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Chapter 11 Molecular Composition of Gases

 

  1. Volume-Mass Relationships of Gases
    a) relationships between volume of gases in balanced equations
    b) relationship between volume, density and molar mass
    1. Measuring and Comparing the Volumes of Reacting Gases

      Gay-Lussac in the early 1800's studied volume relationships of gases in chemical reactions

      hydrogen + oxygen ---> water vapor
      2 L of hydrogen reacted with 1 L of oxygen ---> 2 L of water vapor
      2 volume of hydrogen + 1 volume of oxygen ---> 2 volumes of water vapor
      2 H2 + O2 ---> 2 H2O
      2:1:2 volume ratio for this reaction
      can be 2 mL + 1 mL ---> 2 mL or
      can be 10 L + 5 L ---> 10 L

      found the same situation in

      hydrogen + chlorine ---> hydrogen chloride gas
      1 L + 1 L ---> 2 L or
      1 volume + 1 volume ---> 2 volumes

      Led to Gay-Lussac's Law of Combining Volumes of Gases - statement

    2. Avogadro's Law

      Dalton originally thought that atoms were indivisible and that particles of gases exist as isolated single atoms.

      He also believed that one atom of one element combined with one atom of another element to form a compound.

      This idea created a problem for situation like the reaction to create water vapor:

      hydrogen + oxygen ---> water vapor
      2 L of hydrogen reacted with 1 L of oxygen ---> 2 L of water vapor
      2 volume of hydrogen + 1 volume of oxygen ---> 2 volumes of water vapor
      2 H2 + O2 ---> 2 H2O
      2:1:2 volume ratio for this reaction

      It led scientists to believe that the oxygen split into two parts to explain what was happening.

      Explained by Avogadro in 1811. He suggested that the particles of hydrogen and oxygen and water consisted of more that one atom joined together.

      Also postulated what is called Avogadro's Law - statement.

    3. Figure 11-1

      At the same temperature and pressure, the volume of any given gas varies directly with the number of molecules.

      For the reaction of hydrogen and chlorine to produce hydrogen chloride:
      hydrogen + chlorine ---> hydrogen chloride gas
      1 L + 1 L ---> 2 L or
      1 volume + 1 volume ---> 2 volumes

      Hydrogen chloride was analyzed to contain one hydrogen and one chlorine and so to explain how we get two volumes it is necessary to postulate the diatomic nature of both hydrogen and chlorine.

    4. Figure 11-2

      Gas volume is directly proportional to the number of moles or
      V = kn

      2 H2 + O2 ---> 2 H2O where

      2 molecules + 1 molecule ---> 2 molecules or

      2 mol + 1 mol --->2 mol or

      2 volumes + 1 volume ---> 2 volumes

    5. Molar Volume of Gases
      hydrogen one mol 6.02 x 1023 diatomic molecules 2(6.02 x 1023) atoms mass = 2.015 g
      oxygen one mol 6.02 x 1023 diatomic molecules 2(6.02 x 1023) atoms mass = 32.000 g
      helium one mol 6.02 x 1023 molecules 6.02 x 1023 atoms mass = 4.002 g

      Avogadro's law states that at the same temperature and pressure one mole of any gas will occupy the same volume as one mole of another gas even though their mass may be different.

      That volume is called the standard molar volume of a gas - definition.

      Use 22.4 L concept as a conversion factor to calculate the number of moles (and therefore the mass) if you know the volume a gas occupies at STP.

      Figure 11-3


      Sample Problem 11-1 page 336

      Given: 0.0680 mol oxygen; volume in L = ?; STP

      Conversion factor: 1 mol / 22.4 L or 22.4 L / 1 mol

      0.0680 mol x 22.4 L / 1 mol = 1.52 L



      Sample Problem 11-2 page 337

      A chemical reaction produced 98.0 mL of sulfur dioxide gas, SO2, at STP. What was the mass in grams of the gas produced?



      Homework: 11.1, Volume-Mass Relationship of Gases Problems/Questions.

  2. The Ideal Gas Laws

    This gas law brings the idea of moles into calculations for gases.

    Figure 11-4 page 340

    The Ideal Gas Law - statement

    The equation is called an equation of state for a gas because the particular state of a gas can be defined by its pressure, volume, temperature, and number of moles.
    1. Derivation of the Ideal Gas Law

      Will not go into detail about the derivation.

      PV = nRT

    2. The Ideal Gas Constant

      Figure 11-5

      The ideal gas constant is represented by the R in the ideal gas equation.

      Its value depends on the units used for pressure, volume, temperature, and number of particles.

    3. Note: the dashes are dashes -- not subtraction operators.
      1. Finding P, V, T, or n from the Ideal Gas Law

        a) If you know three of the four variables, you can calculate the fourth, using the ideal gas law, since R is a constant.

        b) can calculate the molar mass if you remember that


        moles equals

        c) can calculate density by manipulating the ideal gas law, keeping in mind that moles = g / molar mass and density is mass / volume. We get



        Sample Problem 11-3 page 343


        Sample Problem 11-5 page 344



        Homework: 11.2, Ideal Gas Constant - Finding P, V, T, or n from the Ideal Gas Law
      2. Finding Molar Mass or Density from the Ideal Gas Law

        for molar mass:


        for density:

        density equals formula
        Sample Problem 11-6 page 345


        Homework: 11.3, Ideal Gas Constant - Finding Molar Mass or Density from the Ideal Gas Law

    4. Stoichiometry of Gases

      2 H2 + O2 ---> 2 H2O where

      2 molecules + 1 molecule ---> 2 molecules or

      2 mol + 1 mol --->2 mol or

      2 volumes + 1 volume ---> 2 volumes

      Volume ratios: 2 volumes of hydrogen: 1 volume of oxygen

      2 volumes of hydrogen: 2 volumes of water etc.

      can use these volume ratios only if both gases are at the same temperature and pressure

      Volume-Volume Calculations

      Sample Problem 11-7 page 347



      Homework: 11.4, Stoichiometry of Gases: Volume-Volume Calculations

      2. Volume-Mass and Mass-Volume Calculations

        Sample Problem 11-8 p 349



        Homework: 11.5, Stoichiometry of Gases: Volume-Mass and Mass-Volume Calculations

  3. Effusion and Diffusion

    Diffusion - definition

    Effusion- definition

    This section deals with calculating the molar mass of a gas using effusion.
    1. Graham's Law of Effusion

      Figure 11-6

      Rates of effusion and diffusion depend on the relative velocities of gas molecules.

      Figure 11-7

      The velocity of a gas varies inversely with its mass. Lighter molecules move faster than heavier molecules at the same temperature.

      Using the equation for K.E. we can derive Graham's Law of Effusion which is




      Graham's Law of Effusion - statement

    2. Applications of Graham's Law

      Graham worked on densities of gases.

      The density of a gas varies directly with its molar mass.

      That means we can restate the equation of Graham's Law as

      rate of effusion of A / rate of effusion of B = square root of density of B / square root of density of A or




      Figure 11-8

      Sample Problem 11-10 page 355



      Homework: 11.6, Effusion and Diffusion



 

 

 

 

 

 

 

 

 

end of notes

Gay-Lussac's Law of Combining Volumes of Gases states that at constant temperature and pressure, the volumes of gaseous reactants and products can be expressed as ratios of small whole numbers. back

 

 

 

 

 

 

 

 

 

 

 

 



Avogadro's Law states that equal volumes of gases at the same temperature and pressure contain equal number of molecules. Back

 

 

 

 

 

 

 

 

 

 

 

 



The standard molar volume of a gas is the volume occupied by one mole of a gas at STP and whose value is 22.4 L. back

 

 

 

 

 

 

 

 

 

 

 

 



The ideal gas law is the mathematical relationship of pressure, volume, temperature, and the number of moles of a gas. Back

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Diffusion is the gradual mixing of two gases due to their spontaneous, random motion. Back

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Effusion is the process whereby the molecules of a gas confined in container randomly pass through a tiny opening in the container. Back

 

 

 

 

 

 

 

 

 

 

 

 

Graham's Law of Effusion states that the rates of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses. Back