Gases
13.1 Gases and Pressure
Gases – constituent atoms and molecules that have
little attraction for one another

Free to move in available volume

Some properties of gases

Mixtures are always homogenous

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Very weak attraction between gas molecules
Identity of neighbor is irrelevant
Compressible – volume contracts when pressure is applied



0.10% of volume of gas is occupied by molecules
Exert a measurable pressure on the walls of their container
13.1 Units of Pressure
Pressure – force exerted per unit area

SI unit equals Pascal (Pa)


Alternative units

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
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1 Pa = 1 N/m2 (1 N = 1 (kg•m)/s2)
Millimeters of mercury (mmHg)
Atmosphere (atm)
1.0 atm = 760 mmHg = 101, 325 Pa
1.0 atm = 14.69 psi
Pressure
Atmospheric pressure – pressure
created from the mass of the
atmosphere pressing down on the
earth’s surface

Standard atmospheric pressure at
sea level – 760 mmHg

Measuring pressure

Barometer – long thin mercury
filled tube sealed at once end and
inverted into a dish of mercury


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Downward pressure of Hg in
column equals outside atmospheric
pressure
Manometer – U-tube filled with
mercury, with one end connected
to the gas – filled container and the
other end open to the atmosphere.
Examples
 The pressure of the air in a tire is measured to be 28 psi.
Represent this pressure in atm, torr and pascals
 On a summer day in Breknridge, Colorado, the atmospheric
pressure is 325 mmHg. What is the pressure in
atmostphere?
13.2 Pressure and Volume; Boyle’s Law
 Showing the relationship between pressure and volume
 P x V = k (constant value @ specific temp and constant moles
of gas)
 k = 1.40 x 103
 P = 1/ V (inverse relationship)
 Can predict a new volume of pressure is changed


P1V1 = k = P2V2  P1V1 = P2V2
Calculate V2 =
Figures 13.6
Examples
 A sample of helium gas has a pressure of 3.54 atm in a
container with a volume of 23.1 L. This sample is
transferred to a new container and the pressure is
measured to be 1.87 atm. What is the volume of the
new container? Assume constant temperature.
 A sample of neon gas has a pressure of 7.43 atm in a
container with volume of 45.1 L. This sample is
transferred to a container with a volume of 18.4 L.
What is the new pressure of the neon gas? Assume
constant temperature
13.3 Volume and Temperature: Charles’s
Law
 Relationship between Volume and Temperature
 V = bT (b is a constant)
 V/T=b
 Can predict the new volume or temperature
 (V1/T1)= (V2/T2)
V vs. T
Examples
 A 2.0 L sample of air is collected at 298K and then cooled
to 278 K. The pressure is held constant at 1.0 atm.
 Does the volume increase of decrease?
 Calculate the volume of the air at 278 K?
Examples
 Consider a gas with a volume of 5.65 L at 27oC and 1 atm
pressure. At what temperature will this gas have a volume
of 6.69 L and 1 atm pressure?
13.4 Volume and Moles: Avogadro’s Law
 Relationship between volume of gas and number moles of
gas
 V is directly proportional to n
 V = an or
V / n = a (a = constant)
 Can predict the new volume or new moles of gas at constant
pressure and temperature
 (V1/n1) = (V2/n2)
V vs. n
Examples
 Suppose we have a 12.2 L sample containing 0.50 mol of
oxygen gas, O2 at a constant pressure of 1atm and a
temperature of 25oC. If all of this O2 is converted to
ozone, O3, at the same temperature and pressure, what will
be the volume of ozone formed?
Examples
 Consider two samples of nitrogen gas (composed N2
molecules). Sample 1 contains 1.5 mol of N2 and has a
volume of 36.7 L at 25oC and 1 atm. Sample 2 has a
volume of 16. L at 25oC and 1 atm. Calculate the number
moles of N2 in sample 2
13.5 The Ideal Gas law
Different gasses show similar physical behavior
(unlike solid or liquid)

Defined by four variables – pressure, temperature, volume,
and number of moles
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Relationship of variable – gas laws
Ideal gas – behavior follows the gas laws exactly
Describes how the volume of a gas is affected by
changes in pressure, temperature and amount.

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PV = nRT;
R = gas constant = 0.08206 L•atm
K•mol
Examples
 A sample of hydrogen gas, H2, has a volume of 8.56 L at a
temperature of 0oC and a pressure of 1.5 atm. Calculate the
number of moles of H2 present in this gas sample.
(Assume that the gas behaves ideally.)
Examples
 What volume is occupied by 0.250 mol of carbon dioxide
gas at 25oC and 371 torr?
 A 0.250 mol sample of argon gas has a volume of 9.00L at a
pressure of 875 mmHg. What is the temperature (in oC) of
the gas?
Combine Gas Law


is an expression obtained by mathematically combining
Boyle’s and Charles’ law
P1V1 = P2V2
@ constant n
T1
T2
can predict P, V or T when condition is changed
Examples
 Suppose we have a 0.240 mol sample of ammonia gas at
25oC with a volume of 3.5 L at a pressure of 1.68 atm. The
gas compressed to a volume of 1.35 L at 25oC. Use the
combined gas law to calculate the final pressure.
Examples
 Consider a sample of hydrogen gas of 63oC with a volume
of 3.65L at a pressure of 4.55 atm. The pressure is changed
to 2.75 atm and the gas is cooled to -35oC. Calculate the
new volume of the gas
13.6 Dalton’s Law of Partial Pressure
 A. Gas laws apply to mixtures of gases
 B. Dalton's law of partial pressure –
 Ptotal = P1 + P2 + P3 + ….. at constant V, T
where P1, P2, ….refer to the pressure of the individual gases in the
mixture
 C.
Partial pressures refer to the pressure each individual gas
would exert if it were alone in the container (P1, P2, …)
1. Total pressure depends on the total molar amount of gas
present
 3.
Ptotal = ntotal (RT/V)
Examples
 Mixture of helium and oxygen are use in the “air” tanks of
underwater divers for deep dives. For a particular dive, 12
of O2 at 25oC and 1.0 atm and 46 L of He at 25oC and 1.0
atm were both pumped into a 5.0 L tank. Calculate the
partial pressure of each gas and the total pressure in the
tank at 25oC
Examples
 A 2.0 L flask contains a mixture of nitrogen gas and oxgyen
gas at 25oC. The total pressure of the gas mixture is 0.91
atm, and the mixture is known to contain 0.050 mol of N2.
Calculate the partial pressure of oxygen and the moles of
oxygen present
13.8 The Kinetic Molecular Theory of Gas
A.
Model that can explain the behavior of gases
.Assumptions
1.
A gas consists of particles in constant
random motion
2.
Most of the volume of a gas is empty spaces
3.
The attractive and repulsive forces between
molecules of gases are negligible
4.
The total kinetic energy of the gas particles
is constant at constant T
5.
Average Ek α T
13.10 Gas Stoichiometry
Stoichiometric calculations involves the application of the
ideal gas law

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One of the variables in the ideal gas law equation is
unknown.
Example
 E.g Pure oxygen gas was first prepared by heating
mercury(II) oxide, HgO
2 HgO(s)  2 Hg(l) + O2(g)
What volume (in liters) of oxygen at STP is released by
heating 10.57 g of HgO?
Step1: Calculate moles of HgO
Step 2: Calculate mole O2
Step 3:
Calculate volume using Ideal gas law
Examples
 Consider the reaction represented by the equation
P4(s) + 6 H2(g)  4H3(g)
What is the amount of P4 is required to react with 5.39 L of
hydrogen gas at 27oC and 1.25 atm?
Molar volume and STP
 The molar volume of an ideal gas is 22.4L/mole
 STP = Standard Temperature (273K) Pressure ( 1.0 atm)
examples
 A sample of nitrogen gas has a volume of 1.75 L at STP.
How many moles of N2 are present?
examples
 Quicklime, CaO, is produced by heating calcium carbonate,
CaCO3. Calculate the volume of CO2 produced at STP
from the decomposition of 152 g of CaCO3 according to
the reaction
CaCO3(s)  CaO(s) + CO2(g)