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The Behavior of GasesUnit 9

- GENERAL CHEMISTRYSPRING 2013

Air Pressure

- Pressure equation

Newtons (N)

Square meters (m2)

Unit for Air Pressure

f P a

- Pascals
- 1 N/m2 1 Pascal (Pa)
- Standard pressure is 101.325 kPa on Earth

1 kPa 1000 Pa!

Blaise Pascal (French philosopher and

mathematician)

Pascals Triangle

Air Pressure

f P a

- Without changing the mass (force), how can you

increase pressure?

- Without changing the mass (force), how can you

decrease pressure?

Decrease the area

Increase area

Practice Problem

f P a

- The mass of a brick is 2.0 kg (F19.6N), the

sides are 0.05m and 0.03m. What is the pressure

exerted?

19.6 N 13,067 Pa

(0.05 m x 0.03 m) 13,067 Pa

Pressure Units

- Ways to represent pressure

Units of Gas Pressure Units of Gas Pressure

Unit Standard Pressure

Atmosphere 1 atm (exactly)

Inches of Hg 29.9 in Hg

cm of Hg 76 cm Hg

mm of Hg 760 mm Hg

Torr 760 torr

Pounds per sq. in. 14.7 psi

Kilopascal 101 kPa

Torr is named after Evangelista Torricelli

The Barometer

- Etymology of barometer
- In Greek, baros weight
- Meter measure
- Literally means measure the weight of air or

air pressure.

Bariatric surgeory is weight loss surgeory

5 Footlong

The Barometer

- How a barometer works
- Air presses down on an open tray of Hg
- This downward pressure pushes the Hg up into a

tube - Higher air pressure causes the mercury to go

higher up in the tube (measured as height, mm Hg)

Compressibility

- A gas will expand to fill its container
- Compressibility
- A measure of how much the volume of matter

decreases under pressure. - Gases easily compress because of the space

between the particles

http//www.garagelibrary.com/images/airbag.jpg

Kinetic Molecular Theory

- Postulates the theory is based on
- Gases consist of tiny particles (of negligible

mass) with great distances separating them - Gases are in constant random motion
- Molecular collisions are elastic
- Average kinetic energy is dependent only on

temperature

The Kelvin Scale

- As T increases, so does kinetic energy
- Theoretically, kinetic energy can be zero, but it

hasnt been achieved and probably wont ever be

achieved - Absolute zero- The temperature at which a

substance would have zero kinetic energy - The Kelvin Scale- a temperature scale directly

related to kinetic energy - Zero on the Kelvin scale corresponds to zero

kinetic energy

The Kelvin Scale

- Units are Kelvins (K), with no degree (o) sign

Kelvin relates temperature to kinetic energy!

Temperature Conversions

- Easy to convert between Celsius and Kelvin
- How do you think?
- oC ? K? Add 273
- K ? oC? Substract 273
- 25oC ? K?
- (25273) 298 K
- 310 K ? oC?
- (310-273) 37oC
- Fahrenheit Celsius?
- (oF 32oF) x 5/9 oC
- (oC x 9/5) 32oF oF

Factors Affecting Gas Pressure

- Amount of gas
- Volume
- Temperature

http//www.bmumford.com/photo/highspeed/Ted1.jpg

Boyles Law

- Boyles inverse
- States that the volume of a gas varies inversely

(opposite) with pressure if temperature and

amount are held constant - Written
- P1V1 P2V2
- (Demos from website Boyles Law and Scuba

Diving, 400 Marshmallows in a vacuum,

Mythbusters Scuba Crush)

Robert Boyle

Boyles Law in motion

http//www.grc.nasa.gov/WWW/K-12/airplane/Animatio

n/gaslab/Images/chprmt.gif

Boyles Practice 1

- A tank contains a volume of 3 L and a pressure of

4 atmospheres. What volume would the gas from

this tank fill up at a pressure of 1 atmosphere? - P1 4atm
- V1 3L
- P2 1 atm
- V2 ?

Substitute into Boyles Law equation and solve

for V2 P1V1 P2V2

(4 atm)(3L) (1atm)(V2) 12 atmL V2

1 atm

V2 12 L

Boyles Practice 2

- Find the volume of a cylinder needed if you want

to put 50 atmospheres of pressure with a volume

of 3 L into a cylinder that can hold a pressure

of no greater than 20 atmospheres. - P1 50 atm
- V1 3 L
- P2 20 atm
- V2 ?

Substitute into Boyles Law equation and solve

for V2 P1V1 P2V2

(50 atm)(3 L) (20 atm)(V2)

7.5 L V2

Charles Law

- Charles direct
- The volume of a gas varies directly with

temperature if the pressure and amount remain

constant - Mathematically

Demos from Website Charles Law

Charles Law in Motion

Charles Law Problem 1

- Always convert temperature to Kelvin (K)
- A tank contains a volume of 3 L and a temperature

of 100oC. What volume would the gas from this

tank fill up at a temperature of 200oC? - V1 3 L
- T1 100oC 373K
- V2 ?
- T2 200oC 473K

Substitute into equation and solve for V2

3L V2 373K

473K

(3L)(473K) (V2)(373K)

4L V2

Charles Law Problem 2

- A 275 L helium balloon is heated from 20oC to

40oC. Calculate the final volume assuming

pressure remains constant. - V1 275 L
- T1 20oC (273K) 293K
- V2 ?
- T2 40273 313K

275L V2 293K 313K

(293)(v2) (275L)(313K)

V2 294 L

Temperature-Pressure Relationships

- Gay-Lussacs Law
- The pressure of a gas varies directly w/

temperature if volume and amount remain constant. - Mathematically

Tire inflation. Summer vs. winterhmmm how do

these two differ?

Demos from website Live balloon, Steel drum

implosions, Mythbusters Water Heater Rocket

Joseph Louis Gay-Lussac 1778-1850

Gay-Lussac Problem 1

- Temperature in Kelvin (K)
- A tank contains a pressure of 3 atm and a

temperature of 100oC. What pressure would the

gas from this tank be at a temperature of 200oC? - P1 3 atm
- T1 100oC (273K) 373K
- P2 ?
- T2 200oC 473K

3 atm P2 373 K 473 K

P2 4 atm

Gay-Lussac Problem 2

- Find the pressure needed if you wanted to put gas

at 50oC and 75 atm into a vessel that is at 65oC. - P1 75 atm
- T1 50oC 323 K
- P2 ?
- T2 65oC 338 K

75 atm P2 323 K 338 K

P2 78 atm

Combined Gas Law

- Puts together several scientists work on how

gases behave when conditions are change. - You can change three things about a gas to affect

pressure - Amount of gas- this stays the same for now
- Temperature
- Volume

STP??Temperature 273KPressure 1 atm

CBL Problem 1 (1 p.11)

- A 50 mL sample of hydrogen gas is collected at

772 mm Hg and 21oC. Calculate the volume of

hydrogen at STP. - P1 772 mm Hg ? atm
- V1 50 mL ? L
- T1 21oC 294 K
- P2 1 atm
- V2 X
- T2 273K

Since your final conditions are at STP, you need

to convert initial conditions to atm and L

CBL Problem 1 solution

P1 772 mm Hg x 1 atm/760 mm Hg 1.016 atm V1 50

mL / 1000 mL 0.05 L

(1.016 atm)(0.05L) (1atm)(V2) 294

K 273 K

Cross multiply, then solve for V2

(1.016 atm)(0.05L)(273 K) (1atm)(294K)(X)

0.05 L V2

Ideal Gases

- Ideal gases are
- Gases that behave under all conditions as

predicted by the kinetic molecular theory - Gases are not ideal
- When they dont behave as predicted by kinetic

molecular theory - Kinetic energy is
- Energy associated with motion

The Ideal Gas Law

- piv-nert
- PVnRT ALL UNITS MUST BE IN
- P Pressure (atm)
- V Volume (L)
- n moles (mol)
- R Ideal gas constant 0.0821 (Latm)/(molK)
- T Temperature (ALWAYS Kelvin)

IGL Problem 1

- If a container has a volume of 3 L and is at a

temperature of 60oC and a pressure of 6 atm, how

many moles of gas are in the container? - V 3L
- T 60oC 333K
- P 6 atm
- R 0.0821 Latm/molK
- n ?

IGL Problem 1 Solution

- Substitute in PVnRT and solve for n

(6 atm)(3 L) (n)(0.0821)(333 K)

n 0.7 mol

The unit for R is Latm

molK Be sure units match this, and units will

cancel

IGL Problem 2

- If a container has 50 moles of O2 and is at a

temperature of 40oC and a pressure of 3 atm, how

many liters are in this container? - n 50 mol O2
- T 40oC 313 K
- P 3 atm
- R 0.0821 Latm/molK
- V ?

IGL Problem 2 Solution

- Substitute in PVnRT and solve for V

(3atm)(V) (50 mol)(0.0821)(313 K)

V 428 L