The kinetic theory of gases describes a gas as a large number of small particles (atoms or molecules), all of which are in constant, random motion. The rapidly moving particles constantly collide with each other and with the walls of the container. Kinetic theory explains macroscopic properties of gases, such as pressure, temperature, and volume, by considering their molecular composition

1. The molar gas Constant R
• By: Dr. Robert D. Craig, Ph. D.

2. Relationship Between the Ideal-Gas
Equation and the Gas Laws
• Boyle's law, Charles's law and Avogadro's law all
represent special cases of the Ideal Gas law
(equation)
• If the quantity of gas and the temperature are
held constant then:
pV = nRT
V = nRT / p
V= (nRT) * (1/p)
V= constant * (1/p)
(Boyle's law)

3. Relationship Between the Ideal-Gas
Equation and the Gas Laws
• If the quantity of gas and the pressure are
held constant then:
pV = nRT
V = (nR/p) * T
V = constant * T
(Charles's law)

4. Relationship Between the Ideal-Gas
Equation and the Gas Laws
• If the temperature and pressure are held
constant then:
pV = nRT
V = n * (RT/p)
V = constant * n
(Avogadro's law)

5. The 'General"case...
• Suppose everything changes at once.
• One thing we are very sure of is that the gas
constant, R, is in fact a constant. If we label
the properties of the state of the gas initially
by the subscript 1, then the state of the gas
initially is defined by:
• { n1, p1, V1, T1 }

6. .
• Later, the gas will be in a different
state, defined by new variables:
• { n2, p2, V2, T2 }

7. For any change in state of the
gas, (pV/nT) = R remains
unchanged, so

8. The Ideal Gas Equation of State
The Ideal Gas Equation of State
The three 'historical' gas laws are relationships
between two physical (state) properties of a
gas, with two other properties constant. (Why
does it take just four properties to define the
state of a gas?):

9. The Ideal Gas Equation of State.

10. .
These relationships can be combined into a
single relationship to make a more general gas
law:

11. .
If the proportionality constant is called "R", then
we have:

12. .
Rearranging to a more familiar form:
This equation is known as the Ideal-Gas
Equation of State

13. .
This equation works (approximately) for all gases
regardless of their Chemical Identity!

14. .
The constant R is called the UNIVERSAL GAS
CONSTANT, and is a fundamental conversion
factor. When we first contact an advanced
alien civilization, they will know a value of R
but it will convert their temperature to their
energy units, and will not be of great use to
us. We already have enough different units for
R (see below).

15. .
• The value and units of R depend on the units
used in determining P, V, n and T.
• Temperature, T, must always be expressed on
an absolute-temperature scale (K) (otherwise
Charles' Law doesn't work)

16. .
• The quantity of gas, n, is normally expressed
in moles. This is just a baker's dozen for
expressing the number of molecules

17. Units for the Gas Constant, R
Units Numerical Value
L . atm / mol . K 0.08206
cal / mol . K 1.987
J / mol . K 8.314
m3 . Pa / mol . K 8.314
L . torr / mol . K 62.36

18. Density
• Mass Density has the units of mass per unit
volume.
• Number Density has the units of molecules
(moles) per unit volume and is directly derived
from the Ideal Gas Equation of State:
• pV = nRT
(n/V) = p/RT

19. .
• (n/V) is the number density and has the units
of moles/liter. If we know the molecular mass
of the gas, we can convert this into
grams/liter (mass/volume). The molar mass
(M) is the number of grams in one mole of a
substance. If we multiply both sides of the
above equation by the molar mass:

20. where d is the number of grams per unit volume, or the mass
per unit volume (which is the MASS DENSITY)

21. Use of the Ideal Gas Equation
• Numerical Example:
1.00 mol of gas at 1.00 atm of pressure at
0.00°C (273.15 K) occupies what Volume?
• pV = nRT
V = nRT/p
V = (1.00 mol)(0.0821 L atm/mol K)(273.15 K)
/ (1.00 atm)
Therefore: V = 22.4 L

22. Relationship Between the Ideal-Gas
Equation and the Gas Laws
• Boyle's law, Charles's law and Avogadro's law all
represent special cases of the Ideal Gas law
(equation)
• If the quantity of gas and the temperature are
held constant then:
pV = nRT
V = nRT / p
V= (nRT) * (1/p)
V= constant * (1/p)
(Boyle's law)