1. Borrowed from: L. Scheffler Lincoln High School
Gas Laws
Borrowed from:
L. Scheffler
Lincoln High School
Scheffler 1

2. Properties of Gases Variable volume and shape
Expand to occupy volume available
Volume, Pressure, Temperature, and the number of moles present are interrelated
Can be easily compressed
Exert pressure on whatever surrounds them
Easily diffuse into one another
Scheffler 2

3. Kinetic Molecular Theory
Matter consists of particles (atoms or molecules) that are in continuous, random, rapid motion
The Volume occupied by the particles has a negligibly small effect on their behavior
Collisions between particles are elastic (no Energy is lost)
Attractive forces between particles have a negligible effect on their behavior
Gases have no fixed volume or shape, but take the volume and shape of the container
The average kinetic energy of the particles is proportional to their Kelvin temperature
Scheffler 3

4. Maxwell-Boltzman Distribution
Molecules are in constant motion
Not all particles have the same energy
The average kinetic energy is related to the temperature
An increase in temperature spreads out the distribution and the mean speed is shifted upward
Scheffler 4

5. Velocity of a Gas The distribution of speeds of three different gases
at the same temperature
The distribution of speeds
for nitrogen gas molecules
at three different temperatures
Scheffler 5

6. Mercury Barometer Used to define and measure atmospheric pressure
On the average at sea level the column of mercury rises to a height of about 760 mm.
This quantity is equal to 1 atmosphere
It is also known as standard atmospheric pressure
Scheffler 6

7. Barometer
The mercury barometer was the basis for defining pressure, but it is difficult to use or to transport
Furthermore Mercury is very toxic and seldom used anymore
Most barometers are now aneroid barometers or electronic pressure sensors
Scheffler 7

8. Pressure Units & Conversions
The above represent some of the more common units for measuring pressure. The standard SI unit is the Pascal or kilopascal. (kPa)
The US Weather Bureaus commonly report atmospheric pressures in inches of mercury.
Pounds per square inch or PSI is widely used in the United States.
Most other countries use only the metric system.
Two other older units for pressure are still used
millimeters of mercury (mm Hg)
atmospheres (atm)
Scheffler 8

9. Standard Temperature and Pressure (STP)
The volume of a gas varies with temperature and pressure. Therefore it is helpful to have a convenient reference point at which to compare gases.
For this purpose, standard temperature and pressure are defined as:
Temperature = 0oC K
Pressure = 1 atmosphere
= torr
= kPa
This point is often called STP
Scheffler 9

10. Dalton’s Law of Partial Pressures
The total pressure of a mixture of gases is equal to the sum of the pressures of the individual gases (partial pressures).
PT = P1 + P2 + P3 + P
where PT = total pressure
P1 = partial pressure of gas 1
P2 = partial pressure of gas 2
P3 = partial pressure of gas 3
P4 = partial pressure of gas 4
Scheffler 10

11. Dalton’s Law of Partial Pressures
Determine the partial pressure of each gas in a vessel that holds 2.50 mole of O2, 1.00 mole of N2 and 0.50 mole of CO2.
The total pressure in the vessel is 96.0 kPa.
2.50 mol mol mol = 4.00 mol
2.50/4.00 = x 96.0 kPa = 60.0 kPa O2
1.00/4.00 = x 96.0 kPa = 24.0 kPa N2
0.50/4.00 = x 96.0 kPa = 12.0 kPa CO2
kPa Total
Scheffler 11

12. Dalton’s Law of Partial Pressures
Applies to a mixture of gases
Very useful correction when collecting gases over water since they inevitably contain some water vapor.
Scheffler 12

13. Sample Problem 7
Henrietta Minkelspurg generates Hydrogen gas and collected it over water.
If the volume of the gas is 250 cm3 and the barometric pressure is torr at 25oC, what is the pressure of the “dry” hydrogen gas?
(PH2O = 23.8 torr at 25oC)
Scheffler 13

14. Boyle’s Law
According to Boyle’s Law the pressure and volume of a gas are inversely proportional at constant temperature.
PV = constant.
P1V1 = P2V2
Scheffler 14

15. Boyle’s Law A graph of pressure and volume gives an inverse function
A graph of pressure and the reciprocal of volume gives a straight line
Scheffler 15

16. Sample Problem 1:
If the pressure of helium gas in a balloon has a volume of 4.00 dm3 at 210 kPa, what will the pressure be at 2.50 dm3?
P1 V1 (conditions 1) = P2 V2 (new conditions)
(210 kPa) (4.00 dm3) = P2(2.50 dm3)
P2 = (210 kPa) (4.00 dm3)
(2.50 dm3)
= 340 kPa
Scheffler 16

17. Charles’ Law
According to Charles’ Law the volume of a gas is proportional to the Kelvin temperature as long as the pressure is constant
V = kT
Note: The temperature for gas laws must always be expressed
in Kelvin where Kelvin = oC (or 273 to 3 significant digits)
How do you remember? (Use Zero, get a Zero) V1 = T1 V2 T2
Scheffler 17

18. Pressure, Temperature, Volume
Pressure, temperature and volume of gases also have a relationship to each other.
That relationships is summarized with:
PTV
Scheffler 18

19. Charles’ Law A graph of temperature and volume yields a straight line.
Where this line crosses the x axis (x intercept) is defined as absolute zero
Scheffler 19

20. Sample Problem 2
A gas sample at 40 oC occupies a volume of 2.32 dm3. If the temperature is increased to 75 oC, what will be the final volume?
V1 = V2
T T2
Convert temperatures to Kelvin. 40oC = 313K
75oC = 348K
2.32 dm3 = V2
313 K K
(313K)( V2) = (2.32 dm3) (348K)
V2 =
2.58 dm3
Scheffler 20

21. Gay-Lussac’s Law P1 = P2 T2 T1
Gay-Lussac’s Law defines the relationship between pressure and temperature of a gas.
The pressure and temperature of a gas are directly proportional
P = P2 T2 T1
Scheffler 21

22. Sample Problem 3:
The pressure of a gas in a tank is 3.20 atm at 22 oC. If the temperature rises to 60oC, what will be the pressure in the tank?
P1 = P2
T T2
Convert temperatures to Kelvin. 22oC = 295K
60oC = 333K
3.20 atm = P2
295 K K
(295K)( P2) = (3.20 atm)(333K)
P2 =
3.6 atm
Scheffler 22

23. The Combined Gas Law
1. If the amount of the gas is constant, then Boyle’s Charles’ and Gay-Lussac’s Laws can be combined into one relationship
P1 V = P2 V2 T1 T2
Scheffler 23

24. Sample Problem 4:
A gas at 110 kPa and 30 oC fills a container at 2.0 dm3. If the temperature rises to 80oC and the pressure increases to 440 kPa, what is the new volume?
P1V1 = P2V2
T T2
Convert temperatures to Kelvin. 30oC = 303K
80oC = 353K
V2 = V1 P1 T2
P2 T1
= (2.0 dm3) (110 kPa ) (353K)
(440 kPa ) (303 K)
V2 = 0.58 dm3
Scheffler 24

25. Advogadro’s Law
Equal volumes of a gas under the same temperature and pressure contain the same number of particles.
If the temperature and pressure are constant the volume of a gas is proportional to the number of moles of gas present
V = constant * n
where n is the number of moles of gas
V/n = constant
V1/n1 = constant = V2 /n2
V1/n1 = V2 /n2
Scheffler 25

26. Universal (Ideal) Gas Equation
Based on the previous laws there are four factors that define the quantity of gas: Volume, Pressure, Kelvin Temperature, and the number of moles of gas present (n).
Putting these all together: PV nT
= Constant = R
The proportionality constant R is known as the
universal (Ideal) gas constant
Scheffler 26

27. Universal (Ideal) Gas Equation
The Universal (Ideal) gas equation is usually written as
PV = nRT
Where P = pressure
V = volume
T = Kelvin Temperature
n = number of moles
The numerical value of R depends on the pressure unit (and perhaps the energy unit) Some common values of R include:
R = dm3 torr mol-1 K-1
= dm3 atm mol-1 K-1
= dm3 kPa mol-1 K-1
Scheffler 27

28. Sample Problem 5 Example: What volume will 25.0 g O2 occupy
at 20oC and a pressure of atmospheres? :
(25.0 g)
n = = mol
(32.0 g mol-1)
Data
Formula
Calculation
Answer
V =? P = atm; T = ( )K = 293K
R = dm3 atm mol-1 K-1
PV = nRT so V = nRT/P
V = (0.781 mol)( dm3 atm mol-1 K-1)(293K)
0.880 atm
V = 21.3 dm3
Scheffler 28

29. d is the density of the gas in g/L
Universal Gas Equation –Alternate Forms
Density (d) Calculations PV=nRT
d = mass/Volume
n= moles …which can be equal to: mass (g)
Molar Mass (g/mol)
Substituting: = PM RT m V
m is the mass of the gas in g
d =
M is the molar mass of the gas
Molar Mass (M ) of a Gaseous Substance
dRT P
d is the density of the gas in g/L
M =
Scheffler 29

30. Sample Problem 6 dRT m M = d = = = 2.21 V P x 0.0821 x 300.15 K M =
A 2.10 dm3 vessel contains 4.65 g of a gas at 1.00 atmospheres and 27.0oC. What is the molar mass of the gas?
dRT P
M =
d = m V
4.65 g
2.10 dm3 =
= 2.21 g
dm3
2.21 g
dm3
1 atm
x x K
dm3•atm
mol•K
M =
M =
54.6 g/mol
Scheffler 30

31. “Stupid” Gas Laws… How did all these gas laws “come to be”????
All are based on the Ideal Gas Law for 2 sets of conditions.
Remember: PV = nRT
we can rearrange things to solve for a constant (R)
R=PV/nT n=# moles. (Not going to change when conditions change)
Therefore, if moles don’t change: R=PV/T
If we look at a gas that changes from one condition
P1V1 = nRT1 to a new condition P2V2 = nRT2, we can set up a relationship (moles don’t change and R is constant)
P1V1/T1 = R = V2P2/T2
P1V1/T1 = V2P2/T2 (Combined Gas Law)
Scheffler 31

32. “Stupid” Gas Laws (cont.)
P1V1 = P2V2 If Temperature is constant P1V1 = P2V2
T T2 (Boyle’s Law) T T2
P1V1 = P2V2 If Volume is constant P1V1 = P2V2
T T2 (Gay-Lassac’s Law) T T2
P1V1 = P2V2 If Pressure is constant P1V1 = P2V2
T T (Charles’ Law) T T2
P1V1 = P2V2 If Pressure & T are constant P1V1 = P2V2
n1T1 n2T n1T1 n2T2
Scheffler 32

33. Diffusion
Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties.
NH4Cl
NH3
17.0 g/mol
HCl
36.5 g/mol
Scheffler 33

34. DIFFUSION AND EFFUSION
Diffusion is the gradual mixing of molecules of different gases.
Effusion is the movement of molecules through a small hole into an empty container.
Scheffler 34

35. Graham’s Law (For Information only: do not need to know how to do this)
Graham’s law governs effusion and diffusion of gas molecules.
KE=1/2 mv2
(don’t need to know this)
The rate of effusion is inversely proportional to its molar mass.
Thomas Graham, Professor in Glasgow and London.
Scheffler 35

36. Kinetic Molecular Theory
Matter consists of particles (atoms or molecules) that are in continuous, random, rapid motion
The Volume occupied by the particles has a negligibly small effect on their behavior
Collisions between particles are elastic (no Energy is lost)
Attractive forces between particles have a negligible effect on their behavior
Gases have no fixed volume or shape, but take the volume and shape of the container
The average kinetic energy of the particles is proportional to their Kelvin temperature
Scheffler 36

37. Ideal Gases v Real Gases
Ideal gases are gases that obey the Kinetic Molecular Theory perfectly.
The gas laws apply to ideal gases, but in reality there is no perfectly ideal gas.
Under normal conditions of temperature and pressure many real gases approximate ideal gases.
Under more extreme conditions more polar gases show deviations from ideal behavior.
Scheffler 37

38. Real Gases
For ideal gases the product of pressure and volume is constant. Real gases deviate somewhat as shown by the graph pressure vs. the ratio of observed volume to ideal volume below.
These deviations occur because
Real gases do not actually have zero volume
Polar gas particles do attract if compressed
Scheffler 38

39. In an Ideal Gas ---
The particles (atoms or molecules) in continuous, random, rapid motion.
The particles collide with no loss of momentum
The volume occupied by the particles is essentially zero when compared to the volume of the container
The particles are neither attracted to each other nor repelled
The average kinetic energy of the particles is proportional to their Kelvin temperature
At normal temperatures and pressures gases closely approximate ideal behavior
Scheffler 39

40. van der Waals Equation (For Information only: do not need to know how to do this)
The van der Waals equation shown below includes corrections added to the universal gas law to account for these deviations from ideal behavior
(P + n2a/V2)(V - nb) = nRT
where a => attractive forces between molecules
b => residual volume or molecules
The van der Waals constants for some elements are shown below
Substance
a (dm6atm mol-2)
b (dm3 mol-1) He
0.0341
CH4
2.25
0.0428
H2O
5.46
0.0305
CO2
3.59
0.0437
Scheffler 40