1. Chapter 5 Gases

2. Reactions Involving Gases
in reactions of gases, the amount of a gas is often given as a volume
the ideal gas law allows us to convert from the volume of the gas to moles; then we can use the coefficients in the equation as a mole ratio
when gases are at STP, use 1 mol = 22.4 L
P, V, T of Gas A
mole A
mole B
P, V, T of Gas B

3. Examples
How many grams of H2O form when 1.24 L H2 reacts completely with O2 at STP? O2(g) + 2 H2(g) → 2 H2O(g)
What volume of O2 at atm and 313 K is generated by the thermolysis of 10.0 g of HgO? 2 HgO(s)  2 Hg(l) + O2(g)
The reaction used in the deployment of automobile airbags is the high- temperature decomposition of sodium azide, NaN3, to produce N2 gas. How many liters of N2 at 1.15 atm and 30.0 °C are produced by decomposition of 45.0 g NaN3?
2Na(s) + 3N2(g)
2NaN3(s)

4. Kinetic Molecular Theory
the particles of the gas (either atoms or molecules) are constantly moving
the attraction between particles is negligible
when the moving particles hit another particle or the container, they do not stick; but they bounce off and continue moving in another direction
like billiard balls
there is a lot of empty space between the particles
compared to the size of the particles
the average kinetic energy of the particles is directly proportional to the Kelvin temperature
as you raise the temperature of the gas, the average speed of the particles increases

5. Density & Pressure
Because there is a lot of unoccupied space in the structure of a gas, gases do not have a lot of mass in a given volume, the result is they have low density
result of the constant movement of the gas molecules and their collisions with the surfaces around them
when more molecules are added, more molecules hit the container at any one instant, resulting in higher pressure
also higher density

6. Gas Laws Explained – Dalton’s Law of Partial Pressures
Dalton’s Law says that the total pressure of a mixture of gases is the sum of the partial pressures
kinetic-molecular theory says that the gas molecules are negligibly small and don’t interact
therefore the molecules behave independent of each other, each gas contributing its own collisions to the container with the same average kinetic energy
since the average kinetic energy is the same, the total pressure of the collisions is the same

7. Dalton’s Law & Pressure
since the gas molecules are not sticking together, each gas molecule contributes its own force to the total force on the side

8. Kinetic Energy and Molecular Velocities
average kinetic energy of the gas molecules depends on the average mass and velocity
KE = ½mv2
gases in the same container have the same temperature, the same average kinetic energy
if they have different masses, the only way for them to have the same kinetic energy is to have different average velocities
lighter particles will have a faster average velocity than more massive particles

9. Molecular Speed vs. Molar Mass
in order to have the same average kinetic energy, heavier molecules must have a slower average speed

10. Temperature vs. Molecular Speed
as the absolute temperature increases, the average velocity increases
the distribution function “spreads out,” resulting in more molecules with faster speeds

11. Mean Free Path
molecules in a gas travel in straight lines until they collide with another molecule or the container
the average distance a molecule travels between collisions is called the mean free path
mean free path decreases as the pressure increases

12. Diffusion and Effusion
the process of a collection of molecules spreading out from high concentration to low concentration is called diffusion
the process by which a collection of molecules escapes through a small hole into a vacuum is called effusion
both the rates of diffusion and effusion of a gas are related to its rms average velocity

13. Graham’s Law of Effusion
for gases at the same temperature, this means that the rate of gas movement is inversely proportional to the square root of the molar mass
for two different gases at the same temperature, the ratio of their rates of effusion is given by the following equation:

14. Examples
Determine how much faster Helium atoms moves, on average, than a carbon dioxide molecule at the same temperature
Calculate the molar mass of a gas that effuses at a rate times N2

15. Ideal vs. Real Gases
Real gases often do not behave like ideal gases at high pressure or low temperature
Ideal gas laws assume
no attractions between gas molecules
gas molecules do not take up space
based on the kinetic-molecular theory
at low temperatures and high pressures these assumptions are not valid

16. The Effect of Molecular Volume
at high pressure, the amount of space occupied by the molecules is a significant amount of the total volume
the molecular volume makes the real volume larger than the ideal gas law would predict
van der Waals modified the ideal gas equation to account for the molecular volume
b is called a van der Waals constant and is different for every gas because their molecules are different sizes

17. Real Gas Behavior
because real molecules take up space, the molar volume of a real gas is larger than predicted by the ideal gas law at high pressures
Tro, Chemistry: A Molecular Approach

18. The Effect of Intermolecular Attractions
at low temperature, the attractions between the molecules is significant
the intermolecular attractions makes the real pressure less than the ideal gas law would predict
van der Waals modified the ideal gas equation to account for the intermolecular attractions
a is called a van der Waals constant and is different for every gas because their molecules are different sizes

19. Real Gas Behavior
because real molecules attract each other, the molar volume of a real gas is smaller than predicted by the ideal gas law at low temperatures

20. Van der Waals’ Equation
combining the equations to account for molecular volume and intermolecular attractions we get the following equation
used for real gases
a and b are called van der Waal constants and are different for each gas

21. Real Gases
a plot of PV/RT vs. P for 1 mole of a gas shows the difference between real and ideal gases
it reveals a curve that shows the PV/RT ratio for a real gas is generally lower than ideality for “low” pressures – meaning the most important factor is the intermolecular attractions
it reveals a curve that shows the PV/RT ratio for a real gas is generally higher than ideality for “high” pressures – meaning the most important factor is the molecular volume

22. Example
A sample of 3.50 moles of NH3 gas occupies 5.20 L at 47oC. Calculate the pressure of the gas (in atm) using
A) the ideal gas equation
B) the van der Waals equation
a = 4.17 atm •L/mol2 b = L/mol