1. *Gas Laws*

2. Physical Characteristics of Gases Physical Characteristics
Typical Units
Volume, V
liters (L)
Pressure, P
atmosphere
(1 atm = 1.015x105 N/m2)
Temperature, T
Kelvin (K)
Number of atoms or molecules, n
mole (1 mol = 6.022x1023 atoms or molecules)

3. “Father of Modern Chemistry” Chemist & Natural Philosopher
Boyle’s Law
Pressure and volume are inversely related at constant temperature.
PV = K
As one goes up, the other goes down.
P1V1 = P2V2
“Father of Modern Chemistry”
Robert Boyle
Chemist & Natural Philosopher
Listmore, Ireland
January 25, 1627 – December 30, 1690

4. Boyle’s Law: P1V1 = P2V2

5. Boyle’s Law: P1V1 = P2V2

6. Jacques-Alexandre Charles Mathematician, Physicist, Inventor
Charles’ Law
Volume of a gas varies directly with the absolute temperature at constant pressure.
V = KT
V1 / T1 = V2 / T2
Jacques-Alexandre Charles
Mathematician, Physicist, Inventor
Beaugency, France
November 12, 1746 – April 7, 1823

7. Charles’ Law: V1/T1 = V2/T2

8. Charles’ Law: V1/T1 = V2/T2

9. Avogadro’s Law
At constant temperature and pressure, the volume of a gas is directly related to the number of moles.
V = K n
V1 / n1 = V2 / n2
Amedeo Avogadro
Physicist
Turin, Italy
August 9, 1776 – July 9, 1856

10. Avogadro’s Law At the same P and T equal Volumes of gas
contain the same # of molecules
Na = 6.023X1023 molecules/ mole

11. Avogadro’s Law: V1/n1=V2/n2

12. Joseph-Louis Gay-Lussac
Gay-Lussac Law (Pressure Law)
At constant volume, pressure and absolute temperature are directly related.
P = k T
P1 / T1 = P2 / T2
Joseph-Louis Gay-Lussac
Experimentalist
Limoges, France
December 6, 1778 – May 9, 1850

13. Eaglesfield, Cumberland, England
Dalton’s Law
The total pressure in a container is the sum of the pressure each gas would exert if it were alone
in the container.
The total pressure is the sum of the partial pressures.
PTotal = P1 + P2 + P3 + P4 + P5 ...
(For each gas P = nRT/V)
John Dalton
Chemist & Physicist
Eaglesfield, Cumberland, England
September 6, 1766 – July 27, 1844

14. Dalton’s Law

15. Only at very low P and high T
Differences Between Ideal and Real Gases
Ideal Gas
Real Gas
Obey PV=nRT
Always
Only at very low P and high T
Molecular volume
Zero
Small but nonzero
Molecular attractions
Small
Molecular repulsions

16. Johannes Diderik van der Waals Mathematician & Physicist
Van der Waal’s equation
Corrected Pressure
Corrected Volume
“a” and “b” are
determined by experiment
different for each gas
bigger molecules have larger “b”
“a” depends on both
size and polarity
Johannes Diderik van der Waals
Mathematician & Physicist
Leyden, The Netherlands
November 23, 1837 – March 8, 1923

17. The Ideal Gas Ideal gas properties
Volume of gas molecules is negligible compared with gas volume
Forces of attraction or repulsion between molecules or walls of container are zero
No loss of internal energy due to collisions

18. Derivation of the kinetic theory formula
This proof was originally proposed by Maxwell in He considered a gas to be a collection of molecules and made the following assumptions about these molecules:
molecules behave as if they were hard, smooth, elastic spheres
molecules are in continuous random motion
the average kinetic energy of the molecules is proportional to the absolute temperature of the gas

19. Assumptions contd.
the molecules do not exert any appreciable attraction on each other
the volume of the molecules is infinitesimal when compared with the volume of the gas
the time spent in collisions is small compared with the time between collisions

20. Consider a volume of gas V enclosed by a cubical box of sides L
Consider a volume of gas V enclosed by a cubical box of sides L. Let the box contain N molecules of gas each of mass m, and let the density of the gas be r. Let the velocities of the molecules be u1, u2, u3 . . . uN. (Figure 2)

21. Consider a molecule moving in the x-direction towards face A with velocity u1. On collision with face A the molecule will experience a change of momentum equal to 2mu1.
It will then travel back across the box, collide with the opposite face and hit face A again after a time t, where t = 2L/u1.

22. The number of impacts per second on face A will therefore be 1/t = u1/2L. Therefore rate of change of momentum = [mu12]/L = force on face A due to one molecule. But the area of face A = L2, so pressure on face A = [mu12]/L3

23. But there are N molecules in the box and if they were all travelling along the x-direction then Total pressure on face A = [m/L3](u12 + u22 +...+ uN2)

24. But on average only one-third of the molecules will be travelling along the x-direction.  Therefore: pressure = 1/3 [m/L3](u12 + u22 +...+ uN2)

25. If we rewrite Nc2 = [u12 + u22 + …+ uN2 ] where c is the mean square velocity of the molecules: pressure = 1/3 [m/L3]Nc2 But L3 is the volume of the gas and therefore:
Pressure (P) = 1/3 [m/V]Nc2 and so PV = 1/3 [Nmc2] and this is the kinetic theory equation.

26. Pressure (P) = 1/3 [ρc2]
The root mean square velocity or r.m.s. velocity is written as c r.m.s. and is given by the equation: r.m.s. velocity = c r.m.s. = [c2]1/2 = [u12 + u22 + …+ uN2 ]1/2/N We can use this equation to calculate the root mean square velocity of gas molecules at any given temperature and pressure.