Chemistry - Relative strength of desiccants

Solution 1:

I'd say no, because there is also a reactivity dimension to desiccants. Some drying agents react with some solvents and therefore can't be used as a desiccant. This happens for many organic solvent and desiccant pairs. Some desiccants also react as desiccants and this changes their drying power. This is the case for phosphorous pentoxide, for example, which gradually forms a viscous layer of phosphoric acid which stops any drying. So any linear ordering you are attempting is likely to be overwhelmed by the reactivity side effects of the many desiccants.

On the other hand, if you are only interested in some theoretical point in time estimate of desiccant efficiency, this might be possible but would have virtually no practical import. A desiccant has to react over time and the side effects cannot be ignored.

Solution 2:

At hydrous equilibrium will the "stronger" desiccant contain virtually all of the water? Or is the equilibrium distribution of water a function of the desiccants' relative "hygroscopy," rates of sorption, or some other factor(s)?

"Rates" aren't relevant for questions about equilibrium.

I am trying to imagine a series of tests in which two different desiccants are put in a humid chamber in adequate quantities that either could completely sorb all the water.

For that particular test, consider two dessicants $\ce{X}$ and $\ce{Y}$. The winner of the test will be determined by the thermodynamics of the two reactions:

$$\ce{H2O(g) <=> H2O_{(X)}}$$ $$\ce{H2O(g) <=> H2O_{(Y)}}$$

which represents the the absorption of water vapor into phase $\ce{X}$ (or $\ce{Y}$) respectively. The two reactions can be combined to yield

$$\ce{H2O_{(X)} <=> H2O_{(Y)}}$$

and the free energy change $\Delta G_r$ of that reaction will determine which dessicant is "stronger" in the sense of that particular test.

This test doesn't take into account many practical considerations that other answers have noted, such as reactivity.

I'd bet that liquid sulfur trioxide would win most desicating contests.$%edit$

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Solution 3:

Yes, it is meaningful, but often ignored for practical reasons. In the lab, e.g. in a desiccator, you would just use a large excess of the desiccant of choice which would always work. It’s often more meaningful to classify them as to whether they are acidic, basic or neutral.

But let’s assume we wanted to create that scale. For simplicity reasons, let’s check a single desiccant first. We need to consider the following equilibrium:

$$\ce{H2O_{(g)} <=> H2O_{(x)}}$$

With (x) again being the water bound to the desiccant in whichever way. (Do not think of this as chemical bonding; it usually is not). It is important to remember that this is an equilibrium with an equilibrium constant k.

$$k_{\mathrm{x}} = \frac{[\ce{H2O_{(x)}}]}{[\ce{H2O_{(g)}}]}$$

One could rearrange this in numerous ways resulting in a representation that essentially says the partial pressure of water in the surrounding atmosphere is more or less proportional to the concentration of water in the desiccant.

$$p_{(\ce{H2O})} \approx c \cdot [\ce{H2O_{(x)}}]$$

Now let’s add a second desiccant into our consideration. The first equation now rearranges itself to the following:

$$\ce{H2O_{(y)} <=> H2O_{(g)} <=> H2O_{(x)}}$$

For each of the two subsystems we again get an equilibrium constant $k$ which we can rearrange to proportionalise the partial pressure to the concentration of water in x or y. $k_{\mathrm{x}} \neq k_{\mathrm{y}}$. There will be one partial pressure of water where both the left side and the right side of the double equation will be at equilibrium; that partial pressure is the final equilibrium that will be reached. This gives us the following conclusions:

• Never will the air be completely dry in the presence of (only) a (or two, or a hundred) desiccant(s).

• Neither of the two desiccants will fall completely dry again; rather unlike when heating (in an open atmosphere).

• Say you start the experiment with the weaker desiccant and then add a dry sample of the stronger desiccant:

  • The stronger desiccant will further reduce the vapour pressure;
  • The reduced vapour pressure will remove water from the weaker desiccant;
  • That water will partly be absorbed by the stronger desiccant
  • However neither will the weaker desiccant be completely dried nor will the partial pressure of water in the atmosphere be completely zero.

• How dry (or wet) either desiccant will end up/how low the partial pressure of water will end up, depends on the strengths of the desiccants. If you use a very strong and a very weak one, the strong one will absorb much more water than the weak one. If the two are similar in strength, they will absorb similar amounts of water.