Exam Intelligence

Image via Wikipedia Critical Temperature is the temperature above which, no matter how much pressure you apply, you cannot force a gas to become a liquid. Interestingly enough, though, if you apply sufficiently high pressures, you can form a solid. Essentially, distinct liquid and solid phases of a substance no longer exist.

If you measure the vapour pressure of a substance at the critical temperature, that pressure is called the critical pressure. Alternatively it could be defined as the pressure which is required to liquefy a vapour at its critical temperature.

A substance is a vapour when it is in equilibrium with the substance in another phase, and a gas when there is no liquid or solid present. Therefore, by definition, except at the extremely high pressures mentioned above, any substance above its critical temperature, is a gas. A liquid does not have to boil, nor a solid to sublime (change state directly from solid to vapour/gas-Ed.) to form a vapour. You can draw a serious of lines, plotted on a graph where the x-axis shows volume, and the y-axis shows pressure, which correspond to different temperatures and called isotherms, which demonstrate what will happen to a substance as you increase temperature with a given volume (or pressure). The one with most relevance of course is nitrous oxide…(see here).

Pseudo-critical temperature is the critical temperature of a mixture of gases. In anaesthesia it is commonly used to describe the temperature at which a 50:50 mixture of oxygen and nitrous oxide separates (laminates) forming liquid nitrous oxide and gaseous oxygen, which occurs at (depending on the pressure) temperatures in the range -7 to -5.5 degrees Celsius in cylinders, and lower temperatures in a pipeline (due to lower pressures) at around -20 degrees Celsius.

EI has been asked about this concept, and spent some time trying to explain it. However, although EI understood the concept, it actually became quite difficult to explain. So we’ve thought about it some more, and here is our attempt at trying to explain it.

Firstly, an adiabatic change is one in which NO HEAT is TRANSFERRED TO or FROM a fluid (gas/liquid) doing work, or having work done on it. Normally this occurs when there is a change in pressure in a gas.

In other words, as a gas is compressed, it’s temperature will increase. Have you ever pumped up your bicycle tyre, and the nozzle or barrel of the pump has got really hot, almost too hot to touch by the time you’ve finished pumping the last bit of air in? That’s because of adiabatic HEATING. Diesel engines work on the same process of compression generating enough heat to cause ignition. There is no external source of heat, but the temperature has still increased. This must all have come from the act of pumping, i.e. pressurising, the air. The energy of the pumping has been converted to heat energy (internal energy) of the compressed gas.

Conversely, if a gas is suddenly allowed to expand, it will cool. A CO2 fire extinguisher (They used to be solid black, didn’t they? Now we’ve just got those EU compliant red things with different labels on. How the hell are you supposed to recognise the difference in a hurry now?? – Ed.)…when it is used, or any gas cylinder opened and allowed to vent suddenly will rapidly cool. In fact, if you are using a CO2 extinguisher, don’t put your hand on the funnel, because it might freeze to it. Why does this happen? As the gas expands, it does work on the surrounding air, pushing it out of the way. Since energy cannot be created or destroyed, merely converted from one form to another, the energy has to come from somewhere, and it comes from the internal energy of the gas doing the expanding, which we conveniently refer to as temperature.

So, as a gas is compressed or expands rapidly, it’s temperature changes, but no HEAT energy has been transferred into or out of the system. If heat is added to or lost from the surroundings, this is NOT a-diabatic. So for example a gas expanding as a result of being heated is not adiabatic, and a gas contracting as a result of being cooled is not adiabatic either. These processes involve a transfer of heat energy.

Eventually, after the sudden compression or expansion, there will be a transfer of heat energy, but at the time of the expansion or compression, there is not.

And that, in a nutshell, is adiabatic changes.

(It also happens with magnets, apparently, and they’re not fluids…- Ed.) Okay, yes it does happen with magnets, but don’t try and complicate the issue. (If you want to know more, see Adiabatic Demagnetisation on Wikipedia, but make sure you have your maths head on. You have been warned!)

EI has relations with a Street Style blog over at Stitsh.com, and recently a little vid caught our attention over there. Click here and scroll down to 28.06.08.

It reminded us of a little law that the examiners sometimes like to question, that is Henry’s Law:

At a constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid.

Okay, so what does that mean.

Most of the time we refer to Henry’s law by the formula p=kc (that’s one way of looking at it - Ed).

Another way is to say:

where:

is approximately 2.718, the base of the natural logarithm

is the partial pressure of the solute (the gas being dissolved) above the liquid in which is being dissolved.

is the concentration of the solute in the solution

is the Henry’s Law constant, which has units such as L·atm/mol, atm/(mol fraction) or Pa·m³/mol (this is so that the dimensions all work out correctly - the funny thing about constants is that they usually can be expressed in many different units, depending on what units the rest of the equation is being calculated in….more on that another time).

(In other words, most of the time, we take the natural logarithms of both sides).

The pressure above a solution dictates how many collisions occur between the gas and the liquid. So if you increase the pressure above the solution, the partial pressure of the gas increases, the number of collisions increases, and more gas is dissolved. What will then happen is that an equillibrium will be achieved, where the number of molecules of gas crashing into the surface of the liquid will be the same as the number of molecules leaving the surface of the liquid.

The more observant amongst you will have realised that temperature hasn’t been mentioned yet except in the definition….

So what effect does temperature have?

Well, think of a can of “fizzy pop” (you’re showing your age there - Ed). When it comes out of the fridge, it’s not that fizzy, is it? However, the longer you leave it standing around, the closer it’s temperature comes to room temperature, and then when you go back to the can, first it will seem quite gassy, and then eventually it will go flat. This is because the gas in the drink is coming out of solution. The gas solubility relationship with temperature is very similar to the reason that vapor pressure increases with temperature. (This is Gay-Lussac’s Law: The pressure of a given number of moles (given amount) of gas, is directly proportional to its temperature in Kelvin (absolute temperature scale), when the volume is kept constant. Better known as P/T=k).

Increased temperature causes an increase in kinetic energy, which in a gas causes either expansion or an increase in pressure, or in this instance, more movement of the molecules, which break free of the surface of the solution! (The surface could be the gas side of a small bubble of gas trapped within the solution, which is one reason we get bubbles!)

If you want to see another demonstration of Henry’s law in action, look at a pan of water. As you warm the pan, small bubbles start to form, well before the pan reaches 100°C (373K). Those bubbles are air coming out of solution.

So why do the examiners like this concept: the Bends.

Decompression Sickness occurs when gas (specifically nitrogen) is breathed at higher than atmospheric pressure, and the diver then returns to atmospheric pressure without allowing the gas to come out of solution slowly, resulting in gas bubble formation, and hence, “the bends” (gas in the joints) and “the staggers” (gas bubbles in the brain causing confusion and ataxia) and “the chokes” (probably PE).

It is also a concept that comes into play when talking about Ostwald and Bunsen coefficients….(more on that another time).

(Equations courtesy of Wikipedia)