Process Gas Chromatographs. Tony Waters
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assume that the gas space in Figure 2.3a is full of helium. This is equivalent to the carrier gas in a column; it's always there. The helium molecules contact the liquid phase, and a few of them dissolve in it. Since helium is always there, the amount dissolved soon becomes constant and can be ignored.
Now consider what happens when a small sample of (say) propane is injected into the helium gas in the enclosed space. To keep it simple, let's say there are only 32 propane molecules. The same logic applies to 32 trillion molecules, or to any other number of them. This is shown in Figure 2.3b.
The propane molecules move randomly in the gas phase and soon encounter the liquid surface where some of them dissolve. Initially, all the propane molecules are in the gas phase, so they frequently collide with the liquid surface and their rate of entry into the liquid is high. Then, as more of the molecules dissolve in the liquid, there are less of them in the gas phase, and their rate of entry declines.
The dissolved propane molecules move slowly in the liquid phase and eventually encounter the gas‐liquid surface, where some of them have enough energy to escape back into the gas phase. Initially, there are no propane molecules dissolved in the liquid phase, so none can escape; their rate of escape is zero. As more and more propane molecules dissolve, their rate of escape increases, as in Figure 2.3c.
With the rate of entry falling and the rate of escape rising, there must soon come a time when the two rates become equal. At this instant and beyond, every molecule that dissolves replaces one that escapes. The number of molecules in the gas phase is then constant, as is the number of molecules in the liquid phase. They will stay that way forever, as long as the operating conditions don't change.
This balancing act between two opposing and dependent processes is common in chemistry. Chemists call it a dynamic equilibrium.
There is nothing in our example that specifies the number of propane molecules in the gas phase and in the liquid phase once equilibrium has been achieved. That would depend on the solubility of propane in the selected liquid phase and would vary with different chemical compounds. To make it easy, though, let's assume that 50 % of the propane dissolves. Then, after reaching equilibrium, half of the molecules will be in the liquid phase, and the other half will be in the gas phase. This is the situation shown in Figure 2.3d.
Actually, it's reasonable to assume the propane solubility is 50 %, as that would generate a pretty good chromatogram. Yes, we can predict the position of peaks on the chromatogram from their solubility! You'll soon see how that works out.
In practice, it would not be difficult to set the propane solubility to exactly 50 %. We already know that the solubility of a given substance in a given liquid depends on temperature and pressure. So, to adjust the propane solubility simply change the temperature. It really is that simple. In fact, that's one way you can optimize the performance of a column.
The effect of movement
So far, the discussion about equilibrium cannot explain chromatography. There is something missing from Figure 2.3, something that is essential for chromatography to occur. Figure 2.3 starts to explain what happens in a column, but it's not enough.
What is missing?
The gas phase is not moving! Recall that chromatography occurs when something moves across something that doesn't move. And in a gas chromatograph, it's the carrier gas that moves.
When the carrier gas moves, any propane molecules that happen to be in the gas phase are carried along with it, as illustrated in Figure 2.4a. In this figure, fresh carrier gas enters from the left and pushes the propane molecules out to the right replacing them with pure helium. In Figure 2.4b, the 50 % propane molecules are gone from the gas phase, and the other 50 % are stuck in the liquid phase. Pure helium now occupies the gas space, upsetting the original equilibrium.
Figure 2.4 The Carrier Gas Moves.
Let's see what happens next. Imagine the small enclosed space is again sealed. The absence of propane molecules in the gas phase doesn't affect the behavior of the molecules trapped in the liquid. They continue to escape from the liquid into the clean helium above, as they did before. See Figure 2.4b. It should come as no surprise that as soon as some of the molecules reenter the gas phase, they start to dissolve in the liquid again, quickly forming the new equilibrium in Figure 2.4c.
Of course, it doesn't stop there. When the carrier gas again moves it disrupts the equilibrium of Figure 2.4c and the cycle starts again, as shown in Figure 2.4d – but with fewer molecules this time.
Pause for a moment to reflect. Figure 2.4 suggests that the carrier gas moves, then stops until a new equilibrium forms, then moves again. Clearly, this is not true. Chromatography is a smooth process, not a jerky one. But the jerky model is very useful for explaining what happens inside a column. It's a bit like taking a movie of the process and then looking at each frame in turn.
It's a long movie. The number of equilibria generated by a typical column ranges from about 5,000 to 50,000. Even a slow peak with a retention time of 1000 s would need to average one equilibrium every 50 ms to get 20,000 plates. That's equivalent to 20 movie frames per second − not a bad analogy!
With such a large number of data points, our jerky model is not so jerky after all. And it's a powerful way of evaluating column efficiency. We shall soon discover that having more equilibria in the column causes better separations.
There is a theoretical connection between the shape of a peak on the chromatogram and the number of times that equilibrium has occurred. Yes, we can figure the effective number of equilibria by measuring the resulting peak shape. This is yet another glimpse of the information buried in a chromatogram. We'll exhume it later.
A peak appears
An important thing just happened.
In Figure 2.4c, notice that the same percentage of the molecules dissolved in the liquid phase even when there were fewer molecules available; the solubility ratio is constant. In our example, for instance, we always end up with exactly half of the propane molecules dissolved in the liquid phase. Constant solubility is a very useful property of liquid phases because it generates symmetrical peak shapes. You are about to see how that happens.
There are some rare exceptions to the rule of constant solubility. When solubility varies with solute concentration, some adverse distortion of peak shape occurs that you will need to recognize when troubleshooting. This isn't the time to discuss the problem, so let's leave it for later.
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