Chapter 9

The Gaseous State



9-1 The Nature of Gases and the Kinetic Molecular Theory

l   Describe the qualitative properties common to all gases

l   List five common properties of all gases.

l   Apply the kinetic molecular theory of gases to explain their common properties.

l   Apply Grahams Law to the relationship between the average velocity of a gas and its molar mass.


9-2 The Pressure of a Gas

l   Distinguish between force and pressure

l   Convert among the various units used to describe pressure.

9-3 Boyle’s Law

l   Apply Boyle’s Law to calculate the effect of pressure changes on the volume

l   Describe the basis for Boyle’s law from kinetic theory.

9-4 Charles’s Law and Gay-Lussac’s Law

l   Use Charles law to calculate the effect of temperature changes on the volume

l   Calculate the effect of a change of temperature on the pressure of a gas by application of Gay Lussac’s law.

l   Apply Kinetic theory to describe the basis of Charles’s Law and Gay-Lussac’s Law

l   Apply the combined gas law.

9-5 Avagadro’s Law

l   Describe the effect on the volume of a gas by adding a specified amount of gas

9-6 The Ideal Gas Law

l   Calculate a milling variable (P, V, T) for a gas under two sets of conditions

l   Describe the effect on the volume of a gas by adding a specified amount of gas.

l   Use the Ideal Gas Law to calculate an unknown property of a sample of gas (P, V, T, or n) when the other properties are known.

9-7 Dalton’s Law of Partial Pressures

l   Carry out gas law calculations for a mixture of gases.

l    Convert between moles of gas and volume at STP using the molar volume as a conversion factor

9-8 The Molar Volume and Density of a Gas

l    Calculate the density of a gas at STP or other conditions

l   Apply the ideal gas law or the molar volume relationship to stoichiometry problems involving gases


      Gases are all around us and are necessary for life

l    Greenhouse

l    Ozone Depletion

      Development of Earth as an environment suitable for living

      They can be harnessed to do work

l    Engines

l    Pneumatic devices

Characteristics of Gases

      Primarily made up of nonmetals

      Have low densities

      Diffuse rapidly and completely through each other

      Expand volume to completely fill container


      Exert pressure uniformly on container

Kinetic Molecular Theory

      Explains the properties of gases


l    Gases consist of small molecules that are in constant random motion.

l    The volumes of all molecules of a gas are small compared to the space between molecules (A gas is mostly empty space).

l    Intermolecular forces between particles are negligible

l    Collisions between molecules and with their container are perfectly elastic.

l    Ave. K.E. of the molecules is proportional to absolute T.

Temperature and Kinetic Energy

       Average k.e.  = ª = 1/2mv2

l   m = mass

l   v = velocity

      Ave K.E. encompasses molecules that have varying speeds.


Graham’s Law

      ½m1v12 = ½m2v2 2  rearranging gives

      r1/r2 =[M2/M1]1/2  = v1/v2         r = rate

      The rates of diffusion (mixing) of two gases under identical conditions is inversely proportional to the square root of their molar masses.

      lighter molecules diffuse faster.

Measuring Gases

      In order to describe a sample of gas completely four quantities have to be addressed

l    Amount of gas (n) - moles of gas    n =   mass

                                                    Molar Mass

l    Volume (V) - The volume of a container holding a gas

l    Temperature (T)- in Kelvin

l    Pressure (P)- Force per unit area F/A (SI unit is Pascal)

Atmospheric Pressure

      Gravity causes our atmospheric gases to exert force and therefore a pressure on the Earth’s surface

l   A column of air 1 m2  has a mass of 10,000 kg  

l   F=ma    agravity= 9.8m/s2

l   10,000 kg (9.8m/s2)  = 1 x105 kg-m/s2 = 1 x 105 Newtons (N)


= [1 x 105 N / 1 m2] = 1 x 105 N/m2 = 1 x 105 Pascal (Pa)

      Atmospheric pressure depends on altitude and weather conditions






       Used to Measure Atmospheric Pressure

       Made by inverting a glass tube containing mercury into a dish containing mercury.

l    all air evacuated.

l    Void space is nearly a vacuum, only small amount of mercury vapor present.

       The mercury in the dish experiences atmospheric pressure

l    As atmospheric pressure changes the level of mercury in the tube will change

l    Standard atmospheric pressure at sea level is  = 760 mmHg = 760 torr = 1 atm = 101.3 kPa

Boyle’s Law
 Pressure -Volume

      The volume of a fixed quantity of gas maintained at constant temperature is inversely proportional to the pressure.

l    V = constant x  1/P or PV = constant

l     Therefore,   P1V1 = P2 V2

      The value of the constant depends on the temperature and the amount of gas in the sample

l    Examples:

l   Breathing

l   scuba

l   Cartesian divers

Charles Law
Temperature - Volume

      The volume of a fixed amount of gas maintained at constant pressure is directly proportional to its absolute temperature.

l    V = constant x T   or   V/T = constant

l     Therefore,  V1/T1 = V2/T2

       Based on Charles’ observation, Lord Kelvin (William Thomson)  noted that extrapolation of volume temperature lines for all gases intersect the temp axis at –273.15 ¢ªC, lead to the development of the absolute temperature scale. 0 K corresponds to no translational motion.


Guy Lussac’s Law

      The pressure of a gas is directly proportional to the Kelvin temperature at constant volume.

      P= kT

       P1 = P2

   T1     T2


Combined Gas Law

      Puts Charles, Boyles and Guy Lussac’s all together in one law

      PV = k


       P1V1 = P2V2

     T1        T2

       P1V1 T2 = P2V2 T1

Avogadro’s Law

      Equal volumes of gases at the same temperature and pressure contain the same number of molecules.

      The volume of a gas is proportional to the number of molecules (moles)  of gas present at constant pressure and temperature

       V = kn              V1 = V2

                          n1     n2

Molar Volume

      Molar Volume – the volume of one mole of gas at STP, 22.4 L.

      Because the particle size of gas molecules is so small compared to the space between them all gas samples containing equal numbers of particles at similar conditions will occupy the same volume.

Ideal gas Law

      Boyles law:      V = k1 1/P  (constant n,T)

      Charles law       V = k2 T        (constant n,P)

      Avogadro’s law  V = k3 n (constant P, T)

      Combining the constants (k1, k2, k3) into a proportionality constant R and combing the equations we get

      V= R[nT/P]   or  PV = nRT



Ideal Gas Law (Cont’d)

      An ideal gas is a hypothetical gas whose pressure, volume and temperature behavior is completely explained by the ideal gas equation.

      R – is called the Universal Gas Constant

l    The value of R depends on the units of P, V, n and T.

l    Most commonly R = 0.08206 L-atm/mol-K

Dalton’s Law of Partial Pressures

      The total pressure of a gas in a system is the sum of the partial pressures of each component gas

      Partial Pressure - The pressure exerted by a particular component in a mixture of gases.

      PT = P1 + P2 + P3 + …

      PT = n1[RT/V] + n2[RT/V] +…

Density of a Gas

      Density = mass/volume

      Ideal Gas Law can be expressed as

l   N/V = P/RT

l   nM/V =PM/RT

l   M is molar mass

      Therefore density of a gas is

l   D = PM/RT  and

l   M = dRT/P