Gas Laws
Chapter 13
Warm Up!
• If you have a balloon filled with air and the
temperature increased what would you
observe?
• what happens to the gas particles inside the
balloon?
• What would happen if the temperature was
decreased?
Today’s Agenda
• QOTD: What are the variables involved in the
behavior of gases and what are the laws that
govern gas behavior?
• Boyle’s Law
• Charles’ Law
• Gay-Lusacc’s Law
Gas Laws
• We are considering 4 variables:
• V = volume n = moles
• T = temperature
P = pressure
• Simulation: http://phet.colorado.edu/en/simulation/gasproperties
• We want to know if you change one variable, how
does that affect the other measurements?
Relationships of P,V,T,n
• Remember that:
P=F
A
• Volume is related to area, so as volume gets larger
the area will increase and P will decrease
• Volume and pressure are INVERSELY related.
• Temperature and moles are related to force because
as T increases it will result in more collisions –
meaning larger forces. Also, more moles means
more “stuff” to collide and larger forces . The larger
the forces the higher the pressure .
• Temperature/moles are DIRECTLY related to pressure.
Gas Law’s
• The individual gas laws assume that you hold all
other variables that are NOT used constant!
• Boyles Law – Describes the inverse relationship
between volume and pressure
• As volume decreases, pressure increases.
P1V1=P2V2
Using Boyle’s Law
When conditions change, you solve for a new
volume or pressure.
Example!
A balloon filled with gas at a pressure of 1.3 atm
has a volume of 2.2 L. When the volume is
increased to 4.1 L what is the new pressure?
Boyle’s Law
• Your turn!
• What is the volume of a gas if 0.76 L of a gas is
in a piston at 820 mmHg of pressure if the
pressure is reduced to 610 mmHg?
Gas Laws
• Charles’ Law - Describes the direct relationship
between volume and temperature.
• As volume increases, temp increases!
• V1 = V 2
T1 T2
is the same as T1 = T2
V1 V2
Using Charles’ Law
When conditions change, you solve for a new
temperature or volume.
Example!
A balloon filled with gas has a volume of 2.2 L at
298K . When the balloon is heated to 355 K
what is the new volume?
Charles’ Law
• Your turn!
• A gas mixture at 400K occupies a volume of
2.76 L. If the volume is decreased to 1.32 L
what is the temperature?
Gas Laws
• Gay-Lussac’s Law – Describes the direct
relationship between temperature and pressure.
• As temperature increases, pressure increases.
• P1 = P2 is the same as T1 = T2
T1 T2
P1 P2
Using Gay-Lussac’s Law
When conditions change, you solve for a new
temperature or pressure.
Example!
• Gas particles are at standard pressure and
temperature in a rigid container. When the
container is heated at 373 K, what is the new
pressure?
Gay-Lussac’s Law
• Your turn!
• What is the temperature of a gas in a sealed
rigid container at 268 kPa, if initially it was at a
temperature of 200 K and a pressure of 85 kPa.
Gas Laws
• Combined Gas Law – relates pressure,
temperature and volume and assumes moles
is held constant.
• All the relationships in one tidy law!
• P1V1 = P2V2
T1
T2
is the same as T1 = T2
P1V1 P2V2
Combined Gas Law
• When conditions change, you solve for a new
pressure, temperature, or volume!
• Example
• A 350 mL sample of helium gas is collected at
22.0 oC and 99.3 kPa. What volume would this
gas occupy at STP?
Combined Gas Law
• Your turn!
• Initially a gas is at a pressure of 12 atm, a
volume of 23 liters, and a temperature of
200 K. The pressure is raised to 14 atm and
temperature increased to 300 K, what is the
new volume of the gas?
Warm Up!
• A gas has a final volume of 22.4 L at STP. What
was the initial volume measured at 810 mmHg
and 200 K?
• What is the missing variable in the combined
gas law?
• Considering P= F/A, where would this last
variable belong if added to the combined gas
law?
Todays Agenda
• QOTD: What is the ideal gas constant and how
is it calculated?
• Avogadros Principle
• Ideal gas constant and law
• Calculating density and molar masses
• Lab Books Due Thurs pm (Baking Soda Lab)!
• All bookwork and Gas Law Packet due Friday
Combined Gas Law
• Combined Gas Law – relates pressure,
temperature and volume and assumes moles
is held constant.
• P=F
F related to T
Where does moles fit?
A
A related to V
• P1V1 = P2V2
T1
T2
is the same as T1 = T2
P1V1 P2V2
The missing variable – n!
Avogadro’s Principle - Equal volumes of gases
contain the SAME number of particles
• Molar volume of a gas – volume that 1 mol
occupies at STP (273K and 1 atm)
• What is that volume??? 22.4 L
Ideal Gas Constant
• Combined Gas law, plug in values from warm
up and see if both sides are equal…
P1V1 = P2V2  0.0821 = 0.0821
T1
T2
• For a specific sample of gas – relationship
between pressure, volume, and temp is
ALWAYS the same PV = R = .0821 L atm/mol K
T
Deriving the Ideal Gas Law
• Use the combined gas law and R, add in moles
and…..
PV = R
rearranges to PV = nRT
nT
In class practice:
Calculate the number of moles of ammonia gas
(NH3) contained in a 3.0 L vessel at 300 K and
1.50 atm of pressure.
Your turn!
• Determine the temperature (in °C) of 2.49 mol
of a gas contained in a 1.0 L vessel at 143 kPa.
(Remember that because of R, your
calculations have to be in Kelvin and atm!)
Make an inventory and remember your
conversions!
Warm Up!
• Find the pressure at which 2.05 moles of gas
occupy 1.5 L at 298K.
• How many moles of oxygen gas occupy a 3 L
tank at STP?
Today’s Agenda
• QOTD: How can you calculate density of gases
using the ideal gas law and when are gases
non-ideal?
• Density and mass derivations
• REAL gases
• Practice Problems
Finding Molar Mass
• You can use the ideal gas law to find the molar
mass of an unknown gas!
• Remember: moles (n) = mass (g)
molar mass (g/mol)
So we replace n with m/MM in PV = nRT
PV = mRT which rearranges to MM = mRT
MM
PV
Substituting with Density
• Since MM = mRT , and we know that
PV
D = m/v how can we use density to find MM?
MM =
DRT
P
In summary,
PV = nRT and since n = m/MM then MM = mRT/PV
AND since d = m/v now MM = DRT/P!
Practice Problem
• What is the molar mass of gerinol (a
compound found in perfumes) if its vapor has
a density of 0.480 g/L at a temperature of
260 °C and a pressure of 0.140 atm?
Your Turn!
1. Rearrange MM= DRT/P to solve for D.
2. Determine the density of chlorine gas at
295K and 1 atm.
Warm Up!
• Find the pressure at which 2.05 moles of gas
occupy 1.5 L at 298K.
• How many grams of oxygen gas are contained
in 3.25 L at STP?
• Find the density of Kr gas at STP.
Today’s Agenda
• QOTD: How do real gases behave?
• Non-ideal behavior
• Practice Problems
Deviations of REAL gases
• Remember that the IDEAL gas law assumes
that all gases behave ideally as described by
kinetic molecular theory.
• Gas particles are tiny - take up negligible
volume
• Gases experience no intermolecular
attractions
• Collisions of gas particles are perfectly elastic
and do not lose energy.
Gases aren’t really IDEAL
• Gas particles are small but do take up volume.
• Gases do experience some intermolecular
attractions
• Collisions are not perfectly elastic and some
energy is lost.
BUT
• Most gases behave similarly to ideal so we can
still use the ideal gas law to approximate
them!
Factors Contributing to Non-Ideal
Behavior
• Gases can not be approximated accurately by
the ideal gas law at
really HIGH PRESSURE and really LOW
TEMPERATURE
Why?
Consider IMF’s and phases
Factors Contributing to Non-Ideal
Behavior
• Gases are less ideal when:
A gas is HIGHLY POLAR or has LARGE PARTICLES
Why?
Warm Up!
• A 250 mL flask is filled with helium gas at a
pressure of 1.2 atm and a 130 K. What is the
mass of helium in the flask?
• If the same sample of helium was stored at
STP, what is the final volume?
• How do you determine if the units of P, V, and
T are the RIGHT units??
Today’s Agenda
• QOTD: None, review!
• Combined/Ideal worksheet – classwork only
• Quiz tomorrow: Combined gas law, ideal gas,
law, ideal gas with mass and density.
You will be given PV=nRT, R = 0.0821 Latm/molK, and
P1V1/T1 = P2V2/T2
• Lab books due TODAY (baking soda lab)
• HW: Completed Gas Law, Ideal gas law packets
and Combined Gas Law Sheet due tomorrow!
Warm Up!
• Write the balanced equation for the reaction
of nitrogen and hydrogen gases reacting to
form ammonia (NH3).
• What is the mole ratio of nitrogen and
hydrogen gases?
• What is the mole ratio of hydrogen gas to
ammonia?
Today’s Agenda
• QOTD: How can you use the ideal gas law with
the chemical reaction to calculate
stoichiometry of a gas reaction.
•
•
•
•
•
Stoichiometry with gas reactions
Volume – Volume Problems
Mass – Volume Problems
Classwork Problems
Homework (Due Wed) – Ch 13: 80 to 98 evens
Stoichiometry with Ideal Gas Law
• Remember the key to stoichiometry is a
balanced chemical eqn.
– Review formula writing/naming, types of
reactions, and balancing reactions if you need
help!!
• When gases react the coefficients in the
balanced equation represent both molar
amounts and relative volumes!
Volume-Volume Stoich of Gases
• What volume of oxygen gas is needed for the
combustion of 4.0 L of propane gas (C3H8)?
• C3H8 + 5O2  3CO2 + 4H2O
• Given : V = 4.0 L C3H8
Want : V = ? L O2
• 4.0 L C3H8 x 5 volume units O2 = 20.0 L O2
1 volume unit C3H8
Your Turn!
• How many liters of propane gas (C3H8) will
undergo complete combustion with 34.0 L of
O2 gas?
• Determine the volume of hydrogen gas
needed to react completely with 5.0 L of
oxygen gas to form water.
Volume-Mass Stoich of Gases
• Ammonia (NH3) is synthesized from nitrogen
and hydrogen. If 5.0 L of nitrogen reacts
completely with hydrogen at a pressure of 3.0
atm and a temperature of 298 K, how much
ammonia, in grams, is produced?
• Write the balanced equation!
N2 + 3H2  2NH3
• Given: V = 5.0 L
P = 3.00 atm
T = 298 K
Want: m = ? g NH3
2. Convert from liters of N2 to liters of NH3
5.0 L N2 x 2 volume units NH3 = 10.0 L NH3
1 volume unit N2
N2 + 3H2  2NH3
3. Use the ideal gas law to calculate moles of NH3
PV = n
RT
3 atm x 10.0 L NH3 = 1.23 mol NH3
0.0821Latm/molK x 298 K
4. Convert moles of NH3 to grams
1.23 mol NH3 x 17 g NH3 = 21 g NH3
1 mol NH3
Set up Eqn and Solve!
Your Turn!
• Ammonium nitrate decomposes into
dinitrogen monoxide and water. Calculate the
mass of solid ammonium nitrate that must be
used to obtain 0.1 L of dinitrogen monoxide
gas at STP.