Gas Laws

Learning Objectives

• TLW know the variables that influence the behavior of gases (TEKS 9)

• TLW be able to describe interrelationships between temperature, number of moles, pressure, and volume of gases in an enclosed system (TEKS 9.A)

• TLW perform stoichiometric calculations to determine mass and volume relationships between reactants and products involving gases (TEKS 9.B)

• TLW describe the postulates of kinetic molecular theory (TEKS 9.C)

I. Gas LawsA. Four properties of gases

1. Volume - V – gases do not have a defined volume

– particles of a gas expand to fill their container

– volume is measured in L (liters)

2. Pressure – P– collisions of particles with a surface

– P measured in atm, kPa, torr, mm Hg

3. Temperature – To

–the measure of average particle speed

–gas particles are in constant motion

–To for gases are measured in K (Kelvin)

4. Quantity – n–measure of how much there is of a gas

–MOLES!!!!!

– 22.4 L of gas = 1 mole

Postulates of Kinetic Molecular Theory

• Gases are composed of a large number of particles that behave like hard, spherical objects in a state of constant, random motion.

• These particles are much smaller than the distance between particles. Most of the volume of a gas is therefore empty space.

• There is no force of attraction between gas particles or between the particles and the walls of the container.

• These particles move in a straight line until they collide with another particle or the walls of the container.

• Collisions between gas particles or collisions with the walls of the container are perfectly elastic. None of the energy of a gas particle is lost when it collides with another particle or with the walls of the container.

• The average kinetic energy of a collection of gas particles depends on the temperature of the gas and nothing else.

Postulates of Kinetic Molecular Theory

• Check out this interactive tool which demonstrates the postulates in action

http://www.chm.davidson.edu/vce/kineticmoleculartheory/basicconcepts.html

B. Gas laws are based mathematically on the relationship of the four

properties of gas

volume

pressure

temperature

quantity

II. The Gas Laws (4 major ones)A. Boyle’s Law

1. Discovered that gas pressure and volume are related

2. If pressure is increased then volume decreases

3. Pressure and volume are inversely related

4. Meaning = whatever pressure does volume does the opposite

NASA Video

Boyle’s Law

V

P

P1V1 = P2V2

5. Example of Boyle’s Law

A sample of gas has a volume of 4.2 L and a pressure of 0.95 atm. If the pressure on the balloon increases to 1.90 atm what will the new volume be? 0.95 atm

4.2 L

1.90 atm

V = ?P1V1 = P2V2

(.95 atm)(4.2L) = (1.90 atm)V2

V2 = 2.1 L

B. Charles’ Law

1. Discovered the relationship between volume and temperature

2. If To increases then the volume increases

3. To and volume are directly proportional

4. Meaning = whatever volume does To does the exact same thing

NASA Video

Charles’ Law

T

V

V1/T1 = V2/T2

NOTE: All To must be Kelvin!!!!

oC + 273 = K

5. Example of Charles’ Law

Another sample of gas has a volume of 2.0 L and a To of 100 oC. If the To is increased to 200 oC, what will the new volume be?

V = 2.0L

100ºC

V = ?

200ºCV1/T1 = V2/T2

2.0L/(100 oC + 273) = V2/(200 oC + 273)

V2 = 2.54 L KELVIN!!!!!!!!

C. Gay-Lussac’s Law

1. Discovered the relationship between Pressure and To

2. If To increases then Pressure increases

3. To and P are directly proportional

4. Meaning = whatever To does pressure does the exact same thing

Gay-Lussac’s Law

P1/T1 = P2/T2

T

P

Example of Gay-Lussac’s LawAnother sample of gas has a volume of 2.0 L a To of 25 oC, and a pressure of 2.00 atm. If the To is increased to 75 oC, what will the new pressure be?

25ºC

2.00 atm

V = 2.0L 75ºC

V = 2.0L

P = ?

P1/T1 = P2/T2

2.00 atm/(25 oC + 273) = P2/(75 oC + 273)

P2 = 2.34 atm

D. Avogadro’s Law

• If pressure and temperature are kept constant, the volume of a gas is directly proportional to number of moles of a gas

• This is why a balloon gets larger as you blow it up… not the pressure

• 1 mole of gas = 22.4 L• Mathematically speaking…..

V1 = V2

n1 n2

Example of Avogadro’s Law

I have a balloon with 0.25 moles of air in it and its volume is 0.30 L. If I blow it up more to 0.75 L, how many moles have I added of air?

V1/n1 = V2/n2

0.30 L = 0.75 L = 0.63 moles

0.25 moles n2 moles

E. Combined Gas Law1. Sometimes the pressure, temperature, and/or change2. So must “combine” formulas from

all three “dudes”. 3. Looks like this

P1V1 = P2V2

T1 T2

Example of combined gas law8.0L of neon gas at 23 oC and 900 mm Hg is then

compressed to 2.0 L and the To is raised to 225 oC. What will the new P be?

P1V1/T1 = P2V2/T2

(900 mm Hg)(8.0 L)/(23 ºC + 273) = P2(2.0 L)/(225 ºC + 273)

P2 = 6057 mm Hg

F. Ideal Gas Law

PV = nRT

Where R = 0.08206 L atm/mol °K

Web Exploration

• ASPIRE Animation Activity (link)

• Gas Law Investigation (link)

– Data Collection Sheet (link)

More Practice on Following Slides

Sample problem #1

We will use Boyle’s Law: P1V1 = P2V2

(500.mm)(400.mL)=(250.mm)(V2)

V2= (500)(400) = 800. mL 250

A gas occupies a volume of 400. mL at 500. mm Hg pressure. What will be its volume, at constant temperature, if the pressure is changed to 250 torr? (1 mm Hg = 1 torr)

GIVEN:

V1 = 473 cm3

T1 = 36°C = 309K

V2 = ?

T2 = 94°C = 367K

WORK:

V1/T1 = V2/T2

Sample #2• A gas occupies 473 cm3 at 36 °C. Find its

volume at 94 °C.

CHARLES’ LAW

T V

(473 cm3)/(309 K)=V2/(367K)

V2 = (V1T2)/T1

V2 = 562 cm3

GIVEN:

P1 = 765 torr

T1 = 23°C = 296K

P2 = 560. torr

T2 = ?

WORK:

P1/T1 = P2/T2

Sample #3

• A gas’ pressure is 765 torr at 23°C. At what temperature will the pressure be 560. torr? GAY-LUSSAC’S LAW

P T

765 torr/296K = 560torr/T2

T2 = (P2T1)/P1

T2 = 217 K

Sample problem #4• A gas occupies a volume of 410 mL at 27°C and 740

mm Hg pressure. Calculate the volume the gas would occupy at STP. (0 oC & 760 mm Hg)

We will use the combined gas law:

2

22

1

11

TVP

TVP

Oops…use Kelvin 27°C=300K; 0°C=273K

mL363mm760K273

)K300()mL410)(mm740(

PT

TVP

V2

2

1

112

?0mm760C0

)C27()mL410)(mm740(

PT

TVP

V2

2

1

112

Independent Practice

• Calculations using four Gas Law Formulas

• Remember: oK = oC + 273• STP (Standard Temperature and Pressure) is

0oC and 760 mm Hg = 1 atm = 101.325 kPa = 14.7 psi.

• 1 torr = 1 mm Hg• 22.4 L = 1 mole of gas• R = 0.08206 L atm/mol °K

Dalton’s Law of Partial Pressure

• Sum of the pressures of each gas equals total pressure of system

• P1 + P2 + P3 + …. + Pn = Ptotal

A gas is 48% O2 & 52% N2. Total pressure is 100 kPa. What is the pressure of each gas?

100(.48) = 48 kPa for O2 and 100(.52) = 52 kPa for N2

Lab

• Gas Law Smorgasbord (link)

• In Periodic Groups, read the entire procedure

• Determine potential hazards, precautions to take, PPE that might be needed