio between two rate constants. A
larger ratio of rate constants almost always gives a more selective
reaction. You can use the relationship between k and ?G‡ to make this
proof. Which equation defines the relationship between k and ?G‡?
Important Q: Why is this only an approximation? Under what
conditions can the selectivityremain temperature-independent?
For many of the next questions, I recommend using Excel or some
other mathematical software package to, e.g., calculate the slope of
lines.
Last question:
In a way similar to how we proved kH / kD = 7 as the theoretical
limit for primary KIEs in class, now use the same equations to
prove that the theoretical limit for secondary KIEs is kH / kD =
1.4. You will need to use the change in bond bending frequency
shown on our handout and on page 429 of the textbook.
Page 429
Document Preview: 1. Imagine two competing first-order reactions with rate constants k1 >
k2. In other words, the first reaction is faster. Show mathematically that,
as you lower the temperature, the selectivity will normally increase. Hint:
Selectivity can be measured as the ratio between two rate constants. A
larger ratio of rate constants almost always gives a more selective
‡
reaction. You can use the relationship between k and ?G to make this
‡
proof. Which equation defines the relationship between k and ?G ?
Important Q: Why is this only an approximation? Under what
conditions can the selectivityremain temperature-independent?
For many of the next questions, I recommend using Excel or some
other mathematical software package to, e.g., calculate the slope of
lines.