PhysicsLAB Resource Lesson
Ideal Gases

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An ideal gas is defined as a gas in which the molecules can be considered as "point masses" thereby taking up negligible volume compared to the volume of the container. No significant forces, intermolecular interactions, exist between the molecules except during collisions which are considered to be perfectly elastic. All real gases that are far removed from conditions at which they condense, low temperatures or high pressures, display nearly ideal behavior.
 

Avagadro's Number:  NA = 6.022 x 1023
 
The number of carbon atoms in 12 grams of a sample of carbon-12 is called Avogadro's number, NA, which equals 6.022 x 1023 molecules. A mole of any substance contains Avagadro's number of particles.
 
 
Ideal Gas Law: PV = nRT
 
where
 
  • P is the pressure measured in Pa = N/m2 (1 atm = 1.013 x 105 Pa)
  • V is the volume measured in m3
  • n is the amount of gas present measured in moles
  • T is the temperature measured in K
  • R is the ideal gas law constant: 8.314 J/mole K (0.0821 atm L/mole K)


Combined Gas Law:
where
 
  • P1, V1, n1 and T1 are the initial values
  • P2, V2, n2 and T2 are the final values
 

When selected quantities are held constant then this law can be restated as three others.
 
Boyle's Law
temperature and the amount of gas present
held constant
Charles' Law
pressure and the amount of gas present
held constant
Guy-Lussac's Law
volume and the amount of gas present
held constant
 


Some fundamental relationships
 
Often in determining the amount of gas present in moles (n), you need be familiar with the following relationships between Avogadro's number (NA), the amount of mass present (m), molecular mass (N), and the mass of a single molecule ().
 
The relationship between N, n, and NA is
 
    N = nNA
  • n is measured in moles
  • N equals the number of molecules present in the sample
 
This relationship let's us rewrite the ideal gas law as:

PV = (N/NA) RT
PV = N (R/NA) T
PV = NkBT where kB is Boltzmann's constant, 1.38 x 10-23 J/K.
 
The relationship between m, n and M is
 
    m = nM
  • m is the mass present in the sample in grams or kilograms
  • M is the molar mass in grams or kilograms
  • n is the number of moles
 
The relationship between m, N and is
 
    m = N
  • m is the mass present in the sample in grams or kilograms
  • N is the total number of molecules present in the sample
  • is the mass of a single molecule in grams or kilograms
 
The relationship between M, NA and is
 
    M = NA   
  • M is the molar mass in grams or kilograms
  • NA is Avagadro's number of molecules present a mole
  •  is the mass of a single molecule in grams or kilograms
 
 
Now let's take some time and practice several problems that will allow you to become familiar with these formulas.
 
Refer to the following information for the next two questions.

An unknown quantity of oxygen occupies 0.02 m3 at one atmosphere of pressure (1 atm = 101 kPa), and 5 ºC.
 What will be its new volume if the pressure is increased to 108 kPa and its temperature is also changed to 30 ºC?

 What mass of oxygen was present in the sample?

Refer to the following information for the next two questions.

A sample of oxygen has a mass of 4 grams and is being held in a container at STP (101 kPa and 0 ºC).
 How many moles of oxygen are present in that sample?

 What is the volume of the container?

Refer to the following information for the next two questions.

A tank of volume 590 liters (1000 liters = 1 m3) contains oxygen at 20 ºC and 5 atm pressure.
 How many moles of oxygen are in the tank?

 Calculate the mass of oxygen present in the tank.

Refer to the following information for the next three questions.

A certain mass of hydrogen gas occupies 370 cm3 at 16 ºC and 150 kPa.
 Find its volume at -21 ºC and 420 kPa.

 How much mass of hydrogen is present in the sample?

 How many hydrogen molecules are present?








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