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.
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 = CaT/V .........................................eq 1
We will see in the next section what Ca is. Using this equation we can work any problems that involve changes in these state variables (P, n, T, V). Because Ca is a constant, it will have the same value for any set of values of the state variables:
Ca = 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.
Do not proceed to the next section until you have mastered working the following problems:
Web Author: Dr. Leon L. Combs
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