Kelvin Sheng
AP Chemistry
Period 1
Chapter 5 – Gases
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Matter exists as three states: solid, liquid, gas
Gases are important and surrounds us
Our atmosphere consists of a mixture of gases.
Pressure is a major property of gas.
A barometer is used to measure atmospheric pressure (invented by Evangelista Torricelli)
Atmospheric pressure measures the weight of air.
Based on Torricelli’s barometer, atmospheric pressure is measured in mmHg (millimeters of
Mercury) or torr – both are interchangeable.
Another unit for pressure is standard atmosphere (atm)
The relationship between mmHg, torr, and atm is
1 standard atmosphere = 1 atm = 760 mmHg = 760 torr
Pressure is defined as force divided by area
The SI unit for force is the Newton (N) and pressure is in Newtons per meters squared. This unit is
called the Pascal (Pa)
1 atm = 101325 Pa
There are several laws that apply to properties of gases: Boyle’s Law, Charles’s Law, and
Avagadro’s Law
Boyle’s Law: PV = k where k is a constant for a given sample of air at a specific temperature.
Any gas that strictly follows Boyle’s Law is an ideal gas.
Boyle’s Law can be used to relate the same gas at different pressures or volumes but constant
temperatures.
Jacques Charles noticed that the graph of volume versus temperature is linear at constant pressure
on the Celsius scale.
When using K= C+273 where K is units of Kelvin, volume is directly proportional to temperature.
Charles’s Law: V=bT.
Charles’s Law can be used to relate the same gas at constant pressure with different temperatures
or volumes.
Avogadro’s Law states that for a gas at a constant temperature and pressure, the volume is directly
proportional to the number of moles of gas.
Avogadro’s Law can be used to relate the same gas with different moles or volume at constant
pressure and temperature.
By considering the three laws, the Ideal Gas Law can be derived: PV=nRT, where R is the
universal gas constant .08206 L*atm/mol*K
The Ideal Gas Law is an equation of state for a gas. Gases that follow the Ideal Gas Law are said
to behave ideally.
For one mole of ideal gas, the volume of gas can be determined with the Ideal Gas Law.
22.42 L is the molar volume of an ideal gas.
The conditions of 0 degrees C or 273 K and 1 atm are referred to as STP (Standard Temperature
and Pressure)
The molar mass of a gas can be determined by the equation MM=dRT/P where d is the density of
gas.
John Dalton realized that for a mixture of gases in a container, the total pressure exerted is the sum
of the pressures that each gas would exert if it were alone. Ptotal = P1+P2+P3+…
By plugging in Dalton’s Law of Partial Pressures into the ideal gas law, Ptotal can be represented
as ntotal(RT/V)
Mole fraction is the ratio of the number of moles of a given component in a mixture to the total
number of moles in the mixture.
Mole fraction (X) plugged into the ideal gas law shows that X can be represented as P2/Ptotal
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The KMT (Kinetic Molecular Theory) attempts to explain the properties of an ideal gas.
The KMT consists of 4 postulates:
o The particles are so small compared with the distances between them that the volume of
the individual particles can be assumed to be negligible.
o The particles are in constant motion. The collisions of the particles with the walls of the
container are the cause of the pressure exerted by the gas.
o The particles are assumed to exert no forces on each other; they are assumed neither to
attract nor to repel each other.
o The average kinetic energy of a collection of gas particles is assumed to be directly
proportional to the Kelvin temperature of the gas.
The KMT indicates the average kinetic energy of gas particles. KEavg = 3/2*RT.
The root means square velocity equation is urms = square(3RT/M), where R is 8.3145 J/k*mol.
Diffusion is the mixing of gases.
Effusion is the passage of a gas through a tiny orifice into an evacuated chamber.
Thomas Graham found that: Rate of effusion for gas 1/ Rate of effusion for gas 2 = square(M2/M1)
where M1 and M2 are the molar masses of the gases.
Ideal gases are conditions approached by real gases. The properties of real gases can be
determined through the ideal gas laws with correction factors included.
MC Questions
1. Under which conditions will a gas behave most ideally?
A. Low P, High T
B. Low P, Low T
C. High P, Low T
D. High P, High T
2.
A.
B.
C.
D.
How many millimoles of methane, CH4, are present in 6.4g of this gas?
.40
4.0
40.
4.0 x 10^2
3.
Three balloons are filled with the same number of atoms of He, Ar, and Xe, respectively. Which
statement is true under the same conditions of temperature and pressure?
The balloons contain the same mass of gas.
All balloons have the same volume.
The densities of the three gases are the same.
The average speed of the different types of atoms is the same.
A.
B.
C.
D.
4.
A.
B.
C.
D.
5.
A.
B.
C.
D.
A gas has a volume of 6.0 L at a pressure of .80 atm. What is the volume if the pressure is
changed to 2.0 atm at a constant temperature?
1.5 L
3.0 L
12 L
24 L
What pressure (atm) will be exerted by a 1.00 g sample of methane, CH4, in a 4.25 L flask at 115
degrees C?
.139
.330
.467
7.50
Free-response
In 5 identical balloons, each is filled with a different gas at the same volume, 25 degrees C, and 1.0 atm.
The balloons are filled with CO2, O2, He, N2, CH4.
a.
Which balloon contains the greatest mass of gas? Explain.
b.
Compare the average kinetic energies of the gas molecules in the balloons. Explain.
c.
Which balloon contains the gas that would be expected to deviate most from the behavior of an ideal
gas? Explain.
d.
Twelve hours after being filled, all the balloons have decreased in size. Predict which balloon will be
the smallest. Explain your reasoning