CHEM 1406 Concept Review: Gases

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The Kinetic Molecular Theory of Gases

This theory can be summarized in the following 5 statements:

1. Gases consist of large numbers of particles (molecules or atoms) that are in continuous, random motion.
   
   
2. The combined volume of all the particles of the gas is negligible relative to the total volume of the container.
   
   
3. Attractive and repulsive forces between gas particles are negligible (so small as to be ignored).
   
   
4. Gas particles move constantly and rapidly in straight paths. Energy can be transferred between molecules during collisions but, as long as temperature remains constant, the average kinetic energy of the particles remains the same.  The collisions of gas particles with the walls of their containers are what cause pressure.
   
   
5. The average kinetic energy of the particles is proportional to the absolute temperature. At the same temperature, the particles of all gases have the same average kinetic energy.

Atmospheric Pressure:  The pressure due to the column of air weighing down on an object at any given time.  Atmospheric pressure changes with the weather (Temperature, air density, etc.)

 

 

The Gas Laws

(For all of the gas laws, the temperature used MUST be in Kelvin)

Boyle’s Law:  States that pressure (P) and volume (V) have an inverse relationship.  As one increases, the other decreases.  This relationship can be written as follows:

$V=constant\times\frac{1}{P}$          OR          $P_1\cdot V_1=P_2\cdot V_2$

 

Charles’ Law:  States that volume (V) and temperature (T) have a direct relationship.  As one increases, the other increases.  The relationship can be written as follows:

$V=constant\times T$         OR          $\frac{V_1}{T_1}=\frac{V_2}{T_2}$

 

Gay-Lussac’s Law:  States that pressure (P) and temperature (T) have a direct relationship.  As one increases, the other increases.  The relationship can be written as follows:

$P=constant\times T$           OR            $\frac{P_1}{T_1}=\frac{P_2}{T_2}$

 

Avogadro’s Law:  States that volume (V) and number of moles (n) have a direct relationship.  As one increases, the other increases.  The relationship can be written as follows:

$V=constant\times n$         OR          $\frac{V_1}{n_1}=\frac{V_2}{n_2}$

 

The Combined Gas Law shown below can be used any time two sets of conditions are listed.  If a variable is not listed or held constant, it can be removed from the equation to give the equation in the form you need.

$\frac{P_1\cdot V_1}{T_1}=\frac{P_2\cdot V_2}{T_2}$        (Combined Gas Law)

where the “1” represents the initial set of conditions and the “2” represents the final set of conditions.

 

Dalton’s Law of Partial Pressures:  states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases.  This is expressed in the following formula:

$P_{total}=P_1+P_2+P_3+...\:P_n$        (where "n" is the number of gases in the mixture)

 

STP or Standard Temperature and Pressure:  Standard temperature is 0˚C.  Standard atmospheric pressure is the typical atmospheric pressure at sea level.  The values for standard atmospheric pressure in the different units of pressure are as follows:

$1\:atm=760.0\:mmHg=760.0\:torr=14.7\:psi=101,325\:Pa=101.3\:kPa=1.013\:bar$

 

At STP, the volume of 1 mole of ANY gas will occupy a volume of 22.4 L.  Or in other words:

$1\:mol\:of\:gas\:at\:STP=22.4\:L$