GENERAL CHEMISTRYSPRING 2010Mr. HoffmanMrs. Paustian

The Behavior of GasesUnit 9

Air Pressure

Pressure equation

Newtons (N)

Square meters (m2)

Unit for Air Pressure

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

f

P a

Blaise Pascal(French philosopher and mathematician)

Pascal’s Triangle

1 kPa = 1000 Pa!

Air Pressure

Without changing the mass (force), how can you increase pressure?

Without changing the mass (force), how can you decrease pressure?

f

P a

Decrease the area Increase area

Practice Problem

The mass of a brick is 2.0 kg (F=19.6N), the sides are 0.05m and 0.03m. What is the pressure exerted?

f

P a

19.6 N = 13,067 Pa

(0.05 m x 0.03 m)

Pressure Units

Ways to represent pressure

Units of Gas PressureUnit 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…1. Gases consist of tiny particles (of negligible

mass) with great distances separating them2. Gases are in constant random motion3. Molecular collisions are elastic

4. Average kinetic energy is dependent only on temperature

The Kelvin Scale

As T increases, so does kinetic energyTheoretically, kinetic energy can be zero,

but it hasn’t been achieved and probably won’t 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? (25+273)= 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 gasVolumeTemperature

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Boyle’s 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

Robert Boyle

Boyle’s Law in motion

http://www.grc.nasa.gov/WWW/K-12/airplane/Animation/gaslab/Images/chprmt.gif

Boyle’s 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 Boyle’s Law equation and solve for V2

P1V1 = P2V2

(4 atm)(3L) = (1atm)(V2)

12 atm*L = V2

1 atmV2= 12 L

Boyle’s 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 Boyle’s 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:

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= 40+273= 313K 275L = V2

293K 313K

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

V2= 294 L

Temperature-Pressure Relationships

Gay-Lussac’s Law The pressure of a gas varies directly w/ temperature if

volume and amount remain constant. Mathematically:

Joseph Louis Gay-Lussac 1778-1850

Tire inflation…. Summer vs. winter…hmmm how do these

two differ?

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 changes.

You can change three things about a gas Amount of gas- this stays the same for now Temperature Volume Pressure changes in response to these

STP??Temperature= 273K

Pressure= 1 atm

CBL Problem 1

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

(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

P1= 772 mm Hg x 1 atm/760 mm Hg= 1.016 atm

V1= 50 mL / 1000 mL= 0.05 L

Ideal Gases

Ideal gases are…Gases that behave under all conditions as

predicted by the kinetic molecular theoryGases are not ideal…

When they don’t behave as predicted by kinetic molecular theory

Kinetic energy is…Energy associated with motion

The Ideal Gas Law

“piv-nert”PV=nRT

P= Pressure (atm) V= Volume (L) n= # moles (mol) R= Ideal gas constant= 0.0821 (L*atm)/(mol*K) 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 L*atm/mol*K n= ?

IGL Problem 1 Solution

Substitute in PV=nRT and solve for n

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

n= 0.7 mol

The unit for R is

L*atm mol*K

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 L*atm/mol*K V= ?

IGL Problem 2 Solution

Substitute in PV=nRT and solve for V

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

V = 428 L