Gas Laws (Experimental)

Learning Goals

You will learn Charles's law and Boyle's law and how they are combined into a general gas law. You will also see how Gay-Lussac's law and Avogadro's law help us solve some chemical reaction problems dealing with gases.

Synopsis

Whenever we use T for temperature, the temperature must be expressed in kelvins. The pace of scientific development from 1600 - 1900 was considerably slower than is today. There was almost a two hundred year span between the development of Boyle's law and the last piece of the puzzle, Avogadro's law. Boyle discovered that pressure and volume were inversely proportional; Charles discovered that pressure and temperature were directly proportional; and Avogadro discovered that, at constant T and P, equal volumes of gases have equal numbers of molecules. The latter led to Avogadro's law that volume is directly proportional to the number of moles of gas. If we put all three of these proportionalities together we get

P is proportional to nT/V

We can transform this proportionality into an equality by using a proportionality constant, Ca, so that the equation becomes

P = C_aT/V .........................................eq 1

We will see in the next section what C_a is. Using this equation we can work any problems that involve changes in these state variables (P, n, T, V). Because C_a is a constant, it will have the same value for any set of values of the state variables:

C_a = P₁V₁/n₁T₁ = P₂V₂/n₂T₂ ........................eq 2

So if T is constant (T₁ = T₂) this equation becomes

P₁V₁/n₁ = P₂V₂/n₂ --> P₁V₁ = P₂V₂ if n is also constant ....eq 3

And if V is constant the equation becomes

P₁/n₁T₁ = P₂/n₂T₂ --> P₁/T₁ = P₂/T₂ if n is also constant ..eq 4

You see that you can derive whatever equation you need to work a particular problem starting with equation 1. A very important philosophy to have in studying a science is to minimize memorization and maximize understanding. An application of that principal is to only memorize equation 1 and to derive whatever equation is needed to work a problem.

Review Questions

Do not proceed to the next section until you have mastered working the following problems:

A balloon has a volume of 2.00 liters at 25.5^oC. Assuming that the pressure remains constant (the balloon freely expands) and that the number of moles of gas does not change, what is the volume at 12.6^oC? Derive the needed equation from equation 1 above.
A gas is in a cylinder (no expansion possible) at 25.5^oC at 1.00 atm pressure. The temperature increases to 100.6^oC. What is the new pressure? Derive the needed equation from equation 1above.
Avogadro's law states that V is directly proportional to the number of moles, or using a proportionality constant, that V = C*n. This law allows us to work with volumes instead of moles in stoichiometry problems, but it is an excellent idea to make sure that the proportionality constant cancels when you set up the problem. Use this equality to work Exercise 12.5 on page 550.
Discuss among your study group why scientific progress was so slow in the early years of the gas law's development compared to the progress of the last 20 years.