Kinetic Theory of Gases

Gas Phase

Kinetic Molecular Theory (KMT)-Ideal Gases The particles are in constant motion. The volume of the individual particles of a gas are negligible compared to the distances between them. The particles are assumed not to exert attracting or repelling forces (no intermolecular forces) on each other. The collisions are perfectly elastic. No kinetic energy is lost before and after the collision. The collisions of the particles with the walls of the container cause pressure. *Real gases DO have volume & intermolecular forces!

State Variables of a Gas: describe the State of a Gas (PVT) SI Unit Pressure (P) Pascals Pa Volume (V) m3 Temperature (T) Kelvin Amount of gas molecules mol (n)

Simulation http://www2.biglobe.ne.jp/~norimari/science/JavaApp/Mole/e-gas.html

Standard Temperature and Pressure (STP) 1 atm =760mmHg (torr) = 101.3 kPa 273K =0 0C

Pressure P= F A Units of Pressure: pascal, mmHg, atm 1 Pa = 1 N/m2 CONVERSION: 1 atm =760mmHg (torr) = 101.3 kPa

Factors Affecting Gas Pressure Number of Moles (Amount of gas) As the number of particles increases, the number of collisions with the container wall increases (more force). Volume The smaller the volume, the greater the pressure exerted on the container (less area). Temperature As temperature increases, kinetic energy increases, increasing the frequency of collisions AND the forcefulness of each collision (MORE IMPORTANT). Thus pressure increases (more force). .

Manometer- Open End PC=PB PA= Atmospheric Pressure PB=PA+ PAB PAB is measured in mmHg (torr) PAB is called gauge pressure. Gas Sample

Manometer- Closed End “Barometer” Gas Sample PC=PB PA= 0 atm PB= PAB

Temperature How hot – cold Average kinetic energy of molecules. The average kinetic energy of a gas is directly proportional to the Kelvin temperature. KE = (3/2)RT

Temperature Scales Celsius 0 100 Kelvin 273 373 Fahrenheit 32 212 Freezing Point of Water Boiling Point of Water Celsius 0 100 Kelvin 273 373 Fahrenheit 32 212 K=273+C (absolute zero: 0 K) F=(9/5)C +32 When you increase T by one degree C, how many K do you increase by? THE SAME!!!! The Kelvin & Celsius scale are the same, it’s just the numeric values in Kelvin are higher.

Kinetic Energy KE= ½ m v2 KE = 3/2 RT (for 1 mole of gas) Average speed, v = √((3RT)/MM) v speed, m mass Example: speed of oxygen molecule at 25oC = 443 m/s

Molecular speed… The “Maxwell-Boltzmann distribution” Inversely related to MASS (lighter molecules are faster) Directly related to TEMPERATURE (hotter molecules are faster) *Remember, even though a lighter molecule may be FASTER, it has the SAME KINETIC ENERGY as a heavier molecule if they are at the SAME TEMPERATURE (because kinetic energy is related to both velocity (aka speed) AND mass; when one goes up, the other goes down!) Bell-curve distribution with an average speed ….particles are NOT ALL at the same speed COMPARISON OF MASS COMPARISON OF TEMPERATURE

Gas Laws

Ideal Gas Law vs. P V = n R T Van der Waals equation P = pressure Pa = N/m2 V = volume measured in L n =# of moles T = temperature K R=Universal gas constant =8.314 kPa L / (mol K) =0.0821 L atm/(mol K) =62.3 mmHg L/(mol K) correction for molecular attraction (increases pressure as the concentration of molecules increases)

Ideal Gas Laws mostly hold at: Low pressure High temperature

If Mass and Temp are Constant

If Mass and Pressure are Constant

Boyle’s Law P1V1=P2V2 T constant P vs V hyperbola # moles constant Isotherm High Temp P V

Charles Law V1 = V2 P constant T1 T2 # Moles constant Isobar V T (K)

Gay-Lussac P1 = P2 V constant T1 T2 # moles Constant isochoric P T

Combined Gas Law P1V1 = P2V2_ T1 T2

-Diffusion -Graham’s Law of Effusion -Dalton’s Law of Partial Pressures

Diffusion

Diffusion The process in which particles of matter move from areas of high concentration to areas of low concentration.

Effusion The passage of gases through a small hole or pores of a membrane.

Note Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass.

Graham’s Law of Effusion ________ va= √ MMb vb MMa v = rate of effusion = (1/ time) MM= molar mass -The rate of effusion of a gas is inversely proportional to the square root of its molar mass.

Example Compare the rates of effusion of CO2 to oxygen gas.

Dalton’s Law of Partial Pressures Ptot=P1+P2+…. Total pressure of a mixture of gases in a container is the sum of the individual pressures (partial pressures) of each gas, as if each took up the total space alone.

Dalton’s Law of Partial Pressures http://cwx.prenhall.com/bookbind/pubbooks/hillchem3/medialib/media_portfolio/text_images/CH05/FG05_14.JPG

Dalton’s Law of Partial Pressures: The total pressure in a gas mixture is the sum of the partial pressures of each individual gas. Ptotal = Pgas 1 + Pgas 2 + Pgas 3 + … Pgas 1 = ( 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝑔𝑎𝑠 1 𝑡𝑜𝑡𝑎𝑙 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝑔𝑎𝑠 ) (Ptotal)

Partial Pressure of a Gas: The pressure that the gas would exert if it were the only gas present in the container.

Liquids

Liquids Intermolecular attractions hold molecules of liquids together. Incompressible, definite volume. More dense than gases. Molecules have kinetic energy.

Vaporization Change of phase from a liquid to a gas

Evaporation Vaporization occurring at the surface of the liquid. Responsible for the vapor pressure, Pvapor , of a liquid.

Evaporation example: Bromine Gas (Vapor) Liquid

Evaporation in a Closed Container

Evaporation in a Closed Container Liquid  Vapor  When the rate of evaporation equals the rate of condensation the system is in Equilibrium

Vapor Pressure The pressure resulting from the gas that would evaporate from a liquid at a specific given temperature, in an equilibrium situation (closed container).

What happens to the rate of evaporation as the liquid is heated? The rate of evaporation increases. As T increases, more particles have the minimum speed to escape the liquid surface (Pvapor increases…). Minimum speed to escape liquid surface

The vapor pressure increases with increasing temperature. Why? Because the kinetic energy of the liquid molecules increases and more leave the liquid and collide with the walls of the container.

Evaporation is a cooling process Why? The particles with the higher kinetic energy escape the liquid first; the process of evaporation still requires the breaking of IMFs (absorption of energy).

Boiling Vaporization occurring beneath the liquid’s surface (i.e. throughout the liquid). This only occurs when the Pvapor = Pexternal. Pvapor = vapor pressure of liquid Pexternal = pressure above liquid from atmosphere, etc.

Boiling Point The temperature at which a liquid boils.

Pvapor < Pexternal = no boiling When the external pressure is greater than the vapor pressure of the bubbles in the liquid the bubbles cannot come to the surface. Boiling does not happen.

Pvapor = Pexternal, then boiling! When the external pressure is equal to the vapor pressure of the bubbles in the liquid, boiling occurs.

Why does water boil at a lower temperature at high altitudes? Because the external pressure is lower.

Normal Boiling Point The boiling point at 1 atm or 101.3kPa

Solids

Solids Atoms vibrate about fixed positions.

Properties of Solids Depend on their arrangement of their atoms.

Melting Points Temperature at which a solid changes to a liquid. Vibrations of particles are strong enough to overcome the attraction that holds them in fixed locations. Melting point is same as freezing points.

Melting Points of Ionic and Molecular Solids Ionic Solids have high melting points because strong forces are holding the particles together. Molecular Solids have lower melting points. Not all solids melt (ex. Wood, cane sugar, some plastics)

Most Solids are Crystalline Unit cell : the smallest group of particles that retains the shape of the crystal. Crystal Lattice: a repeating array of unit cells.

Simple Cubic,Body-Centered and Face-Centered

Allotropes Two or more different molecular forms of the same element in the same physical state.

Allotropes of Carbon Diamond Graphite Bucky Balls

Buckminsterfullerene “Bucky Ball”

Amorphous Solids No order internal structure Examples: glass, plastics, asphalt

Formula for calculating heat input for kinetic energy changes: q = mC∆T Formula for calculating heat transfer for potential energy changes: q = m∆Hfus or vap

Phase diagram of water