Unit 10 - Gases
Kinetic Molecular Theory
• All matter is composed of tiny
particles that are in constant motion
• Gases are point masses that:
– Are in constant motion
– Have elastic collisions
– Have no attractive forces between
particles
http://phet.colorado.edu/new/simulations
/sims.php?sim=Gas_Properties
14.1
The Gas Laws
Defining Gas Pressure
• According to the
kinetic theory, all
matter is composed
of particles in
constant motion,
and pressure is
caused by the force
of gas particles
striking the walls of
their container.
– The more often gas
particles collide with
the walls of their
container, the
greater the pressure.
– Therefore the
pressure is directly
proportional to the
number of particles.
Physical Properties
• Temperature (average kinetic
energy)
– ↑ temperature, ↑ velocity
– Units – always Kelvin
(add 273 to Celsius temp.)
– Standard Temperature –
0°C (273 K)
– Absolute Zero – All motion stops
• 0 K or -273°C
Physical Properties
• Volume (space taken up by
movement of molecules)
– Gas will always occupy total volume of
container
• Transfer gas from a 2 L to a 1 L bottle & its
volume changes from 2 L to 1 L
– Gases can expand or be compressed
• Ex. 1 mol dry ice = 28 cm3
1 mol CO2 gas = 25000 cm3
Physical Properties
• Volume cont.
– To expand or compress gas must have:
• Container capable of changing volume (ex.
balloon)
• ↑ T = more volume
• ↑ P = ↓ V (squeezes)
– Gases diffuse from high to low
concentrations
Physical Properties
• Pressure
– Force over a given area exerted by
moving gas molecules
– Depends upon number & force of
collisions
• Amount of gas (moles)
• Volume of gas
• Temperature
Physical Properties
• Pressure cont.
– Units:
• Pascals (N/m2)
• Mm Hg
• Torrs
• Atmospheres
• PSI (pounds per square inch)
– Standard Pressure:
1 atm = 101.3 kPa = 760 mm Hg = 760 torrs
Physical Properties
• Barometer – An instrument that measures
atmospheric pressure (the pressure
exerted by the atmosphere).
– The height of the mercury column measures
the pressure exerted by the atmosphere.
• Manometer – measures pressure of other
gases compared to atmospheric pressure
14.1
The Gas Laws
Defining Gas Pressure
• The pressure of a
gas is the force per
unit area that the
particles in the gas
exert on the walls
of their container.
– As you would expect,
more air particles
inside the ball mean
more mass inside.
• Note: the pressure
of a gas is directly
proportional to its
mass.
Physical Properties
• Pressure cont.
– You can change pressure by:
• Adding heat – molecules move faster; more
collisions; more pressure
• Increase volume – same # atoms;
↑ space; ↓ pressure
– STP = Standard Temperature & Pressure
(0°C & 1 atm)
Physical Properties
• Atmospheric pressure is the result of
collisions of air molecules with objects.
• Atmospheric pressure decreases with an
increase in altitude. The air around the
earth “thins out” at higher elevations.
Physical Properties
Pressure decreases with increasing altitude
Graham’s Law
• Diffusion – gas molecules move from
high concentration to low
concentration
• Effusion – gas molecules pass
through a small hole
• At the same temperature heavier
molecules are slower, lighter
molecules are faster
14.1
The Gas Laws
The Gas Laws
The gas laws apply to ideal gases, which are
described by the kinetic theory in the
following five statements.
– Gas particles do not attract or repel each other.
– Gas particles are much smaller than the spaces
between them.
– Gas particles are in constant, random motion.
– No kinetic energy is lost when gas particles
collide with each other or with the walls of
their container.
– All gases have the same kinetic energy at a
given temperature.
Gas Laws
• Relate: Volume – Temperature –
Pressure
• Boyle’s Law – Effect of pressure on
volume
– ↑P ↓V (inverse relationship)
– Temp. is constant
– If you double P; V will be halved
– a) If the pressure of a gas increases, its
volume decreases proportionately.
– b) If the pressure of a gas decreases, its
volume increases proportionately.
– P1V1 =P2V2
Gas Laws
• Charles’ Law – Effect of temperature on
volume (the volume of the gas increases
in proportion to the increase in Kelvin
temperature).
–
–
–
–
–
↑T ↑ V (direct relationship)
T must be in Kelvin
Pressure is constant
If you double T, V will double
V1 = V2
T1 T2
Gas Laws
• Gay-Lussac’s Law – Effect of
temperature on pressure
– ↑T ↑P (direct relationship)
– T must be in Kelvin
– Double T, P will also double
– Half T, P will also be one-half
– P1 = P2
T1 T2
Gas Laws
• Combined Gas Law
P1V 1 P 2V 2

T1
T2
• If you do not have a change in one of the
variables replace it with a one or omit it!
• Only need ONE FORMULA!!!!!!
Practice Problems
• Write down all givens; Change °C to K;
Think about relationship; Finally solve
problem
A balloon inflated in an air conditioned room at
27oC has a volume of 2.0 L. If it is heated to 57oC
and the pressure remains constant, what is the
new volume?
T1= 27°C + 273= 300K
V1= 2.0 L
P1= constant
V1
T1

V2
T2

2.0 L
300K

?L
330K
T2= 57°C + 273= 330K
V2 = ? L
P2= constant
?L 
( 330K )( 2.0 L )
300K
 2.2 L
Practice Problems
1. A gas in an aerosol can is at a pressure
of 1 atm and 27°C. If the can is thrown
into a fire, what is the internal pressure
of the gas if the temperature reaches
927°C?
2. A 25 mL balloon at 1.25 atm and 45°C is
released and rises up to an atmospheric
pressure of 0.816 atm where the volume
of the balloon changes to 100 mL. What
temperature is the gas at the new
pressure?
Real vs. Ideal Gases
Real
Ideal
Made up of particles
Made up of particles
Particles in constant motion
above 0 K
Particles in constant motion
above 0 K
When particles collide, one loses
energy & one gains energy
Particles have elastic collisions
Particles attract each other
Particles have no attraction for
each other
Particles (atoms, etc.) actually
take up some space
Particles occupy no space.
Volume of gas is volume of
container
Ideal Gases
• Ideal gases don’t really exist, but
many gases do act ideally under
certain conditions
• When gas molecules are far apart
and not able to attract one another,
they act ideally
• This usually occurs at High
Temperatures and Low Pressure
14.3
The Ideal Gas Law
The Ideal Gas Law
• The pressure, volume, temperature,
and number of moles of gas can be
related in a simpler, more convenient
way by using the ideal gas law.
– The following is the law’s mathematical
expression, PV = nRT where n
represents the number of moles.
– The ideal gas constant, R, already
contains the molar volume of a gas at
STP along with the standard
temperature and pressure conditions.
Ideal Gas Law
• Solving Problems
– Write down the givens in the problem
– Make sure all the units are in L, mol,
atm, and K
– Plug into the equation (PV=nRT) and
make sure unwanted units cancel
Ideal Gas Law
2.0 mol oxygen gas are placed in a 10 L
container at 20°C. What is the pressure?
n=2.0 mol
V=10 L
T=293K
R= 0.0821 L atm/mol K
P=?
PV=nRT P=nRT/V
P=[(2.0mol)(0.0821 L atm/mol K)(293K)]/(10 L)
P=4.8 atm
Ideal Gas Law: PV=nRT
• Relates P, V, T and Moles (n)
• For any ideal gas VP/nT is constant; we
call this contant R
• We can calculate R by inserting the values
for STP and the molar volume of a gas at
STP… so that…
R
VP
nT

( 22.4 L )(1atm)
(1mol )( 273K )
 0.0821
L atm
mol K
• Watch units when using Ideal Gas Law!!!!
Practice Problems
1. How many moles of H2 must be put
into a 200 mL container at 25°C to
get 1.5 atm?
2. 0.8 g of gas occupies a volume of
372 mL at 100°C and 800 torr. Find
its molar mass.
3. Find the density of NO2 at 100°C
and 800 torr
Dalton’s Law of Partial
Pressure
• If several gases are mixed together
– They behave as if they were each alone
in the container
– Each gas exerts its own pressure
– So Dalton said:
Total Pressure = sum of the partial
pressures of each gas
PT=P1+P2+P3+…
Dalton’s Law of Partial
Pressure
• Examples:
• Gas A exerts a pressure of 1.5 atm in
a 2 L container. Gas B exerts a
pressure of 2.0 atm in the same
container. What is the total pressure?
• Gas A & B (above) are in a 1 L
container. What is the total pressure
Dalton’s Law of Partial
Pressure
• 2 mol O2, 3 mol N2, and 5 mol CO2
are in a 3 L container at 1000 torr.
What is the volume of each gas?
(mol gas/total mol) x total pressure
O2 = (2/10) x 1000 = 200 torr
N2 = (3/10) x 1000 = 300 torr
CO2 = (5/10) x 1000 = 500 torr
Gas Density
• Density = Mass/Volume (units=g/L)
• At STP, Gas density = Molar mass/22.4L
– Remember 1 mol=22.4L, Molar Mass=g/mole
• If two gases have the same T, P, V; they
will have the same number of particles or
moles!
• 22.4L can be use to change mol & volume
ONLY AT STP
• Example: 11.2 L H2 1 mol H2
22.4 L H2
Gas Density
• Gas density changes with P & T
– If T or P changes does mass change? Does
volume change?
– If volume increases, density will ________?
• To predict density changes, determine
what volume will do. Density will do the
opposite.
Gas Density
• To find the new density
– Find the new volume using Combined
Gas Law
– Divide same mass by new volume
T 1D1 T 2 D 2

P1
P2
Touch Down Pass 1 =
Touch Down Pass 2
Gas Density
The density of a gas is 1.5 g/L at 20°C and
700 torr. Find the density at STP.
P1 = 700 torr
P2 = 760 torr
V1 = 1L
V2 = ? L
T1 = 293K
T2 = 273K
( 700torr)(1L )
293K

( 760torr)(V 2 )
273K
 V 2  0.86 L
New Density: mass = 1.5g = 1.74 g/L
V2
0.86L
Practice Problems
1. The density of O2 is 1.43 g/L at
STP. Find the density at 50°C.
2. What is the density of CO2 at STP?
3. What is the density of CO2 at 50°C
and 780 mmHg?
Stoichiometry Review
• Remember that the coefficients stand for
moles, molecules, and Liters @STP
• Review the steps
• Balance the equation
• Write want and given
• Convert given to moles
• Multiply by ratio want / given
• Convert to what you want
• Adjust from STP if required
14.4
Gas Stoichiometry
Gas Stoichiometry
• Now that you know how to relate volumes,
masses, and moles for a gas, you can do
stoichiometric calculations for reactions
involving gases.
• Ammonium sulfate can be prepared by a
reaction between ammonia gas and
sulfuric acid as follows.
• What volume of NH3 gas, measured at
78°C and a pressure of 1.66 atm, will be
needed to produce 5.00 x 103 g of
(NH4)2SO4?
14.4
Gas Stoichiometry
Gas Stoichiometry Using Mass
• Finally, use the ideal gas law
equation to calculate the
volume of 75.68 mol NH3
under the stated conditions.
– Solve the equation for V,
the volume to be
calculated.
– Convert the temperature to
kelvins, substitute known
quantities into the equation,
and compute the volume.
• Notice that the values for the
molar mass of (NH4)2SO4 and
the number of moles of NH3
have more than three
significant figures, whereas the
calculated volume has only
three.
14.4
Gas Stoichiometry
Gas Stoichiometry Using Mass
• When you do a problem in a stepwise
way, you should maintain at least
one extra significant figure in the
intermediate values you calculate.
• Then, round off values only at the
end of the problem.