Gas Laws : Relationships

GL1

P-V Relationship

If you have ever pumped up a bicycle tire or a ball, you know that as you push the handle of the pump in, you feel an increasing resistance against your hand. The same is true for a syringe connected to an FS-522 interface. So, as your students push the handle in, the volume of the syringe decreases and the pressure within increases. This is Boyle’s Law. As shown in the figure above, this is an inverse relationship (P µ 1/V) at constant T and n, and can be made into an equality by introducing a ‘constant of proportionality ‘k1’ to obtain P = k1/V.

V-T Relationship

When a balloon of air is placed in ice water, the size of the balloon shrinks, and when placed in hot water, it swells, thus the volume of the balloon is directly proportional to the temperature, or V µ T. This is Charles’ Law and can show V = k2×T at constant P and n. A fit of this data allows your students to experimentally determine absolute zero.

GL2

V-n Relationship

When you blow up a balloon, each breath you push into the balloon increases the amount of air in the balloon, or, increases the number of moles of air. Thus, V µ n and also, V = k3×n at constant P and T.

P-n Relationship

GL3

In the case of the balloon, the pressure remained relatively constant because the volume could change as governed by the external pressure on the balloon. If you were to do the same process, adding air, but to a container of fixed volume, such as a sealed glass Erlenmeyer, you would observe an increase in pressure. This is Dalton’s Law (link to experiment 6.4.Dalton’s.Law.Part.Press) and can be easily demonstrated with MicroLab equipment When you pumped up the tire, each time you pushed the handle of the pump in, you put more air in the tire and the pressure increased, thus P µ n and P = k4×n at constant V and T.

P-T Relationship

GL4You are cautioned not to throw aerosol cans into an incinerator, why is that? It is a result of the relationship between P and T: P µ 1/T at constant V and n and P = k5/T. So by heating an aerosol can in an incinerator, the pressure of gas inside increases until it explodes.

Your students can explore both n, T and P, T relationships using MicroLab’s Gas Pressure Apparatus Kit. This setup fixes the volume of gas while monitoring pressure. The syringe outlet lets your students insert a syringe to add reactants which produce gaseous products, such as when you add acid to calcium carbonate (link to experiment Determination of % Carbonate in antacid by gas collection). Or your students can insert a temperature probe to the syringe outlet and track how pressure changes with temperature (link to Gay-Lussac’s Law)

T-n Relationship

The final relationship is between T and n. Your students may have come across this relationship if they have ever used compressed air to clean their computer. As the air is expelled, the number of molecules contained within the can decreases and the can becomes cold. When you let most gases escape from a higher pressure, the gas inside the container cools down (except in the case of Helium, which warms up). We see here that T µ n and T = k6×n.

These six relationships can be mathematically combined to produce the ideal gas equation, PV = nRT where R is the product of k1×k3×k5/k2×k4×k6.