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How do gases behave under different conditions?
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What are the properties and behavior of gases
under different conditions such as pressure,
volume and temperature?
Gas Particles
Liquid Particles
Solid Particles
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An important property of gases is
Compressibility
◦ Measure of how much the volume of matter
decreases under pressure
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Why are gases so compressible?
◦ Large spaces between particles
Explains why ideal gases behave the way they
do
 Assumptions that simplify the theory, but
don’t work in real gases:
1. The particles are so small we can ignore
their volume
2. The particles are in constant motion and
their collisions cause pressure.
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The particles do not affect each other,
neither attracting or repelling.
4. The average kinetic energy is proportional
to the Kelvin temperature.
5. The molecules move in a straight path
6. All collisions are elastic
3.
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We need the formula KE = 1/2 mv2
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Force per unit area
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Factors Affecting Pressure
◦ Amount of gas
 More particles – more pressure
◦ Volume
 More volume – less pressure
◦ Temperature
 Higher temperature – more pressure
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Gas molecules fill container
Molecules move around and hit sides
Collisions are the force
Container is the area
Vacuum
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1 atm
Pressure
760
mm
Hg
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Measures air pressure
The pressure of the
atmosphere at sea level
will hold a column of
mercury 760 mm Hg.
1 atm = 760 mm Hg
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h
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Gas
Column of
mercury to
measure pressure
of a gas
One end has gas,
the other is open
h is how much
lower the pressure
of the gas is than
atmosphere
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h
Gas
h is how much
higher the gas
pressure is than
the atmosphere.
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1 atmosphere = 760 mm Hg
1 mm Hg = 1 torr
1 atm = 101,325 Pascals = 101.325 kPa
Occasionally, we must convert between
these
Examples:
◦ What is 724 mmHg in torr?
◦ in atm?
0.953 atm
◦ in kPa?
96.5 kPa
724 torr
Summary of Units of Pressure
Unit
Abbreviation
Unit Equivalent
to 1 atm
Atmosphere
Atm
1 atm
Millimeters of
Hg
mm Hg
760 mm Hg
Torr
Torr
760 torr
Pascal
Pa
101,325 Pa
Kilopascal
kPa
101.3 kPa
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There are several laws we use to quantify the
behavior of gases
The laws describe some combination of
changes in pressure (P), volume (V),
moles/amount of gas (n),or temperature (T)
Standard Temperature and Pressure (STP)
◦ 0ºC and 1 atm
◦ 1 mole of gas occupies 22.4 L
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BE CAREFUL!!
◦ Units are vital to solving these problems
◦ Temperature must ALWAYS be in KELVIN
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Pressure and volume are inversely related at
constant temperature
PV= k, where k is a constant
As one goes up, the other goes down
P1V1 = P2 V2
V
P (at constant T)
V
Slope = k
1/P (at constant T)
22.41 L atm
PV
O2
CO2
P (at constant T)
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Given the volume of gas as 200.mL at 1.05atm
pressure, calculate the volume of the same gas at
1.01atm.
◦ 208mL
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30.6 mL of carbon dioxide at 740 torr is
expanded at constant temperature to 750 mL.
What is the final pressure in kPa?
◦ 4.0kPa
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20.5 L of nitrogen at 25ºC and 742 torr are
compressed to 9.8 atm at constant T. What is the
new volume?
◦ 2.0L
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Volume of a gas varies directly with the
absolute temperature at constant pressure.
V = kT (if T is in Kelvin)
One goes up, the other goes up
V1 = V2
T1
T2
He
CH4
V (L)
H2O
H2
-273.15ºC
T (ºC)
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What would the final volume be if 247 mL of
gas at 22ºC is heated to 98ºC , if the pressure
is held constant?
◦ 311mL
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At what temperature would 40.5 L of gas at
23.4ºC have a volume of 81.0 L at constant
pressure?
◦ 593K or 320ºC
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At constant volume, pressure and absolute
temperature are directly related.
P=kT
One goes up, the other goes up
P1 = P2
T1
T2
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A steel tank contains a gas at 27.0°C and a
pressure of 12.0atm. Determine the gas
pressure when the tank is heated to 100.°C.
◦ 14.9 atm
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At 120°C, the pressure of a sample of
nitrogen is 1.07atm. What will the pressure
be at 205°C, assuming constant volume?
◦ 1.30 atm
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At constant temperature and pressure, the
volume of gas is directly related to the
number of moles.
V = k n (n is the number of moles)
V1 = V2
n1
n2
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Combines Boyles’, Charles’ and Gay-Lussac’s
laws
Describes the relationship between pressure,
temperature, and volume
If the moles of gas remains constant, use this
formula and cancel out the other things that
don’t change
P1 V1 = P2 V2
T1
T2
.
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A sample of gas has a volume of 4.18 L at 29ºC and
732 torr. What would its volume be at 24.8ºC and
756 torr?
◦ 3.99L
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5.00L of air at a temperature of -50ºC has a
pressure of 107kPa. What is its pressure if the
temperature is raised to 102ºC and its volume to
7.00L
◦ 129kPa
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The volume of a gas-filled balloon is 30.0 L at 313
K and 153 kPa pressure.What would the volume be
at standard temperature and pressure (STP)?
◦ 39.5 L
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PV = nRT
An Equation of state
◦ Independent of how you end up where you are at
◦ Does not depend on the path
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An Empirical Equation
◦ Based on experimental evidence
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Tells you about current state of gas
◦ The other laws tell you about a gas when it changes
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Given 3 factors you can determine the fourth
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PV = nRT
R is the ideal gas constant
V = 22.41 L at P = 1 atm, T = 0ºC, n = 1
mole
What is R?
◦ R = 0.08206 (L·atm)/(mol·K)
◦ With different units: R = 8.31 (L·kPa)/(mol·K)
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Ideal gases are hypothetical substances
Think of it as a limit
Gases only approach ideal behavior at low
pressure (< 1 atm) and high temperature
Use the laws anyway, unless told to do
otherwise
They give good estimates
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A 47.3 L container containing 1.62 mol of He
is heated until the pressure reaches 1.85 atm.
What is the temperature?
◦ 658K
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Kr gas in a 18.5 L cylinder exerts a pressure of
8.61 atm at 24.8ºC What is the mass of Kr?
◦ 546g Kr
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Real gas particles have volume and there are
attractions between the particles (especially
polar molecules)
A real gas behaves ideally at low pressure and
high temperature.
Under conditions of high pressures and low
temperatures, deviations from the expected
results of the ideal gas law will occur.
Need to add correction factors to the ideal gas
law to account for these.
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D = m/V
Let M stand for molar mass
M = m/n
n= PV/RT
M= m
PV/RT
M = mRT = mRT = DRT
PV
VP
P
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What is the density of ammonia at 23ºC and
735 torr?
M = DRT
P
D = MP / RT
D = (17.04g/mol)(735torr/760 torr/atm)
(0.08206 (L·atm)/(mol·K)(296K)
D = 0.678g/L
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Reactions happen in moles
At Standard Temperature and Pressure (STP),
◦ 0ºC and 1 atm
◦ 1 mole of gas occupies 22.4 L
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If not at STP, use the ideal gas law to
calculate moles of reactant or volume of
product.
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Consider the following reaction:
4NH3(g) + 5O2(g) 4NO(g) +6H2O(g)
What volume of NO at STP will be produced
from 23.7L of NH3?
◦ 23.7L
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What volume of O2 measured at STP will be
consumed when 10.0L NH3 is reacted?
◦ 12.5L
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Mercury can be produced by the following
reaction:
2HgO 2Hg +O2
What volume of oxygen gas can be produced
from 4.10 g of mercury (II) oxide at STP?
◦ 0.229L
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At 400.ºC and 740 torr?
◦ 0.580L
Using the following reaction:
NaHCO3(s)+ HCl(aq)NaCl(aq) +CO2(g)+H2O(l)
 Calculate the mass of sodium hydrogen
carbonate necessary to produce 2.87 L of
carbon dioxide at 25ºC and 2.00 atm
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◦ 19.7g NaHCO3
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The total pressure in a container is the sum
of the pressure each gas would exert if it
were alone in the container.
The total pressure is the sum of the partial
pressures.
PTotal = P1 + P2 + P3 + P4 + P5 ...
For each P = nRT/V
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PTotal = n1RT + n2RT + n3RT +...
V
V
V
In the same container R, T and V are the
same.
PTotal = (n1+ n2 + n3+...)RT
V
PTotal = (nTotal)RT
V
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Air contains oxygen, nitrogen, carbon
dioxide, and trace amounts of other gases.
What is the partial pressure of oxygen at
101.30 kPa of total pressure if the partial
pressures of nitrogen, carbon dioxide,and
other gases are 79.10 kPa, 0.040 kPa, and
0.94 kPa, respectively?
◦ 21.22kPa
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Ratio of moles of the substance to the total
moles.
Symbol is Greek letter chi
c1 =
n1
nTotal
= P1
PTotal
c
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The partial pressure of nitrogen in air is 592
torr. Air pressure is 752 torr, what is the
mole fraction of nitrogen?
◦ 0.787
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What is the partial pressure of nitrogen if the
container holding the air is compressed to
5.25 atm?
◦ 4.13 atm
4.00 L
CH4
1.50 L
N2
3.50 L
O2
2.70 atm
4.58 atm
0.752 atm
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When these valves are opened, what is each
partial pressure and the total pressure?
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Water evaporates!
When that water evaporates, the vapor has a
pressure.
Gases are often collected over water so the
vapor. pressure of water must be subtracted
from the total pressure.
It must be given.
N2O can be produced by the following
reaction
heat
NH 4 NO 3 ( s)  NO 2 (g) + 2H 2 O ( l )
 what volume of N O collected over water at a
2
total pressure of 94 kPa and 22ºC can be
produced from 2.6 g of NH4NO3? ( the vapor
pressure of water at 22ºC is 21 torr)
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Passage of gas through a small hole, into a
vacuum.
The effusion rate measures how fast this
happens.
Graham’s Law the rate of effusion is inversely
proportional to the square root of the mass
of its particles.
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The spreading of a gas through a room.
Slow considering molecules move at 100’s of
meters per second.
Collisions with other molecules slow down
diffusions.
Best estimate is Graham’s Law.