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Gas Laws

Factors That Affect Gas Behavior

- 1. Temperature (T) ? a measure of the average

kinetic energy (movement) of particles in a

sample of matter - If the kinetic energy of particles increases,

the temperature of the substance increases. - KE ½ mv2
- m mass of the particles
- v speed of particles
- http//youtube.com/watch?vEH5v54dmb5U

- Think about a balloon in hot versus cold weather.

What is happening with the movement of the gas

particles? Kinetic energy?

- Units of temperature can be measured in
- 1. Celsius
- 2. Fahrenheit
- 3. Kelvin
- Who uses these temperature scales?
- U.S.A. uses Fahrenheit
- The rest of the world uses Celsius
- Scientists use Kelvin

- Important equations needed to do temperature

conversions - F 1.8 (C) 32
- K C 273

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- 2. Volume (V) ? the amount of space an object

takes up - Gases have an indefinite shape and size

depending on pressure and temperature - Gases are compressible and expandable
- Units of volume can be measured in
- 1. mL (for irregular shaped objects using H2O

displacement) - 2. cm3 (for regular shaped objects using the

equation l x w x h)

- 3. Amount (n) ? how much of a substance is

present - Units of amount can be measured in
- 1. Moles (the unit of measurement we use for

ALL gas laws) - 2. Grams
- 3. Number of molecules

- 4. Pressure (P) ? the force per unit area
- P force/area

- Ex. 2 female students are going to prom. One

is wearing Stilettos and the other is wearing a

chunky heeled shoe. They decide to take pictures

on the grass at Erickson Park. Assuming both

women have the same mass, which one is going to

have a harder time walking due to the amount of

pressure she is exerting on the ground?

- The pressure exerted by the girl wearing the

Stilettos will be greater than the girl wearing

the chunky heeled shoe.

- Units of pressure can be measured in
- 1. Pascals
- 2. Millimeters of mercury (mm Hg)
- 3. Torr
- 4. Newton per meter squared (N/m2)
- 5. Atmospheres (atm)

- At standard temperature and pressure (STP) O

C and 1 atm, the following pressure conversions

hold true - 1 atm 760 mm Hg 760 torr 101.3 kPa

Unique Properties of Gases According to Kinetic

Molecular Theory

- 1. Expansion
- Gas particles move rapidly and spread out in all

directions without significant attraction or

repulsion between them. - Ex. Perfume diffusing throughout the room

- When gas particles collide, they exhibit elastic

collisions where no kinetic energy is gained or

lost, just transferred from one particle to

another. - Ex. super ball (elastic) versus hacky sack

(inelastic) - Expansion allows gases to take the shape and

volume of the container they are in.

- 2. Compressibility
- Gas particles that are initially apart can

become crowded closer together. - Compression is possible because gases consist of

mostly empty space.

- 3. Low Density (mass/volume ratio)
- Gas particles are much farther apart that in the

liquid or solid state. - The density of gases is about 1/1000 the density

of the same substance in the liquid or solid

state. - http//www.youtube.com/watch?vd-XbjFn3aqE
- http//www.youtube.com/watch?v1PJTq2xQiQ0

- 4. Fluidity
- Gas particles can glide past each other without

being significantly attracted to one another. - This behavior is similar to liquids because you

are able to pour both states of matter. - Ex. Pouring CO2 gas on a lighted candle

Looking at the Relationships Between Variables

Graphically Mathematically

- Dependent versus Independent Variable
- A dependent variable will change based on an

independent variable. - Dependent variables are contingent on other

variables. They depend on the other factors - Ex. Speed (miles per hour)
- Miles are dependent on the amount of hours

traveled - The dependent variable will always be found on

the y-axis when graphing

- Independent variables do not depend on any other

variables to change. - Independent variables will change in their normal

conditions regardless of what happens - Ex. Speed (miles per hour)
- The hours are independent and will continue to

change, regardless of the miles traveled - The independent variable will always be found

on the x-axis

- Direct Versus Inverse Relationships
- Direct relationships represent two variables

acting in the same way. - kX/Y
- If X increases, Y increases to keep k constant
- If X decreases, Y decreases to keep k constant

- Inverse(Indirect) relationships represent two

variables acting oppositely. - k XY
- If X increases, Y must decrease to keep k

constant - If X decreases, Y must increase to keep k

constant

Gas Laws

- Boyles Law ? As pressure of a gas increases,

the volume decreases at the same rate - Temperature and amount of gas must remain

constant - Inverse relationship
- PV k
- Ex. Station 2 from gas laws lab (adding books to

create pressure to the block apparatus)

- This law can be used to predict the result of

introducing a change, in volume or pressure only,

to a fixed amount of gas, by using the following

equation - If P1V1 k and P2V2 k for a fixed amount of

gas, then - http//www.chem.iastate.edu/group/Greenbowe/secti

ons/projectfolder/flashfiles/gaslaw/boyles_law_gra

ph.html - P1V1 P2V2
- 1 initial situation
- 2 final situation

- Sample problem
- If I have 5.6 liters of gas in a piston at a

pressure of 1.5 atm and compress the gas until

its volume is 4.8 L, what will the new pressure

inside the piston be?

- Charless Law ? As the temperature (in Kelvins)

of a gas increases, the volume increases at the

same rate - Pressure and amount of gas must remain constant
- Direct relationship
- V/T k or T/V k
- Ex. Station 3 from gas law lab (placing plungers

with a specific amount of gas into different

temperature water baths)

- This law can be used to predict the result of

introducing a change, in volume or temperature

only, to a fixed amount of gas, by using the

following equation - If V1/T1 k and V2/T2 k for a fixed amount of

gas, then - http//www.chem.iastate.edu/group/Greenbowe/sectio

ns/projectfolder/flashfiles/gaslaw/charles_law.htm

l - V1/T1 V2/T2
- 1 initial situation
- 2 final situation

- Sample Problem
- If I have 45 liters of helium in a balloon at

250 C and increase the - temperature of the balloon to 550 C, what will

the new volume of the balloon be?

- Gay-Lussiacs Law ? As the temperature (in

Kelvins) of a gas increases, the pressure

increases at the same rate - Volume and amount of gas must remain constant
- Direct relationship
- P/T k or T/P k
- Ex. Station 1 from gas law lab (pop can

crushing)

- This law can be used to predict the result of

introducing a change, in pressure or temperature

only, to a fixed amount of gas, by using the

following equation - If P1/T1 k and P2/T2 k for a fixed amount of

gas, then - P1/T1 P2/T2
- 1 initial situation
- 2 final situation

- Sample Problem
- A gas cylinder containing explosive hydrogen gas

has a pressure of 50 atm at a temperature of 300

K. The cylinder can withstand a pressure of 500

atm before it bursts, causing a

building-flattening explosion. What is the

maximum temperature the cylinder can withstand

before bursting?

- Review
- Boyles Law PV k
- Charless Law V/T k
- Gay-Lussiacs Law P/T k
- How can we mathematically represent all 3 of

these gas laws?

- Combined Gas Law ? When 2 variables of a gas

sample change, the third variable will adjust to

keep k a constant - This law incorporates Boyles, Charless, and

Gay-Lussiacs Law - The amount of the gas must remain constant
- PV/T k
- If P1V1/T1 k and P2V2/T2 k, then
- P1V1/T1 P2V2/T2

- Sample Problem
- A 350 cm3 sample of helium gas is collected at

22.0 oC and 99.3 kPa. What volume would this gas

occupy at STP?

- Dalton Law of Partial Pressures
- The total pressure of a mixture of gases is equal

to the sum of the partial pressures of the

component gases - Ptotal P1 P2 P3
- Atmospheric pressure, temperature and volume of

the gas mixture must remain constant

- Sample problem 1
- If you have three 400 L tanks, each filled with a

different gas, - Tank 1 contains N2 and has a pressure valve

reading of 320 kPa - Tank 2 contains CO2 and has a pressure valve

reading of 2.0 atm - Tank 3 contains O2 and has a pressure valve

reading of 380 torr - What would be the total pressure in kPa if all

the gases were contained in the same 400 L tank?

- Sample problem 2
- A container holds 36 g of N2. 28 g of O2 are

added to the container. The total pressure of

the container is 40. kPa. - a. Calculate the mole fraction of each gas
- b. Calculate the partial pressure of the N2 and

O2

- Sample problem 3
- 1.0 mole of oxygen gas and 2.0 moles of ammonia

are placed in a container and allowed to react at

850 degrees Celsius according to the equation - 4NH3(g) 5O2(g) --gt 4NO(g) 6H2O(g)
- If the total pressure in the container is 5.00

atm, what are the partial pressures for the three

gases remaining?

- Avogadros Law ? the volume of a gas will

increase as moles of particles increases - Pressure and temperature of a gas must remain

constant - Direct relationship
- V/n k or n/V k
- Ex. Station 4 from gas law lab (balloons)

- Ideal Gas Law
- This law incorporates Boyles, Charless,

Gay-Lussiacs and Avogadros Laws into one. - P1V1/n1T1 P2V2/n2T2
- The problem with this law is that there are 8

variables to work with. - To make it easier, we can compare the gas in

question to an ideal gas situation (R, which is

always at STP)

- For any gas whose behavior approaches that of an

ideal gas according to the Kinetic Molecular

Theory, we can use a constant situation (R, which

is always at STP) to compare to the gas in

question. Theoretically, any gas in a normal

range will behave in the same manner. - R P2V2/n2T2
- PV nRT
- R P1V1/n1T1 gas situation at STP, where
- P1 1 atm or 760 mm Hg or 101.3 kPa
- V1 22.4 L
- T1 273 K
- n1 1 mol

- The Gas Law Constant (R) will change values

depending on the units of pressure used - ? see Gas Law Constant reference sheet in packet
- When using the ideal gas law equation,
- V must always be in liters!
- T must always be in Kelvins!
- N must always be in moles!

- R P2V2/n2T2
- if atm is used, R .0821 (atm x L)/(mol x K)
- (1 atm x 22.4 L)/(1 mol x 273 K) .0821
- if kPa is used, R 8.314 (kPa x L)/(mol x K)
- (101.3 kPa x 22.4 L)/(1 mol x 273 K) 8.314
- if mm Hg are used, R 62.4 (mm Hg x L)/(mol x

K) - (760 mm Hg x 22.4 L) /(1 mol x 273 K)

- Exceptions to using the ideal gas law
- Under extreme pressure and temperature

conditions, a gas might not behave ideally - For example, gas molecules might become slightly

attracted to each other at extremely high

pressures and low temperatures.

- Grahams Law of Effusion (Diffusion)
- Diffusion ? the gradual mixing of 2 gases due to

their spontaneous, random motion - Ex. Burning incense
- Effusion ? a type of diffusion where gas

molecules are confined to a tiny container and

randomly pass through a tiny opening in that

container - Ex. Perfume escaping through tiny bottle opening

- The rates of effusion of gases are inversely

proportional to the square roots of their molar

masses - Heavier particles effuse at a slower rate
- Lighter molecules travel at a faster rate
- vA/vB ?mB/?mA
- A gas 1
- B gas 2
- v velocity or rate of effusion
- m molar mass

- Effusion Demo
- Who will travel faster?
- NH3 or HCl?

- Sample problem
- If 10 ml of an unknown gas takes 6.3 seconds to

pass through small opening while 10 ml of a

standard gas, Oxygen O2 takes 5.6 seconds to pass

through the same opening under the same

conditions of temperature and pressure, what will

be the molecular mass of the unknown gas?

- Barometer
- An instrument that measures atmospheric pressure

- Sample problem 1
- How will a barometer be affected on a stormy day?
- How will a barometer be affected on a warm, sunny

day? - What will happen to Patm?
- What will happen to the mm Hg inside the tube?

- Sample problem 2
- At STP, how much Hg will be in the tube in

inches?

- Sample problem 3
- Using H2O instead of Hg will force the design if

the barometer to be adjusted. How and why?

(Hint The density of Hg 13.6 g/mL)

- Gas Collection through H2O Displacement
- When collecting a gas through water displacement,

a small amount of water vapor is produced. This

water vapor exerts pressure along with the gas

you are collecting.

- To determine the pressure of the gas collected,

the levels of water both inside and outside of

the flask must be equal to ensure the following

mathematical relationship holds true - PAtmosphere PGas Pwater
- PAtmosphere can be found by reading a barometer
- PWater can be found by measuring the temperature

of the water used for displacement and by reading

the Vapor Pressure of H2O chart for this value. - PGas PAtmosphere - PWater