1. Kinetic Molecular Theory and Gases
Mr. Kinton
Honors Chemistry

2. Review of Gases What can you tell me about gases?
How are they similar to solids and liquids?
How are they different?

3. Characteristics of Gases
Expand spontaneously to fill their container
Volume of a gas is equal to the volume of the container
Highly compressible
Form homogeneous mixtures only
Molecules are spaced far from each other

4. Properties of importance for Gases
Measurable quantities include
Temperature
Volume
Pressure
For now we are going to focus on pressure
Force that acts on a certain area or P= F/A

5. Atmospheric pressure/Other Units
SI unit is the Pascal (N/m2), abbreviated Pa
Standard Atmospheric Pressure:
1 atm (atmosphere)
760 mmHg (millimeters of Mercury)
760 torr
x 105 Pa or kPa
Can be measured many ways:
Barometer
Manometer

6. Conversions Convert .357 atm to torr Convert 6.6 x 10-2 torr to atm
Convert kPa to mmHg

7. Gas Laws
In order to understand gases we need can examine 4 key quantities:
Temperature (T)
Pressure (P)
Volume (V)
Amount of gas (n)
Scientists used these 4 to develop the gas laws

8. Boyle’s Law Discovered by Robert Boyle
Observed that as pressure increased volume decreased
Thus pressure and volume have an inverse relationship
Expressed by PV= constant
Helps explain how we breathe

9. Charles’s Law Discovered by Jacques Charles
Found that as temperature increased so did the volume
Temperature and volume have a direct relationship
Expressed by V/T= constant
Led to the creation of an absolute temperature scale (Kelvin)
K= oC
Explains the hot-air balloon

10. Avogadro’s Law
Discovered by Joseph Louis Gay-Lussac and Amadeo Avogadro
Gay-Lussac: Law of Combining volumes gases react in ratios that are small whole numbers
Avogadro: Equal volumes of gas contain the same number of molecules
Expressed by V/n = constant

11. Ideal Gas Law
Hypothetical gas whose behavior is described by the following equation:
PV= nRT, where R is the gas constant
R= L-atm/mol-K, m3-Pa/mol-K, L- torr/mol-K
Temperature must always be given in Kelvin
Gives us standard conditions:
Temperature: 0 oC
Pressure: 1 atm

12. Example
Calcium carbonate decomposes when heated and produces carbon dioxide. 250 mL of carbon dioxide is collected. The pressure exerted is 1.3 atm at a temperature of 31 oC. How many moles of carbon dioxide were produced

13. Relating the Gas Laws
Due to the ideal gas law we can re-write the previous laws to determine how individual changes occur:
Boyle’s Law: P1V1= P2V2
Charles’s Law: V1/T1= V2/T2
Avogadro’s Law: V1/n1= V2/n2

14. Examples:
A fixed quantity of gas at 23 degrees Celsius exhibits a pressure of 748 torr and occupies a volume of 10.3 L. Calculate the volume if the pressure is increased to 1.88 atm? Calculate the volume the gas will occupy if the temperature is increased to 165 degrees Celsius

15. Application of the Ideal Gas Law
We can use the ideal gas law to help us solve for 2 other physical properties of a gas:
Gas density
Molar mass
We can derive both of these quantities from the Ideal gas equation
d= PM/RT
M= dRT/P

16. Example
What is the density of carbon tetrachloride vapor at 714 torr and 125o C?

17. Application of the Ideal Gas Law
We have seen in chemical reactions that gases can be reactants and products.
Using the ideal gas law we can determine the amount of gas that was consumed or produced in a chemical reaction.
Let’s examine how this works with the production of nitric acid. How many liters of ammonia at 850o C and 5.00 atm are required to react with moles of O2(g)?
4 NH3(g) + 5 O2(g)  4 NO(g) + 6 H2O(g)

18. You Try!
The safety air bags in automobiles inflated by nitrogen gas generated by the rapid decomposition of sodium azide, NaN3: 2NaN3(s)  2Na(s) + 3N2(g). If an air bag has a volume of 36L and is to be filled with nitrogen gas at a pressure of 1.15 atm at a temperature of 26.0o C, how many grams of NaN3 must be decomposed?

19. Gas Mixtures and Partial Pressure
John Dalton observed the contribution of gases in a mixture.
Total pressure is equal to the sum of the pressures
Pt= P1 + P2 +P3…
Pt= (n1 + n2 + n3…)RT/V

20. Example
A gaseous mixture made from 6.00 g of O2 and 9.00 g CH4 is placed in a 15.0-L vessel at 0 oC. What is the partial pressure of each gas and what is the total pressure in the vessel.

21. Collecting a Gas over Water
Pt= Pgas + Pwater
Must use appendix B in the textbook to solve these problems

22. Example
A sample of KClO3 is decomposed and the gas is collected over water. The volume of gas collected is .250L at 26 oC and 765 torr of total pressure. How many moles of O2 are collected?

23. Kinetic-Molecular Theory
Ideal gas equation describes how gases behave but doesn’t explain why.
Rudolf Clausius described a satisfactory theory
A theory that is based on moving molecules

24. Theory of Moving Molecules
Gases consist of a large number of molecules in continuous, random motion
Volume of all molecules of the gas is negligible compared to the total volume
Attractive and repulsive forces are negligible
Energy can be transferred during collisions but the average kinetic energy does not change
Average kinetic energy is proportional to the absolute temperature. At constant temperature gas molecules have the same average kinetic energy

25. Real Gases: Deviate from Ideal Gases
In actuality gases do not behave like ideal gases
Deviate at high pressure
Deviate at lower temperatures
In actuality they occupy space and they do attract one another

26. Root-mean-square Speed
This is the speed of a gas molecule possessing average kinetic energy and denoted by the symbol u
u= √3RT/M
Based on kinetic molecular theory we know that the average kinetic energy of any collection of gas molecules is ½ mu2
This shows us that lighter gases have a higher rms than heavier gases
Effusion- the escape of gas through a tiny hole into an evacuated space
Diffusion- the spread of one substance throughout a space or second substance

27. Example
Calculate the rms, u, of N2 at 25oC

28. Graham’s Law of Effusion
Shows that the effusion rate of a gas is inversely proportional to the square root of it’s molar mass
r1/r2= √M2/M1
An unknown gas composed of diatomic molecules effuses at a rate that is only .355 times that of O2 at the same temperature. What is the identity of this unknown gas?

29. You Try!
Calculate the ratio of the effusion rates of N2 and O2