# The gas laws…

```Review of Gases
The nature of gases…
Gases all have common
physical properties:
1) Mass
2) Easily compressible
3) Take the shape of their container
4) Can move through other gases
5) Exert pressure
6) Pressure depends on
temperature
Postulates of K-M theory…
1) Gas consists of very small particles, each
of which has a mass
2) Distances separating gas particles are
relatively large
3) Gas particles are in constant, rapid,
random motion
4) Collisions of gas particles with each other
or container are perfectly elastic
5) Average kinetic energy of particles
depends only on temperature of the gas
6) Gas particles exert no force on one
another
Measuring Gases
Measuring gases…
4 variables:
1)Amount of gas (n)
2)Volume (V)
3)Temperature (T)
4)Pressure (P)
Measuring gases…
Conversions:
1)1 atm = 101.3 kPa
2)1 atm = 760 mm Hg
3)1 atm = 760 torr
4)1 bar = 100,000 Pa
5)1 bar = 0.9869 atm
Measuring gases…
Atmospheric pressure:
• pressure of air around us
• acts against pressure from
inside object
• varies with altitude
Measuring gases…
Instruments to measure:
• Mercury barometer
Measuring gases…
Sample problem 1
A barometer has a column of
mercury that is 745 mm in
height. What is the
atmospheric pressure in
Pascals?
Measuring gases…
Sample problem 2
The lowest recorded
atmospheric pressure in the
Western Hemisphere is
88.86 kPa. What is this in
mm Hg?
Measuring gases…
Instruments to measure:
•
Mercury barometer
• Manometer
Measuring gases…
Sample problem 3:
A balloon is attached to an
open-ended manometer.
The mercury level is 13 mm
lower on the balloon side
than the open side. The
atmospheric pressure is 745
mm Hg. What is the
pressure in the balloon?
Measuring gases…
Sample problem 4:
A closed container of gas is
attached to a U-tube. The
height of the open side is 27
mm lower than the closed
side. The atmospheric
pressure is 755 mm Hg.
What is the pressure in the
container?
Gas Laws
Chapter 11
The gas laws…
• A useful bit of information:
Conditions for STP are
0.00 C and 1.00 atm
The gas laws…
• Boyle’s Law – relationship
between pressure & volume
1)formula:
P 1 V 1 = P2 V 2
Boyle’s Law
Sample problem:
A helium tank holds 25 L of He
at 30.0 atm, how many
balloons can be filled if each
balloon holds 2.5 L at 1.04
atm?
Boyle’s Law
Sample problem:
A gas at a pressure of 608 mm
3
Hg has a volume of 545 cm .
The volume increases to 1065
cm3. What is the new
pressure?
The gas laws…
• Charles’ Law – relationship
between volume &
temperature
• formula:
V1/T1 = V2/T2
Charles’ Law
Sample problem:
A gas has volume of 8.57 L at
273 K. What is the volume at
355 K?
Charles’ Law
Sample problem:
A balloon has a volume of 1.75
L at 25 C. At what Celsius
temp would the volume be
1.25 L?
The gas laws…
relationship between volume
& amount of gas
• formula:
V = k 3n
Sample problem:
What is the volume of 3.6 moles
of helium at STP?
Sample problem:
How many moles of gas are in
593 L at STP?
The gas laws…
• Dalton’s Law of Partial
Pressures – relates
pressures of gases in a
mixture
• formula:
Ptot = pa + pb + pc + …
Dalton’s Law of Partial
Pressures
Sample problem:
What is the atmospheric
pressure if the partial
pressures of nitrogen, oxygen
and argon are 604.5 mm Hg,
162.8 mm Hg, and 0.5 mm Hg
respectively?
Dalton’s Law of Partial
Pressures
Sample problem:
A person using an oxygen mask
is breathing air with 33 %
oxygen. What is the partial
pressure of O2 if the total air
pressure is 110 kPa?
Dalton’s Law of Partial
Pressures
Sample problem:
The gases CO2, O2, N2, Ne, and
Kr are in a container. Each
gas has the same partial
pressure. The total pressure
is 33,500 Pa. What is the
partial pressure of N2?
Combined Gas Law
The gas laws…
• The combined gas law –
relates pressure, volume, and
temperature (may use in place
of Boyle’s and/or Charles’ Law)
• formula:
(P1V1) = (P2V2)
T1
T2
The combined gas law
Sample Problem:
• The volume of a gas-filled
balloon is 30.0 L at 40. C and
153 kPa. What volume will
the balloon have at STP?
The combined gas law…
Sample Problem:
• A gas occupies a volume of
159.1 mL at 316 K and 4.89
atm. What volume will it
occupy at STP?
Ideal Gases
The ideal gas law…
• Relates pressure,
temperature, volume, and
moles
The ideal gas law…
• Formula:
PV = nRT
R is a constant
R = 0.0821 (atm×L)/(mol×K)
The ideal gas law…
Relates to K-M theory
• P increases as n increases (while V
& T are constant)
• P increases as T increases (while n
& V are constant)
• P increases as V decreases (while n
& T are constant)
The ideal gas law…
Does not work for…
• Very high pressures
• Very low temperatures
The ideal gas law…
Sample Problem 1:
• How many moles of a gas at
100. °C are needed to fill a
1.00 L flask at a pressure of
1.50 atm?
The ideal gas law…
Sample Problem 2:
• What is the volume occupied
by 9.45 g of C2H2 at STP?
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