Ideal Gases

Contents

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Charles' Law

Charles' law states that, at a constant pressure, the volume of a mixed amount of gas is directly proportional to its absolute temperature:

 = k

Where k is a constant unique to the amount of gas and pressure. Just as with Boyle's law, Charles' law can be expressed in its more useful form:

 =

The subscripts 1 and 2 refer to two different sets of conditions, just as with Boyle's law.

Why must the temperature be absolute? If temperature is measured on a Celsius (non absolute) scale, T can be negative. If we plug negative values of T into the equation, we get back negative volumes, which cannot exist. In order to ensure that only values of V≥ 0 occur, we have to use an absolute temperature scale where T≥ 0. The standard absolute scale is the Kelvin (K) scale. The temperature in Kelvin can be calculated via Tk = TC + 273.15. A plot of the temperature in Kelvin vs. volume gives :

Figure %: Temperature vs. Volume
As you can see from , Charles' law predicts that volume will be zero at 0 K. 0 K is the absolutely lowest temperature possible, and is called absolute zero.

Avogadro's law states that the volume of a gas at constant temperature and pressure is directly proportional to the number of moles of gas present. It's mathematical representation follows:

 fracVn = k

k is a constant unique to the conditions of P and T. n is the number of moles of gas present.

1 mole (mol) of gas is defined as the amount of gas containing Avogadro's number of molecules. Avogadro's number (NA) is

 NA = 6.022×1023

1 mol of any gas at 273 K (0_C) and 1 atm has a volume of 22.4 L. The conditions 273 K and 1 atm are the standard temperature and pressure (STP). STP should not be confused with the less common standard atmospheric temperature and pressure (SATP), which corresponds to a temperature of 298 K and a pressure of 1 bar.

The numbers 22.4 L, 6.022×1023, and the conditions of STP should be near and dear to your heart. Memorize them if you haven't already.

The Ideal Gas Law

Charles', Avogadro's, and Boyle's laws are all special cases of the ideal gas law:

 PV = nRT

T must always be in Kelvin. n is almost always in moles. R is the gas constant. The value of R depends on the units of P, V and n. Be sure to ask your instructor which values you should memorize.
UnitsValue of R

0.08206

8.314

8.314

1.987

62.36
You can think of R as a converter that changes the units on the right side of the above equation to the units on the left side of the "=" sign. The values 0.0821 and 8.314 get the most use. Memorizing them will make your life easier.