# In-class Problem Set #3

### Fundamental Resolution Equation

I introduce the fundamental resolution equation, spend a few minutes reminding them about the variables in the equation (each of which we have seen before), and provide them with a photocopy of a derivation of the equation that we quickly go through.  I do not want them to know how to do the derivation, but do want them to appreciate that it is a derivable expression.

1. Describe ways in which the number of plates on a chromatographic column can be increased. Are there any tradeoffs associated with these changes?

Allow students a few minutes to consider this question. They may think of some methods such as decreasing the plate height (remind them to go back to all of the terms in the van Deemter equation and think of experimental variables they can optimize), packing the column more efficiently, using a longer column, using smaller particles, or optimizing the flow rate. Challenge them to think about what each of these changes would mean experimentally.

2. Describe ways in which the separation factor can be increased. Are there limits to the effect that increasing the separation factor has on chromatographic resolution?

Most students have probably had some experience with thin-layer chromatography. If so, they may think of changing the eluent identity to separate compounds. Spend time talking about how you might change the identity of the stationary phase in both liquid and gas chromatography. Mention that changing the identity of the mobile phase in liquid chromatography is considered changing the retention factor.

Is there is any disadvantage to having too large a selectivity factor.

If they are stumped by this, drawing a chromatogram on the board for two components with a large selectivity factor will make apparent that too much time is being spent waiting for the second peak and that the separation is too good (unless one wanted to scale this up for a preparative separation where a higher selectivity means that more compound can be isolated in each injection).

3. Describe ways in which the retention or retention or capacity factor can be increased. Are there any tradeoffs associated with those changes? Are there limits to the effect that increasing the retention factor has on chromatographic resolution?

Since we have just discussed that changing the mobile phase in liquid chromatography is considered a change in capacity, ask students to think of ways in which the mobile phase can be changed. Reminding them that the mobile phase is aqueous-based, they will usually come up with pH.  Since some groups are using LC in their lab project, they also mention varying the percent organic modifier.  I then spend some time talking about the effect of pH on retention time, and how it is often possible to reverse the retention order of organic acids and bases by changing the pH.  We also spend a few minutes talking about the effect of changing the percent organic modifier.

It is then worth reminding them of (or having them look up) the equation we had earlier in this section that defined the retention factor.  I then asking for other ways they might change the capacity in gas chromatography. Some groups immediately see that the volumes of the stationary and mobile phases are in the expression and think of changing them.  At some point we have a discussion about whether it is practical to change the volume of the stationary phase (yes) or mobile phase (no) in GC.  Similarly, we think about bonded phase LC materials and realize that the use of smaller particles leads to both an improvement in the number of plates and the retention factor.  When prompted about GC, and variables that might affect the distribution coefficient, students talking in their groups eventually think of temperature as a variable in gas chromatography.

In order to increase the capacity of the column, would you need to increase or decrease the temperature?

While the students usually seem to want to raise the temperature as a way of “improving” the chromatography, if asked to think and reason their way through the effect that the temperature has on the retention factor and resolution (and I remind them that presumably we have two compounds that are not fully resolved and want to improve this), they usually determine that they will want to lower the temperature of the GC oven.

Is there is any disadvantage to having too large a retention factor.

The groups usually realize immediately that too large a value means a much longer analysis time.

4. Consider the following chromatogram.

The early eluting peaks and the later eluting peaks exhibit a problem.

a) Describe the chromatographic nature (there is a particular chromatographic term that describes each) of the problem.

Let the students spend a few minutes on this problem. Students will probably be tempted to say that the early peaks exhibit an issue with the separation factor. Point out to them that the peaks have started to separate, which is a good sign.  It is likely worth indicating that presumably we want to focus on terms within the fundamental resolution equation and that they may wish to go through them one by one and think about what adjusting each would do.  It may be worth pointing out that the later two eluting peaks are well resolved but stay on the column too long.  Eventually the groups usually get to the realization that the early eluting peaks have too small a retention factor, and that the later eluting peaks have too large a retention factor.  This conclusion should be summarized for the group.

b) Propose a way in gas chromatography to eliminate both problems.

Students will most likely not think of solutions on their own. Remind them of variables that affected the retention factor that were discussed when considering the fundamental resolution equation.  Eventually someone in a group usually brings up the role of temperature and I ask them to consider how temperature might be used to solve this problem.  Groups eventually propose changing the temperature during the chromatogram (it is worth asking them what they would start and finish with to addresses the problem) and we then discuss running a temperature program in gas chromatography.

c) Propose a way in liquid chromatography to eliminate both problems.

When prompted as to whether there is something essentially equivalent in LC to the role of temperature in GC, most groups realize that altering the mobile phase composition (either pH or organic modifier) during the chromatogram could have a similar effect.  I mention the concept of a gradient elution and ask them to determine what they would do with the percentage of organic modifier during the gradient.  They are usually able to reason this out correctly, and we have a brief discussion of the difference between isocratic elution to gradient elution.

At this point in the course I use a lecture format to introduce basic aspects of liquid chromatography and the topic of steric exclusion chromatography.  See the learning objectives and textbook for the topics that are covered.