Transcript Gas Laws - Independent School District 196

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?v=EH5v54dmb5U
• Think about a balloon in hot versus cold
weather. What is happening with the
movement of the gas particles? Kinetic
energy?
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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.
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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 &
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.
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,
then
http://www.chem.iastate.edu/group/Greenbowe/sections/projectfolder/flashfiles/g
aslaw/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/g
aslaw/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 GayLussiac’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, GayLussiac’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