# 3.3 Kinetic Model of an Ideal Gas

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3.3 Kinetic Model of an Ideal Gas
Definition of Properties Pressure Volume

DEFINITION A state of matter where particles are so separated, that intermolecular forces are almost negligible. Particles have a higher kinetic energy than liquid, or solid.

Gas particles move randomly.

Kinetic Model Ideal Gas Assumptions
Molecules are spheres 2) Molecules identical 3) Perfectly elastic collisions (no loss KE). 4) No intermolecular forces – constant v between collisions – straight line. 5) No molecular volume.

Ideal Gasses Obey ideal Gas Law
PV = nRT P Pressure Pascals V in m3. n – number of moles. R – gas constant 8.31 J/K mol. T – Kelvin.

Pressure Force/Area. Pascal = N/m2. 1 Atm = 101 kPa
So if you have 1 m2 window, it has 101,000 N pressing on it.

Ex 1: A 360 N child sits on a stool which weighs 41 N
Ex 1: A 360 N child sits on a stool which weighs 41 N. The bottom of the stools legs touch the ground over an area of 19.3 cm2:

Gas Pressure Gas Molecules Exert Pressure on Container
Collisions between gas molecules with each other & the container. Pressure from Dp / impulse of particle = Ft when they bounce & changes p.

The Dp (mv) causes impulse, J on walls. F t = J. F = Dp/t is a rate.
Low P, less force (KE), lower collision rate. High P, more force (KE), higher collision rate.

Relationships Pressure Volume
P increases, Volume decreases (fixed T) PV = nRT P = nRT 1 V

Pressure & Volume Decrease volume - collision rate increases.
P goes up.

Temperature Volume T increases, V increases (Fixed P)
PV = nRT V = nR T P

Temperature & Volume When you push the piston in to reduce the volume, some molecules are swatted giving them E. Work is done on gas. When a gas pushes the piston out, increasing the volume, it does work & the E of the gas goes down.

Pressure, Temperature (fixed V)
PV = nRT P = nR T V

Pressure, Temperature As T goes up molecular KE goes up, P goes up. Frequency of collisions go up. Dp increases with Dv. Impulse on wall increases.

When gas P reaches zero, T = absolute zero.

1. Why does blowing into a balloon increase its volume?
1. Blowing air into the balloon increases the # of air molecules, increasing the rate of collision inside the balloon, and increasing the pressure on the balloon wall.

Particulate Nature of Matter and Changes of State 4 min.

Homework: Read Hamper Chap 3. 3. Look at purple box pg 62
Homework: Read Hamper Chap 3.3. Look at purple box pg 62. For each assessment statement – write a few sentences to address the learning goal. In Class finish IB packet in groups.

Deleted from IB 2009

Problems

Pressure Calc’s Ex 1. A 360 N child sits on a three legged stool which weighs 41 N. The bottom of the stools legs touch the ground over an area of 19.3 cm2. What is the average pressure exerted by the stool on the ground? (hint: change cm2 to m2) How does the pressure change the student balances the stool on two legs?

2.1 x 105 Pa

Gas Laws

Ideal Gas Laws For given sample of gas, the following factors are related:
Pressure (Pa) Volume (m3) Temperature (K) (mass – number of moles)

At constant volume, P a T The ratio P is a constant T
Pressure Law At constant volume, P a T The ratio P is a constant T

What happens to the volume of a gas when the temperature decreases or increases?

What happens to the volume of a gas when the pressure is increased or decreased?

Pressure & Volume are inversely related.

How do we account for the mass or the amount of substance present?

Avogadro's Law If temperature and pressure remain constant...
What would happen to the volume of a gas if the number of moles (amount of molecules) is increased?

Effect of changing mass (# moles) on volume
Effect of changing mass (# moles) on volume. Density ratio of mass to volume is constant. Direct Relationship.

What would happen to pressure of a gas as mass/moles increased?

Pressure vs Mass is direct
Pressure vs Mass is direct. The density (mass/volume) increases as the volume is held fixed by the piston and the temperature is fixed.

The mass changed by injecting molecules
The mass changed by injecting molecules. The density (mass/volume) changes with the injection of the mass. This would be a very difficult experiment to perform in reality, because both P and V must be held constant.

Avogadro: Equal volumes of gas at STP have equal #of molecules.
Mole is an amount. At STP 1 mol has Avogadro’s number NA of particles (atoms or molecules). NA = 6.02 x 1023 molc/mol.

To find # moles, n, in substance given the mass of substance.
n = m m = mass in g M M = molar mass #g/mol from periodic table. 1 mole of any gas has fixed volume. At STP the volume is 22.4 dm3 or 22.4 L.

Using the ideal Gas Law Ex: A weather balloon volume 1.0 m3 contains helium at a pressure of 1.01 x 105 N/m2 and a temperature of 35oC. What is the mass of the helium in the balloon if one mole of helium has a mass of x 10-3 kg?