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Kinetic Theory(Observing Properties of Gases) Kinetic energy (movement) depends on temperature – (high temperature is more movement)

- Gases are tiny particles, that have mass but a small volume
- (Volume assumed to = 0)

- Gases in constant random motion
- Collisions are elastic with walls and each other (No attraction between molecules)

Measuring Gases

- Amount (n)
moles (number of)

- Volume (V)
liters

- Temperature (T)
Kelvin K= C + 273

- Pressure (P)
mm Hg or atm

Pressure

Particles colliding with objects

- Pressure=force (Pascal)
area

Gas pressure

gas particles colliding with objects

Atmospheric pressure

air particles colliding with objects

Barometer

Measures atmospheric pressure

Measuring pressure

Barometer

760 mm Hg = 1 atmosphere

= 101,300 Pascals

=14.7 lb/in2

STP

Standard temperature 0oC

Standard pressure 1 atm

Manometer problems

Measures pressure in a closed container

Dalton’s Law of Partial Pressures

Each of the components of a gas mixture contributes some of the collisions

Each component contributes part of the total pressure.

Mathematically..

PT = P1 + P2 + P3…..

What is temperature?

- Measure’s average kinetic energy of particles.
- Higher temp means higher energy
- More energy means faster particles

- Lower temp means lower energy
- Less energy means slower particles

- Higher temp means higher energy
- When particles move faster, they collide more often and with more force.

Temperature and Energy Revisited

- If there are a fixed number of gas particles in a container
- And it has a fixed pressure
- What happens when it is heated up?

- The particles go faster
- They collide more
- The volume goes up

Lab: Boyles Law

- Purpose:
To observe changes in pressure with the volume changes

Charles Law(T,V)

- At a constant P, N the volume varies directly with the Kelvin temperature
V1 = V2

T1 T2

Gay-Lussacs Law(P,T)

At a constant V,N the pressure varies directly with the Kelvin temperature.

P1 = P2

T1 T2

Lab: Pressure/temperature

Purpose: To determine the absolute zero using Gay-Lussac’s Law

Avagadro’s Law

- If you hold pressure and temperature constant
- Like at standard temperature and pressure
- Which are?

- Like at standard temperature and pressure
- Volume and moles are related
V

n

Lab: combined gas law

Purpose: To determine the volume of 1 mole of a gas using the combined gas law

Reaction: Hydrochloric acid and Mg

Ideal Gas Law

At STP 1 mole=22.4L

If not at STP use Ideal Gas Law

P V = n R T

R=ideal gas constant

(0.0821 L atm)

moles K

Ideal Gas Law

- All the gas laws are related.
- By the pressure, volume, temperature and number of particles (moles or n)
PV = constant

V/T = constant

n/V = constant

P/T = constant

Gas Proportions

- There are four variables in the Gas Laws
- Pressure
- Volume
- Temperature
- Moles

- We can intuit each gas law using KMT
- For example:
- If moles and temperature are constant
- How does the volume and pressure compare?

Gas Stoichiometry

- C8H18, octane, combusts in your car’s engine. If the cylinder is 0.500 L and the oxygen intake is at 45oC and 1.05 atm, how many grams of octane are needed to completely react with the oxygen?

Gas Collected Over Water

If the water level in the flask is equal to the surrounding water, than the inside pressure is equal to the outside pressure.

Pin = PO2 + PH2O = P atmospheric

PH2O = 21 torr

Pressure of Collected Gas

- The vapor pressure of water @ 20.0 C is 17.54 mmHg
- How many mmH2O is this?
- What data do you need?
- Mercury d = 13.7 g./ml
- 240. mmH2O

- If 100.0 ml of oxygen is collected over 20.0 C
- If the atmospheric pressure is 739 mmHg, what is the pressure of oxygen?
- How many moles of Oxygen gas?
- How many atoms of oxygen

Motion of Gases

- At the same temperature, two samples of gas have the same average kinetic energy
- What has more kinetic energy, a bus moving at 5 mph or a baby on a tricycle moving at 10 mph?
- If mass is important let’s consider molecular motion.

Diffusion

- Gases at the same temp have the same average KE
- More massive gases must be moving slower than less massive gases at the same temp
- If I let out a smelly gas of a flask, how does it get to your nose? What path does it take?
- When a gas spreads out or dissolves into the air, we call this diffusion

Graham’s Law

- The rate of diffusion is directly proportional the speed of the molecule
- The bigger the molecule, the ______ the speed of the molecule (at the same temp)
- The “bigger” really means molar mass.
- We can compare rates or velocities

Graham’s Law

va = Mb

vb Ma

The ratio of the velocities of gas molecules is proportional to the Inverse square root of their molar masses

Problem

- The rate of diffusion of an unknown gas is four times faster than the rate of oxygen gas. Calculate the molar mass of the unknown gas and identify it.
va = 1 = Mb vb 4 32 g/mol

Mb = 2 What gas has a molar mass of 2?

Dalton’s law

- The total pressure equals the sum of the partial pressures of the gases in the container
PT = P1 + P2 + P3 + ……..

Try this

Air contains oxygen, nitrogen, carbon dioxide and other gases. What is the pressure due to oxygen in mm Hg if

PT= 1 atm

PN=593.4 mm Hg

PCO2 = 46.78 mm Hg

problems

- The pressure on 2.50 L of anesthetic gas is changed from 765 mm Hg to 304 mm Hg. What is the new volume if the temperature is constant?

problems

- A balloon inflated in air conditioning at 27oC has a volume of 4.0L. It is heated to 57oC. What is the new volume?

Practice

A gas has a volume of 17.3 mL at 3.5 atm. What is the volume if the pressure is increased to 6.7 atm?

A can contains a gas at 50oC and has a volume of .5L. When released what is its new volume at 20oC?

Try this

If 87.6 mL of hydrogen gas is collected at a room temperature of 23oc and room pressure of 742 mmHg, what will the volume be at STP?

problems

- A gas has a volume of 6.8L at 327oC. What is its volume at 36oC?

Pressure /Temperature

- In a sealed container, with a fixed volume and fixed number of particles
- What happens to the pressure, if the temperature of the system is increased? Why?
- The pressure and the temperature vary directly. Just like in Charles Law.

- 1. Why should the thistle tube be under the water level?
- 2. Why was the first bottle “let go”?
- 3. Why were the bottles placed upside down on the lab bench?
- 4. What was this method called for collecting gas
- using a pneumatic trough and pushing water out?
- 5. Why did the splint go out inside the bottle?
- 6. What was the clear, colorless liquid produced?
- 7. Write a chemical reaction for its production.

Lab: Combined gas law

1.Take room temperature and pressure

2. Get about 5 cm (or less) Mg and mass. Tie onto copper wire

3. Pour 15 ml of HCl into eudiometer and fill to top with water

4. Put Mg into top of eudiometer. Stopper.

5. Put finger over the hole, turn upside down and place into big beaker of water.

6. When reaction is complete, put finger over hole and transfer to large graduated cylinder to measure volume of gas collected.

Kinetic Theory Real vs Ideal

Valid if not at

Low temperatures

– attractive forces apply

high pressures

– volume of particles

- attractive forces apply

Questions

- What happens to the energy of the particles of gas when you put the flask into cold water?
- Why do we use Kelvin when calculating gas law problems? (Hint – is the Celsius temperature directly proportional to pressure below zero degrees?)
- Predict the volume of the gas at 0 K from your data. You do this by getting an equation an plugging in the numbers.
- Compare your answer with the real answer. Why are they different? What could affect your results?
- A flask has a pressure of 1.0 atm at 25 C. What is the pressure at –40 C? (remember to convert to Kelvins)

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