Characteristics of Gases
• Unlike liquids and solids, gases
– expand to fill their containers;
– are highly compressible;
– have extremely low densities.

Pressure
• Pressure is the amount of force applied to an area.
F
P =
A
• Atmospheric pressure is the weight of air per unit of area.

Units of Pressure
• Pascals
– 1 Pa = 1 N/m 2
• Bar
– 1 bar = 10 5 Pa = 100 kPa

Units of Pressure
• mm Hg or torr
–These units are literally the difference in the heights measured in mm
( h ) of two connected columns of mercury.
• Atmosphere
–1.00 atm = 760 torr = 101.3 kPa

Manometer
This device is used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel.

Standard Pressure
• Normal atmospheric pressure at sea level is referred to as standard pressure .
• It is equal to
– 1.00 atm
– 760 torr (760 mm Hg)
– 101.325 kPa

Boyle’s Law
The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.

As P and V are inversely proportional
A plot of V versus P results in a curve.
Since PV = k
V = k (1/ P )
This means a plot of
V versus 1/ P will be a straight line.

Examples
• What would the final volume be if 247 mL of gas at
22ºC is heated to 98ºC , if the pressure is held constant?

Charles’s Law
• The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature.
• i.e.,
V
T
= k
A plot of V versus T will be a straight line.

Examples
• At what temperature would 40.5 L of gas at 23.4ºC have a volume of 81.0 L at constant pressure?

Avogadro’s Law
• The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas.
• Mathematically, this means V = kn

Examples
• A deodorant can has a volume of 175 mL and a pressure of 3.8 atm at 22ºC. What would the pressure be if the can was heated to 100.ºC?
• What volume of gas could the can release at 22ºC and 743 torr?

Ideal-Gas Equation
• So far we’ve seen that
V
=
1/ P (Boyle’s law)
V
=
T (Charles’s law)
V
= n (Avogadro’s law)
• Combining these, we get
V = nT
P

Ideal-Gas Equation
The constant of proportionality is known as R , the gas constant.

Ideal-Gas Equation
The relationship then becomes
V = nT
P
V = R nT
P or
PV = nRT

Examples
• Kr gas in a 18.5 L cylinder exerts a pressure of 8.61 atm at
24.8ºC What is the mass of Kr?
• A sample of gas has a volume of 4.18 L at 29ºC and 732 torr . What would its volume be at 24.8ºC and 756 torr?

Examples
• Mercury can be produced by the following decomposition:
• HgO 
• What volume of oxygen gas can be produced from
4.10 g of mercury (II) oxide at 400.ºC and 740 torr?

Densities of Gases
If we divide both sides of the ideal-gas equation by V and by RT , we get n
V
=
P
RT

Densities of Gases
• We know that
– moles  molecular mass = mass n
 
= m
• So multiplying both sides by the molecular mass (

) gives m P

=
V RT

Densities of Gases
• Mass  volume = density
• So, d = m
V
=
P

RT
Note: One only needs to know the molecular mass, the pressure, and the temperature to calculate the density of a gas.

Molecular Mass
We can manipulate the density equation to enable us to find the molecular mass of a gas:
P
 d =
RT
Becomes

= dRT
P

Examples
• Complete and balance the following equation:
• NaHCO
3
+ HCl 
• calculate the mass of sodium hydrogen carbonate necessary to produce 2.87-L of carbon dioxide at 25ºC and 2.00 atm.
• If 27 L of gas are produced at 26ºC and 745 torr when
2.6-L of HCl are added what is the concentration of HCl?

Examples
• Consider the following reaction
• NH
3
+ O
2
 NO
2
+ H
2
O (balance first!)
• What volume of NO
2 at 1.0 atm produced from 10.0 L of NH
3 and 1000.ºC can be and excess O same temperature and pressure?
2 at the
• What volume of O
2 measured at STP will be consumed when 10.0 kg NH
3 is reacted?

Dalton’s Law of
Partial Pressures
• The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone.
• In other words,
P total
= P
1
+ P
2
+ P
3
+ …

Partial Pressures
• When one collects a gas over water, there is water vapor mixed in with the gas.
• To find only the pressure of the desired gas, one must subtract the vapor pressure of water from the total pressure.

Examples
• The partial pressure of nitrogen in air is 592 torr. Air pressure is 752 torr, what is the mole fraction of nitrogen?
• What is the partial pressure of nitrogen if the container holding the air is compressed to 5.25 atm?

Examples
4.00 L
CH
4
1.50 L
N
2
3.50 L
O
2
2.70 atm 4.58 atm 0.752 atm
• When these valves are opened, what is each partial pressure and the total pressure?

• N
2
Example
O can be produced by the following reaction
NH
4
NO
3
(s)  N
2
O(g) + 2 H
2
O(l)
• What volume of N
2
O collected over water at a total pressure of 94 kPa and 22ºC can be produced from
2.6 g of NH
4
NO
22ºC is 21 torr)
3
? (the vapor pressure of water at

Kinetic-Molecular Theory
This is a model that aids in our understanding of what happens to gas particles as environmental conditions change.

Main Tenets of Kinetic-
Molecular Theory
Gases consist of large numbers of molecules that are in continuous, random motion.

Main Tenets of Kinetic-
Molecular Theory
The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained.

Main Tenets of Kinetic-
Molecular Theory
Attractive and repulsive forces between gas molecules are negligible.

Main Tenets of Kinetic-
Molecular Theory
Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant.

Main Tenets of Kinetic-
Molecular Theory
The average kinetic energy of the molecules is proportional to the absolute temperature.

Effusion
Effusion is the escape of gas molecules through a tiny hole into an evacuated space.

Effusion
The difference in the rates of effusion for helium and nitrogen, for example, explains a helium balloon would deflate faster.

Diffusion
Diffusion is the spread of one substance throughout a space or throughout a second substance.

• (KE) avg
= N
A
(1/2 mu 2 )
• [m is mass of one gas particle in kg]
• (KE) avg
= 3/2 RT so…..
u rms
= (3RT/M kg
) 1/2
• Where M kg is the molar mass in kilograms, and R has the units 8.314 kg-m 2 / s 2 -mol-K or J/K-mol.
• The velocity will be in m/s

Graham's Law
KE
1
= KE
2
1/2 m
1 v
1
2 = m
1 m
2
=
1/2 m
2 v
2
2 v v
2
2
1
2
 m
1
 m
2
=
 v
 v
2
2
1
2
= v
2 v
1

Example
• Calculate the root mean square velocity of carbon dioxide at 25ºC.

Examples
• A compound effuses through a porous cylinder 1.60 times faster than chlorine. What is it’s molar mass?

• If 0.00251 mol of NH
3 effuses through a hole in 2.47 min, how much HCl would effuse in the same time?

• A sample of N
2 effuses through a hole in 38 seconds. what must be the molecular weight of gas that effuses in 55 seconds under identical conditions?

Real Gases
In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure.

Real Gases
Even the same gas will show wildly different behavior under high pressure at different temperatures.

Deviations from Ideal Behavior
The assumptions made in the kinetic-molecular model (negligible volume of gas molecules themselves, no attractive forces between gas molecules, etc.) break down at high pressure and/or low temperature.

Corrections for Nonideal
Behavior
• The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account.
• The corrected ideal-gas equation is known as the van der Waals equation .

The van der Waals Equation
( P + n 2 a
V 2
) ( V − nb ) = nRT

Example
• Calculate the pressure exerted by 0.5000 mol Cl
2
1.000 L container at 25.0ºC in a
• Using the ideal gas law.

• Van der Waals equation given: a = 6.49 atm L 2 /mol 2 b = 0.0562 L/mol