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 particlesv = speed of particles

http://youtube.com/watch?v=EH5v54dmb5U

• 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

• 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?v=d-XbjFn3aqE• http://www.youtube.com/watch?v=1PJTq2xQiQ0

• 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 &

MathematicallyDependent 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.k=X/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• Boyle’s 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, thenhttp://www.chem.iastate.edu/group/Greenbowe/sections/projectfolder/flashfiles/gaslaw/boyles_law_graph.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?

• Charles’s 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/sections/projectfolder/flashfiles/gaslaw/charles_law.html

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-Lussiac’s Law As the temperature (in Kelvin’s) 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:

• Boyle’s Law PV = k

• Charles’s Law V/T = k

• Gay-Lussiac’s 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 Boyle’s, Charles’s, and Gay-Lussiac’s 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) --> 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?

• Avogadro’s 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 Boyle’s, Charles’s, Gay-Lussiac’s and Avogadro’s 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.

• Graham’s 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