Kinetic Molecular Theory and Gas Behavior

Definition Theory – An attempt to explain scientific behavior and properties. Kinetic Molecular Theory (KMT) – An attempt to explain gas behavior based upon the motion of molecules

Assumptions of the KMT 1 All gases are made of atoms or molecules 2 Gas particles are in constant, rapid, random motion The temperature of a gas is proportional to the average kinetic energy of the particles 3 Gas particles are not attracted nor repelled from one another 4 All gas particle collisions are perfectly elastic (no kinetic energy is lost to other forms) 5 The volume of gas particles is so small compared to the space between the particles, that the volume of the particle itself is insignificant 6

What is a “real gas”? Ideal Gas – a gas that is a gas under any conditions of temperature and pressure. There is no such thing as a real gas! Only Real gases that behave ideally! Real Gas – 2 of the assumptions of the Kinetic Molecular Theory are not valid Gas particles are not attracted nor repelled from one another Gas particles do have attractions and repulsions towards one another The volume of gas particles is so small compared to the space between the particles, that the volume of the particle itself is insignificant Gas particles do take up space—thereby reducing the space available for other particles to be

What are the measurable quantities of a gas: The Amount of the gas in Moles (n) The Pressure of the gas (P) The Temperature of the gas (T) The Volume of the gas (V)

Pressure Gas Pressure – Caused by the collisions of billions of gas particles against a surface Watch the Can!

Pressure Units Several units are used when describing pressure Unit Symbol atmospheres atm Pascals, kiloPascals Pa, kPa millimeters of mercury mm Hg pounds per square inch psi 1 atm = 101300 Pa = 101.3 kPa = 760 mm Hg = 14.7 psi

What is Atmospheric Pressure? Atmospheric Pressure – Pressure due to the layers of air in the atmosphere. Climb in altitude Less layers of air Lower atmospheric pressure As altitude increases, atmospheric pressure decreases.

Pressure In Versus Out A container will expand or contract until the pressure inside = atmospheric pressure outside Example: A bag of chips is bagged at sea level. What happens if the bag is then brought up to the top of a mountain. The internal pressure is from low altitude (high presser) The external pressure is high altitude (low pressure). Lower pressure Higher pressure Lower pressure The internal pressure is higher than the external pressure. The bag will expand in order to reduce the internal pressure.

When Expansion Isn’t Possible Rigid containers cannot expand Example: An aerosol can is left in a car trunk in the summer. What happens? The temperature inside the can begins to rise. As temperature increases, pressure increases. Lower pressure Can Explodes! Higher pressure The internal pressure is higher than the external pressure. The can is rigid—it cannot expand, it explodes! Soft containers or “movable pistons” can expand and contract. Rigid containers cannot.

Pressure and Volume As volume increases, pressure decreases because the molecules have to travel farther before colliding with the container!

Boyles’ Law – Mathematical Relationship Boyles’ Law relates pressure and volume Where temperature and # of molecules are held constant P = pressure V = volume The two pressure units must match and the two volume units must match! Example: A gas sample is 1.05 atm in a 2.5 L container. What pressure is it if the volume is changed to 2.7 L?

Boyles’ Law Boyles’ Law relates pressure and volume Where temperature and # of molecules are held constant P = pressure V = volume The two pressure units must match and the two volume units must match! Example: A gas sample is 1.05 atm in a 2.5 L container. What pressure is it if the volume is changed to 2.7 L? P1 = 1.05 atm V1 = 2.5 L P2 = ? atm V2 = 2.7 L P2 = 0.98 atm

What is “Temperature”? Temperature – proportional to the average kinetic energy of the molecules Energy due to motion (Related to how fast the molecules are moving) As temperature increases Molecular motion increases

Temperatures cannot fall below an absolute zero Temperature Units Kelvin (K)– temperature scale with an absolute zero Temperatures cannot fall below an absolute zero A temperature scale with absolute zero is needed in Gas Law calculations because you can’t have negative pressures or volumes

STP Standard Temperature and Pressure (STP) – 1 atm (or the equivalent in another unit) and 0°C (273 K) Problems often use “STP” to indicate quantities…don’t forget this “hidden” information when making your list! 1 atm = 101300 Pa = 101.3 kPa = 760 mm Hg = 14.7 psi

Pressure and Temperature As temperature increases, pressure increases because the particles are moving faster and can collide with the wall at a faster pace.

Gay Lussac’s Law – A mathematical relationship Gay Lussac’s Law relates pressure to temperature Where Volume and # of molecules are held constant P = Pressure T = Temperature in Kelvins Example: A gas at a pressure of 2.0 atm and 273K is heated to 285K. What is the new pressure of the gas?

Gay Lussac’s Law Gay Lussac’s Law relates pressure to temperature Where Volume and # of molecules are held constant P = Pressure T = Temperature in Kelvins Temperature must be in K and units must match! Example: A gas at a pressure of 2.0 atm and 273K is heated to 285K. What is the new pressure of the gas? P1 = 2.0 atm T1 = 273 K T2 = 285 K P2 = ? atm P2 = 2.1 atm

Volume and Temperature As the temperature of a gas increases the volume of the gas increases because the gas particles have more kinetic energy and will spread farther away from each other.

Charles’ Law Charles’ Law relates temperature and volume Where pressure and # of molecules are held constant V = Volume T = Temperature The two volume units must match and temperature must be in Kelvin! Example: What is the final volume if a 10.5 L sample of gas is changed from 25C to 50C? Temperature needs to be in Kelvin! V1 = 10.5 L T1 = 25C V2 = ? L T2 = 50C 25C + 273 = 298 K 50C + 273 = 323 K

Charles’ Law Charles’ Law relates temperature and pressure Where pressure and # of molecules are held constant V = Volume T = Temperature The two volume units must match and temperature must be in Kelvin! Example: What is the final volume if a 10.5 L sample of gas is changed from 25C to 50C? V1 = 10.5 L T1 = 25C V2 = ? L T2 = 50C = 298 K = 323 K V2 = 11.4 L

Moles What is a mole? A mole is a counting unit Other counting units include Dozen = 12 Gross = 144 Baker’s Dozen = 13 You can have half or part of a mole just like you can have half or part of a dozen

Volume and Moles The volume of a gas increases as the moles of the gas increase because the more gas particles you have the larger the space they will take up.

Avogadro’s Law Avogadro’s Law relates # of particles (counted in a unit called moles) and volume. Where Temperature and Pressure are held constant V = Volume n = # of moles of gas (A mole is a counting term like a dozen) The two volume units must match! Example: A sample with 0.15 moles of gas has a volume of 2.5 L. What is the volume if the sample is increased to 0.55 moles?

Avogadro’s Law Avogadro’s Law relates # of particles (moles) and volume. Where Temperature and Pressure are held constant V = Volume n = # of moles of gas The two volume units must match! Example: A sample with 0.15 moles of gas has a volume of 2.5 L. What is the volume if the sample is increased to 0.55 moles? n1 = 0.15 moles V1 = 2.5 L n2 = 0.55 moles V2 = ? L V2 = 9.2 L

Combined Gas Law P = Pressure Each “pair” of units must match and V = Volume n = # of moles T = Temperature Each “pair” of units must match and temperature must be in Kelvin! Example: What is the final volume if a 0.125 mole sample of gas at 1.7 atm, 1.5 L and 298 K is changed to STP and particles are added to 0.225 mole?

Combined Gas Law P = Pressure Each “pair” of units must match and V = Volume n = # of moles T = Temperature Each “pair” of units must match and temperature must be in Kelvin! Example: What is the final volume if a 0.125 mole sample of gas at 1.7 atm, 1.5 L and 298 K is changed to STP and particles are added to 0.225 mole? P1 = 1.7 atm V1 = 1.5 L n1 = 0.125 mole T1 = 298 K P2 = 1.0 atm V2 = ? L n2 = 0.225 mole T2 = 273 K STP is standard temperature (273 K) and pressure (1 atm) V2 = 4.2 L

Transforming the Combined Law Watch as variables are held constant and the combined gas law “becomes” the other 3 laws Hold pressure and temperature constant Avogadro’s Law Hold moles and temperature constant Boyles’ Law Hold pressure and moles constant Charles’ Law Can you show how to prove Gay Lussac’s Law? Which two variables are constant?

Effusion & Diffusion

Effusion Effusion –gas escapes from a tiny hole in the container Effusion is why balloons deflate over time!

Diffusion Diffusion –gas moves across a space Diffusion is the reason we can smell perfume across the room

Effusion, Diffusion & Particle Mass How are particle size (mass) and these concepts related? As mass of the particles increases, rate of effusion and diffusion is lowered because heavier particles, move slower.

Rate of Diffusion & Particle Mass Watch as larger particles take longer to get to your nose