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GAS LAWS PART 2

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The Gas Laws, part 1

by Pat Neligan

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All tutorials located on this site are the property of Patrick Neligan and are for personal study purposes only. They are not peer reviewed and no responsibility is taken for inaccuracies. These tutorials must not be reproduced without permission or used in any other publication

Purpose: to familiarise you with the physical concepts behind gases and vapours.

• The Three Different Phases of Matter
• Melting Point
• Boiling Point
• Critical Temperature

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1.1 All matter exists in one of three phases: solid, liquid and gas. A piece of matter consists of molecules, and the closeness to which these are bound to other "like" molecules determines which phase the matter exists in. In effect solid is a state of constraint, gas a state of freedom.

• Melting Point
• Saturated Vapour Pressure

1.2 Whether a substance is a solid, a liquid or a gas is determined by temperature and pressure. As one heats a solid, the molecular bonds, that hold it in a lattice, start to break down, and the substance gradually liquefies (melting point). When the liquid is heated, molecules acquire enough energy to break free of restraining bonds, and enter the gas phase. These molecules come from the surface of the liquid where the bonds are weakest. When a liquid and its gas coexist at a certain temperature, the gas is known as a vapour (e.g. water and water vapour, the concentration of the latter in the air is known as humidity). Vapour molecules both leave and enter the liquid simultaneously. At any particular temperature and pressure, a state of equilibrium will be reached whereby a particular number of molecules of vapour will exist above the liquid. This vapour will apply a pressure of its own to the surface of the liquid; this is known as the saturated vapour pressure.

• Boiling Point

1.3 There comes a point, as one heats a liquid, when the number of molecules leaving the liquid exceeds the number returning to solution; molecules leaving the substance of the liquid causing turbulence and bubbling. This is the boiling point. At this point, the saturated vapour pressure exceeds the atmospheric pressure. At normal atmospheric pressure (1 atmosphere =76OmmHg), water boils at 100 degrees Celsius. High up in the Andes, the atmosphere is much thinner, atmospheric pressure is lower, and water boils at a lower temperature.

• Critical Temperature

1.4 In order to increase the boiling point we can increase the pressure.Consequently, by pressurising gas we can liquefy it, up to a certain point. That point is the critical temperature: the critical temperature is the point, above which a gas cannot be liquefied no matter how much pressure is applied to it. The critical temperature for water is 374 degrees Celsius, at a pressure of 217 atmospheres.
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1.5 All matter may be affected by temperature and pressure, but solids andLiquids are relatively incompressible. Gases, on the other hand, can be squeezed into a smaller volume, and are therefore affected by a third factor (volume). This is the basis of the gas laws.

1.6 Pick up a syringe, block the end of it with your finger and push the plunger. The further down the plunger goes the harder it is to advance. This is because the pressure inside the syringe is increasing due to compression of air. This is the basis of Boyle’s law which states: where temperature is constant the volume of a gas is inversely proportional to pressure: V is proportional to 1/P or VP = constant.

Charles' Law

1.7 Imagine the same syringe, filled with air, the plunger half way along and the end blocked. A heat source is applied. What happens? The gas expands the plunger moves backwards, and the volume increases. This is Charles’ law which states that volume is proportional to temperature, or V/T=constant.

1.8 Imagine the same scenario as above, except that the plunger is prevented from moving backwards, what happens then? The pressure inside the syringe increases. This is the third gas law, which states that pressure is proportional to temperature or P/T is constant.

1.9 If a mixture of gases is put inside a container, such as a jar of air, which contains Oxygen and Nitrogen. Each of the molecules of Nitrogen and Oxygen bash against the wall of the container, applying a pressure. Dalton’s law states that in a mixture of gases, the pressure exerted by each gas is the same as that which it would exert if it alone occupied the container. We know that the air is 21% Oxygen and 79% Nitrogen, so we can calculate the partial pressure of each gas by multiplying the total pressure by the fractional concentration of each gas: 760 mmHg x 21% = l57mmHg, this is the partial pressure of Oxygen in the jar.

1.12 If the partial pressure of the gas above a liquid is increased, the number of molecules of gas dissolved in the liquid increases proportionately, as long as the temperature is constant. This is Henry’s law.

Deep sea diving: with increasing depth, the prevailing pressure increases proportionately. Nitrogen in inspired air dissolves into body liquids at a greater rate. If the diver comes up too quickly, to normal atmospheric pressure, the reverse process of Nitrogen coming out of solution is accelerated, and bubbles form in the blood and tissues ("the blood turns to 7up") - the bends.

1.15 It is often important to describe the relative ability of a gas to dissolve into a liquid, we do this in anaesthetics using the Ostwald solubility coefficient: the volume of gas, which dissolves in one unit volume of a liquid at a particular temperature. If the pressure in the container is doubled, then the amount of gas dissolved is also doubles, but because of Boyles law (V 1/P), the volume of gas dissolved is halved, so the said volume is the same as it was initially, even though there are twice as many molecules dissolved.

1.16 Of more importance to anaesthetists are partition coefficients. A partition coefficient is the ratio of the amount of a substance present in one phase compared with another. The two phases are of equal volume and in equilibrium with one another. The two substances can be a liquid and a gas (e.g. blood-gas partition coefficient) or two liquids (e.g. oil-blood partition coefficient). The usefulness of partition coefficients is that they indicate the behaviour of anaesthetic gases as they enter and leave the body. This will be further discussed in the next tutorial.

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