Ch 11
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Kinetic Molecular Theory
Theory developed to explain physical behavior of the three states of matter (solid, liquid, and gas) Theory of moving molecules
Assumptions of KMT
Matter is composed of tiny particles (atoms, molecules or ions) that have definite and characteristic sizes that do not change. The particles are in constant, random motions and therefore possess kinetic energy (energy of motion). The particles interact with one another through attractions and repulsions and therefore possess potential energy. The velocity of the particles (and their kinetic energy) increases as the temperature is increased. The particles in a system transfer energy to each other through elastic collisions.
Gaseous State
Characterized by dominance of kinetic energy over potential energy Gas particles have enough kinetic energy to move far apart from each other (moving in straight lines) There is very little attraction between particles
Consequences of the Gaseous State
Indefinite volume and indefinite shape Low density Large compressibility Moderate Thermal Expansion
Four Important Gas Variables
• n = number of moles • T = temperature; must be in Kelvin! • V = Volume, usually measured in Liters • P = Pressure = force/area
Relationship Between Pressure and Volume (Boyle’s Law)
When the pressure is increased on a gas, its volume goes down. PV = constant (T fixed) Useful form: P1V1 = P2V2
Relationship Between Temperature and Volume (Charles’ Law)
When the temperature (K) is increased on a gas, its volume goes up by a constant: V/T = constant (P fixed) useful form: V1/T1 = V2/T2
Relationship between Temperature and Pressure (Gay-Lussac’s Law)
When the temperature (K) is increased on a gas, its pressure goes up as a constant: P/T = constant (V fixed) Useful form: P1/T1 = P2/T2
In Avogadro’s Law:
The volume of a gas is directly related to the number of moles of gas T and P are constant V1/n1 = V2 /n2
Important Simple Gas Relationships
Boyles Law P1V1 = P2V2 (T fixed) Charles Law V1/T1 = V2/T2 (P fixed) Gay-Lussacs P1/T1 = P2/T2 (V fixed) Avogadros Law V1/n1 = V2/n2 (T&P fixed)
STP - Standard Temperature and Pressure (Gases)
T = 273 K (0 oC) P = 1 atm (760 mmHg) 1 mole of a gas at STP = 22.4L
STP
The volumes of gases can be compared when they have the same conditions of temperature and pressure (STP, Standard Temperature and Pressure).
Combined Gas Laws
Relates the changes in pressure, volume and temperature, and quantity change of a gas
The Ideal Gas Law
Describes the relationships among the four variables for gaseous substances: P, T, V, n PV = nRT R is called the ideal gas constant 0.0821 atm·L/mol·K
At standard temperature and pressure (STP), 1 mol of a gas occupies a volume of 22.4 L, which is called its
molar volume.
The molar volume at STP can be used to form conversion factors.
22.4 L/1mol
Density of a Gas at STP
Density= Molar mass/Molar volume (g/L)
Ideal Gas Law - expanded
PV = nRT ; n = grams/Molar Mass n = g/MM PV = gRT/MM
The volume or amount of a gas in a chemical reaction can be calculated from:
STP conditions or the Ideal Gas Law Mole factors from the balanced equation
Dalton’s Law of Partial Pressures
Since gas molecules are so far apart, we can assume they behave independently. Dalton’s Law: in a gas mixture the total pressure is given by the sum of partial pressures of each component: Ptotal = P1 +P2+P3+…
Partial Pressure
The pressure that a gas in a mixture of gases would exert if it were present alone under the same conditions
A gas produced in the Laboratory
Usually contains water vapor
The partial pressure of a gas collected over water is obtained by
subtracting the vapor pressure of water.