Seeing the Unseen
• Air is invisible, but we
know it exists:
– Winds blow.
– Flags fly*.
– We breathe.
*Flags can’t fly on the moon
because there is no
atmosphere – no wind.
Air is a Mixture
• Clean air is a Substance Percentage
mixture of several
pure substances. Nitrogen (N2) 78.10
• The table shows the Oxygen (O2) 20.90
composition at sea
level for dry air. Argon (Ar) 0.93
• Normal air also
Carbon dioxide 0.04
contains water vapor (CO2)
- the cause of Trace gases <0.03
humidity.
Molecular Interactions in
Gases are Negligible
• Gases are mostly empty
space: molecules occupy
<0.1 % volume.
• 1,000 times less dense
than solids and liquids.
• Emptiness allows
complete mixing.
• All gases “dissolve” other
gases.
Keeping the Genie in the Bottle
• Solids and liquids do
not need to be
confined in a sealed
container.
• Without a sealed
container, unconfined
gas molecules disperse
quickly.
• Gas molecules move
quickly – but not all at
the same speed.
Going Nowhere Fast
• Molecules move quickly,
but take a long time to get
anywhere because of
collisions with each other.
• Without collisions, a
molecule would cross a
room in a fraction of a
second.
• Collisions can make the
journey last several
minutes.
Kinetic Molecular Theory
• Matter is composed of tiny particles (atoms, molecules or ions) with
definite and characteristic sizes that never change.
• The particles are in constant random motion, that is they possess
kinetic energy. Ek = 1/2 mv2
• The particles interact with each other through attractive and repulsive
forces (electrostatic interactions), that is the possess potential energy.
U = mgh
• The velocity of the particles increases as the temperature is increased
therefore the average kinetic energy of all the particles in a system
depends on the temperature.
• The particles in a system transfer energy from one to another during
collisions yet no net energy is lost from the system. The energy of the
system is conserved but the energy of the individual particles is
continually changing.
Properties of Gases
DIFFUSION
Diffusion is the ability of two or more gases to mix spontaneously until
a uniform mixture is formed.
Example: A person wearing a lot of perfume walks into an enclosed
room, eventually in time, the entire room will smell like the perfume.
EFFUSION
Effusion is the ability of gas particles to pass through a small opening
or membrane from a container of higher pressure to a container of
lower pressure.
The General Rule is: The lighter the gas, the faster it moves.
Graham’s Law of Effusion:
Rate of effusion of gas A = √(molar mass B / molar mass A)
Rate of effusion of gas B
The rate of effusion of a gas is inversely proportional to the square root
of the molar mass of that gas.
PRESSURE
• A physical property of matter that describes
the force particles have on a surface.
Pressure is the force per unit area, P = F/A
• Pressure can be measured in:
• atmosphere (atm)
• millimeters of mercury (mmHg)
• (torr) after Torricelli, the inventor of the mercury
barometer (1643)
• pounds per square inch (psi)
1 atm = 760 mmHg = 760 torr = 14.69 psi
Got Me Under Pressure
• Gases exert pressure
by virtue of molecular
collisions with the
container surface.
• Gravity makes the air
density higher near the
earth’s surface.
• Pressure decreases
with elevation – air
density decreases.
DALTON’S LAW OF PARTIAL
PRESSURES
If there is more than one gas present in a
container, each gas contributes to the
total pressure of the mixture.
Ptotal = Pgas A + P gas B + Pgas C …
If the total pressure of a system was 2.5
atm, what is the partial pressure of
carbon monoxide if the gas mixture also
contained 0.4 atm O2 and 1.48 atm of N2?
PT - PO2 - PN2 = PCO 2.5 atm - 0.4 atm - 1.48 atm = 0.62 atm
TEMPERATURE
• A physical property of matter that
determines the direction of heat flow.
• Measured on three scales.
• Fahrenheit oF Celsius oC
• Kelvin K
• oF = (1.8 oC) + 32 oC = (oF - 32)/1.8
• K = oC + 273.15
Standard Temperature and Pressure
(STP)
• Standard conditions:
– Standard temperature
is 273 K (0ºC).
– Standard pressure is
760 mm Hg.
• At STP, 1 mole of any
ideal gas occupies
22.414 L.
AvogAdro’s HypotHesis
• Avogadro pictured the moving molecule as occupying a
small portion of the larger space apparently occupied by
the gas. Thus the “volume” of the gas is related to the
spacing between particles and not to the particle size itself.
• Imagine 3 balloons each filled with a different gas (He, Ar,
& Xe). These gases are listed in increasing particle size,
with Xe being the largest atom. According to Avogadro’s
Hypothesis, the balloon filled with one mole of He will
occupy that same volume as a balloon filled with one mole
of Xe.
• So for a gas, the “volume” and the moles are directly
related. V a n
Practice Problem on
AvogAdro’s HypotHesis
• A sample of N 2 gas at 3.0 atm and 20.0oC is known to occupy a
volume of 1.43 L. What volume would a 0.179 mole sample of
NH3 gas occupy at the same pressure and temperature?
First calculate the number of moles of nitrogen gas: PV = nRT
where P = 3.0 atm, V = 1.43 L, R = 0.082 L-atm/mol-K, and T =
20.0 oC + 273 = 293K
n = PV / RT
= (3.0 atm x 1.43L) / (0.082 L-atm/mol-K x 293K)
= 0.179 moles of N2
So since the moles of N2 is 0.179 mol and the moles of ammonia is
0.179 mol according to Avogadro’s hypothesis the volume of NH 3
at that pressure and that temperature is 1.43 L, the same!!!
EMPIRICAL GAS LAWS
Boyle’s Law P1V1 = P2V2
Charles’ Law V1 / T1 = V2 / T2
Guy-Lussac’s Law P1 / T1 = P2 / T2
Avogadro’s Law V1 / n1 = V2 / n2
Combined Gas Law P1V1 / T1 = P2 V2 / T2
Ideal Gas Law PV = nRT
P = pressure (atm) V = volume (L)
n = chemical amount (mol) T = Temperature (K)
R = ideal gas constant = 0.08206 L-atm / mol-K
Lecture PROBLEMS
1. A sample of O2 gas initially at 0oC and 1.0 atm is transferred from a 2-L
container to a 1-L container at constant temperature. a) What effect does
this change have on the average kinetic energy of the gas molecules? b)
What effect does the total number of collisions of O2 molecules with the
container walls in a unit time?
2. At constant pressure, a student needed to decrease a
volume of 155 mL of Ne gas by 32.0%. To what temperature,
(in oC), must the gas be cooled if the initial temperature was
21oC?
3. A sample of CO2 gas has a volume of 125.0 L at a pressure
of 789 torr and a temperature of 30oC. What will be the
temperature if the pressure was increased to 900 torr & the
volume decreased to 95.0 L?
4. F2 gas, which is dangerously reactive, is shipped in steel
containers of 30.0 L capacity, at a pressure of 10.0 atm at 26.0
oC. What should be the volume of the tank if the pressure is
increased to 820.0 torr & the temperature is 43.0 oC?
Empirical Gas Laws
1. At 25oC, a sample of N2 gas under a pressure of 689 mmHg occupies
124 mL in a piston-cylinder arrangement before compression. If the
gas is compressed to 75% of its original volume, what must be the new
pressure (in atm) at 25oC?
First make a list of the measurements made:
P1=689 mmHg V1 = 124 mL
P2 = ? V2 = 75% V1
From the variables, choose the appropriate equation, in this
case Boyle’s Law: P1V1=P2V2
(689 mmHg) (124 mL) = P2 (0.75 x 124 mL)
Solve for P2:
P2 = (689mmHg) (124 mL) / (93 mL) = 919 mmHg
Now convert to atm:
919 mmHg (1 atm / 760 mmHg) = 1.21 atm
Empirical Gas Laws
2. The gas in a Helium filled ball at 25oC exerts a volume of 4.2 L. If the ball is
placed in a freezer and the volume decreases to 1/8 of its original value, what
is the temperature inside the ball?
First make a list of the measurements made:
V1=4.2 atm T1 = 25 oCc + 273.15 = 298.15
V2 = 1/8 P1 T2 = ?
From the variables, choose the appropriate equation, in this case Charles’ Law:
V1/T1=V2/T2
(V1) / (298 K) = (1/8 V1) / T2
Solve for T2:
T2 = [(298 K) (1/8 V1)] / (V1) = 298 / 8 = 37.3 K or -235 oC
3. A balloon containing 6.50 grams of NH3 has a volume of 10.30 L at a
temperature of 20.0oC and a pressure of 689.2 torr. What would be the
pressure of NH3 if the volume decreased to 2.50 L without a change in
temperature?
Pressure of NH3 = 2.84 x 103 torr.
COMBINED GAS LAW
• A gas occupies a volume of 720 mL at 37oC
and 640 mmHg pressure. Calculate the
volume the gas would occupy at 273 K and 1
atm.
P1V1 / T1 = P2V2 / T2
rearranged to solve for V2 is:
V2 = P1 V1 T2 / P2 T1
V2 = (640 mmHg)(720 mL) (273 K) / (760 mmHg) (310 K)
V2 = 534 mL
COMBINED GAS LAW
• A gas occupies a volume of 720 mL
at 37oC and 640 mmHg pressure.
– Calculate the pressure if the
temperature is increased to 1000 oC &
the volume expands to 900 mL.
P2 = 2.1 x 103 mmHg
– Calculate the temperature if the
pressure is decreased to 10 torr & the
volume is reduced to 500 mL.
T2 = 3.4 K or -270 oC
PRACTICE PROBLEM # 20a
1. You prepared carbon dioxide by adding aqueous HCl to marble chips,
calcium carbonate. According to your calculations, you should obtain 79.4
mL of carbon dioxide at 0 oC and 760 mmHg. How many milliliters of gas
would you obtain at 27oC at the same pressure?
87.3 mL
2. Divers working from a North Sea drilling platform experiences pressures of
50 atm at a depth of 5.0 x 102 m. If a balloon is inflated to a volume of 5.0 L
(the volume of a lung) at that depth at a water temperature of 4.0 oC, what
would the volume of the balloon be on the surface (1.0 atm) at a temperature of
11 oC? 256 L
3. What volume would 5.30 L of H2 gas at 0 oC and 760 mmHg occupy if the
temperature was increased to 70oF and the pressure to 830 torr? 5.23 L
4. The pressure gauge reads 125 psi on a 0.140-m3 compressed air tank when
the gas is at 33.0 oC. To what volume will the contents of the tank expand if
they are released to an atmospheric pressure of 751 torr and a temperature of
13oC? 1.126 m3
5. A gas has a volume of 397.0 mL at 14.70 atm. What will be its pressure (in
torr) if the volume is changed to 4.100 L? 1082 torr
PRACTICE PROBLEM # 20a
6. Which of the following statements is false?
a) If the Celsius temperature is doubled, the pressure of a fixed volume of gas would
double.
b) All collisions between gas molecules are perfectly elastic (no energy is lost)
according to KMT.
c) The volume of gas is inversely proportional to the temperature of gas present (P
constant)
d) Gases are capable of being greatly compressed. C
7. Which of the following statements are true?
a) In a large container of O 2 gas the pressure exerted by the oxygen will be greater
at the bottom of the container.
b) Of the three states of matter, gases are the most compact and the most mobile.
c) The formula of ozone is 3 O 2.
d) Molecules of O2 gas and H2 gas at the same temperature will have the same
average kinetic energies and the same average velocities.
D