1. Gases

2. Parameters to describe gases:
Pressure
Temperature
number of molecules
Volume

3. Pressure
force = m x a = kg x m/s2 = Newton
area (N)
Barometer – a device used to measure atmospheric pressure.
Evangelista Torricelli (early
1600s) used mercury for the
first type of barometer

5. Units of pressure
760 mm Hg = 760 torr = 1 atmosphere (atm) = kPa (kilopascals) = 14.7 psi
The SI unit for pressure is named after Blaise Pascal. A Pascal is defined as 1 Newton acting on an area of one square meter. 1 N/m2

6. Relationship between Pressure, Force, and Area
Force = mass x acceleration
(On Earth acceleration is a constant due to gravity)
Force =
500 N
Force =
500 N
Area of contact = 325 cm2
Pressure = force
area
= 500 N = 1.5 N/cm2
325 cm2
Area of contact = 13 cm2
Pressure = force
area
= 500 N = 38.5 N/cm2
13cm2
Area of contact = 6.5 cm2
Pressure = force
area
= 500 N = 77 N/cm2
6.5 cm2

7. STP Kelvin = °C + 273 Standard temperature and pressure are defined
as 1 atm of pressure and 0C.
When describing gases Kelvin temperature is typically used.
Kelvin = °C + 273

8. Graham’s Law

9. NH3 + HCl  NH4Cl

10. Graham’s law of Effusion
The rates of effusion of gases at the same T and P are inversely proportional to the square roots of their molar masses.

11. Derivation of Graham’s Law
Comparing two gases, “A” and “B.”
At the same T their KE is equal.
KEA = KEB
½ MAvA2 = ½ MBvB2
Multiplying both sides by 2 and rearranging to
compare velocities gives:
vA2 = MB
vB MA

12. 𝑉𝐴 𝑉𝐵 = 𝑀𝐵 𝑀𝐴 Now, take the square root of both sides: This shows that
𝑉𝐴 𝑉𝐵 = 𝑀𝐵 𝑀𝐴
This shows that
𝒓𝒂𝒕𝒆 𝒐𝒇 𝒆𝒇𝒇𝒖𝒔𝒊𝒐𝒏 𝒐𝒇 𝑨 𝒓𝒂𝒕𝒆 𝒐𝒇 𝒆𝒇𝒇𝒖𝒔𝒊𝒐𝒏 𝒐𝒇 𝑩 = 𝑀𝐵 𝑀𝐴
This can also be used when dealing with densities
of gases.
𝒓𝒂𝒕𝒆 𝒐𝒇 𝒆𝒇𝒇𝒖𝒔𝒊𝒐𝒏 𝒐𝒇 𝑨 𝒓𝒂𝒕𝒆 𝒐𝒇 𝒆𝒇𝒇𝒖𝒔𝒊𝒐𝒏 𝒐𝒇 𝑩 = 𝑀𝐵 𝑀𝐴 = 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝐵 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝐴

13. Dalton’s Law of partial pressures
The total pressure of a mixture of gases is
equal to the sum of the partial pressures of
the component gases.
PT = P1 + P2 + P
artifacts/images/2-1-med.jpg

14. Collecting gases over water
Many gases are collected over water, thus according to Dalton’s law of partial pressures you must account for the vapor pressure of the water.
Patm = Pgas + PH2O
A table of water vapor
pressures will be
provided for you.

15. P1V1 = P2V2 PV = k Boyle’s Law - 1662
pressure-volume relationship: the
volume of a fixed mass of gas varies
inversely with the pressure at constant
temperature
PV = k
P1V1 = P2V2

16. Boyle’s Law graph

17. Charles’s Law - 1787 V = k V1 = V2 T T1 T2 (Kelvin temp)
volume-temperature relationship: volume of a fixed mass
of gas at constant pressure varies directly with the Kelvin
temperature.)
His experiments showed that all gases expand to the
same extent when heated through the same temperature
interval. Charles found that the volume changes by 1/273
of the original volume for each Celsius degree, at constant
pressure and an initial temperature of 0C.
V = k V1 = V2
T T1 T (Kelvin temp)

18. Charles’s Law graph

19. Gay-Lussac’s Law
pressure-temperature relationship: The pressure
of a fixed mass of gas at constant volume varies
directly with the Kelvin temperature. For every
Kelvin of temperature change, the pressure of a
confined gas changes by 1/273 of the pressure at
0C.
P = k P1 = P2 (Kelvin temp)
T T1 T2

20. Gay-Lussac graph

21. T T1 T2 Combined gas law pressure, volume and temperature relationship
PV = k P1V1 = P2V2
T T T2
(Kelvin temp)

22. Gay-Lussac’s Law of Combining Volumes - 1808
at a constant T and P, the volumes of gaseous reactants and products can be expressed as ratios of small whole numbers.

23. standard molar volume of gas
Avogadro’s Law
equal volumes of gases at the same T and P
contain the same number of molecules.
The volume occupied by one mole of a gas at
STP is known as
standard molar volume of gas
22.4 liters.

24. Ideal Gas Law
The Ideal Gas Law is the mathematical relationship among pressure, volume, temperature, and the number of moles of a gas.
Combining Boyle’s Law, Charles’s Law and Avogadro’s Law gives us V = nRT or more P
commonly seen as PV = nRT

25. R – the ideal gas law constant
R = PV = (1 atm)(22.4 l) = l·atm
nT (1 mol)(273.15K) mol·K
Other values for R (depending on P units)
62.4 l·torr (or mm Hg) l ·kPa
mol ·K mol· K

26. Variations on the ideal gas law
Variations on the ideal gas law can be used to find
Molar mass or density. (n [moles] = m/M)
PV = mRT or M = mRT m= mass
M PV M = molar mass
Density is m/V so substituting that into the ideal gas equation gives us
M = mRT = DRT which then gives us D = MP
PV P RT

27. Deviations of real gases from ideal behavior
The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other. Real molecules, however, do have finite volumes, and they do attract one another.
In 1873, Johannes van der Waals
accounted for this behavior by
devising a new equation (based on
the ideal gas law) to describe these
deviations

28. Van der Waals equation P = nRT - n2a V-nb V2
  Correction for Correction for
volume of molecules molecular attractions
The volume is decreased by the factor nb, which accounts for the
finite volume occupied by gas molecules. The pressure is
decreased by the second term, which accounts for the attractive
forces between gas molecules. The magnitude of a reflects how
strongly the gas molecules attract each other. The more polar
the molecules of a gas are, the more they will attract each other.
At very high pressures and very low temperatures deviations
from ideal behavior may be considerable.

29. Good videos for Gases
Leidenfrost Effect of H2O.
“boiling water at room temperature”
Balloons and marshmallows
Graham’s Law: 

30. Additional videos
Avogadro's Law: Avogadro's Law  (14:47 min)Boyle's Law: Boyle's Law (5:41 min)
Charles' Law: Charles' Law (6:41 min)
Combined Gas Law: Combined Gas Law (6:48 min)
Ideal Gas Law: Ideal Gas Law Introduction (6:18 min) 
How to rearrange the ideal gas law to form any of the other laws: Be Lazy! Don't Memorize the Gas Laws! (7:10 min)
Where the ideal gas law constant, R, comes from: Ideal Gas Law: Where did R come from? (3:31 min)