Temperature and Dissolution

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Temperature and Dissolution: What about gases?

From experience, you probably know that in order to dissolve a solid (like common table salt) into a liquid (like water), you can often accelerate the process by applying heat and agitation (i.e. stir the pot on the stove). There are some solutes (the stuff being dissolved is the solute, the stuff doing the dissolving, here water, is the solvent) that don't need much coaxing to go into solution, but with common kitchen ingredients, this is a fair generalization. Also, you can often dissolve more material into the solvent at higher temperatures, but there are exceptions. Table salt (sodium chloride or NaCl) is only about 11% more soluble in boiling water than in near freezing water. However, sodium bicarbonate is twice as soluble in water at 140 degrees Fahrenheit (60 C) vs. 50 degrees F (10 C).

So, what about gases? Some folks initially express surprise when told that almost the opposite is true for gases. But, think about it. Take your favorite sparkling beverage from the fridge and gently open it (you probably hear some gas escaping) and pour it down the side (make that the inside) of your glass. You see bubbles! That's some of the dissolved carbon dioxide (CO2) coming out of solution because you've reduced the pressure of CO2 above the liquid, your beverage is warming up, and you've provided nucleation sites for the bubbles with modest turbulence from pouring and the surface imperfections of the glass. Now, if I asked you what would happen if you took that same beverage from the fridge, warmed it up, and shook it vigorously before abruptly opening it in the direction of your unsuspecting friend, you'd be able to tell me what would happen, wouldn't you?

See - you know this stuff. But, let's go over it anyway. This discussion thread is about temperature effects on dissolution. In general, gases become more soluble in liquids as the temperature decreases. So, in the case of CO2, you can dissolve roughly twice as much of the gas in water at 50 degrees F (10 C) as you can at 95 F (35 C). With gases, however, pressure is also a factor. (Think SCUBA diving, nitrogen narcosis, and the dreaded bends). To carbonate your soda pop, the manufacturer will use higher pressures to increase dissolution. (Pressure is pretty inconsequential with solid solutes.)

You can stop reading here. For those who like mathematical constructs to better visualize things, I'll go on to mention something called Henry's law, but you might not like it.

Henry's law defines gas solubility using a constant H which is temperature dependent. So solubility is given as H = pa/xa where pa is the partial pressure of the solute gas in atmospheres and xa is the mole fraction of the solute in solution. So, at constant temperature (H stays the same), you would guess that doubling the partial pressure of the solute gas over the liquid solution would double the amount of solute that can go into solution. Good guess, and for many gases at pressures that don't vary more than an atmosphere or so, it's close enough.

Now, H is temperature dependent. You can find values for H versus temperature in various references, especially the "International Critical Tables." Back to CO2, the value for H at 35 C is 2090, whereas at 10 C it is only 1040. Rearranging the equation above to
xa = pa/H, you see that CO2 should be about twice as soluble at the lower temperature, which is what we stated previously. Now, here's the rub. H isn't only dependent on temperature. It varies some with pressure too! See I said you wouldn't like it. You can usually ignore this dependency as long as you stay below partial pressures of one atmosphere. If you need precise calculations where the conditions result in higher partial pressures, then an iterative approach (trial & error) calculation might be needed.

Example: Carbon dioxide is dissolved in water in the amount of 0.05 grams CO2 per 100 grams water. What partial pressure of CO2 would this solution exert at 25 C?

The molecular weight of water is 18, of CO2 is 44. The mole fraction of CO2 in the solution is thus (0.05/44)/[(0.05/44) + (100/18)] = 0.0002045.

pa = Hxa. At 25 C and up to one atmosphere pressure, H for CO2 = 1640. Starting with that: pa = 1640 x 0.0002045 = 0.335 atmospheres. Since this is less than one atmosphere, our guess for the value of H is valid and the answer is correct.

Some of you sadistic types won't want to let me off that easily. So, what if we do the same example, but with 5.38 grams of CO2 per 100 grams of water?

Now xa becomes (5.38/44)/[(0.3/44) + (100/18)] = 0.0215. If we use the same 1640 value for H, we get a partial pressure of 1640 x 0.0215 = 35.3 atmospheres. Whoa! That's quite a bit more than one atmosphere. So, you would go to your International Critical Tables - you know, the ones on the shelf in your bedroom look up H for CO2 at the higher pressure, plug that in to solve for pa, and get a still higher pressure. Now you look up a new value for H at that still higher pressure, maybe fudge it a bit based on your experience thus far, plug it in again, and so on. You will soon wind up with an H value of about 2325. Plug that in: 2325 x 0.0215 = 50 atmospheres. We now verify that the value for H for CO2 at 25 C and 50 atmospheres is pretty darn close to 2325. Fifty atmospheres it is!

Now, aren't you glad you kept reading?

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