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Chapter 6: Gases
I. Properties of Gases
Gases are distinguished from liquids and solids by 1) gas mixtures are always homogeneous, 2)
gases are compressible. Homogenous mixing and compressibility both result from the fact that
molecules in gases are far apart. Four properties determine the physical behavior of a gas: the
amount of gas (in mole), the gas volume, temperature and pressure.
The concept of pressure
Pressure is defined as a force per unit area, that is a force divided by the area over which the
force is distributed.
The SI unit of pressure is defined as pascal(Pa) which is a pressure of one Newton per square
meter
E. g. consider the pressure on a table from block of metal with mass of 20.0g on a area of 4 cm2
Liquid Pressure
A pressure of liquid is only depends on the height of the liquid column and the density of the
liquid. Consider a liquid with density d, contained in a cylinder with cross-section A, filled to
height h.
E.g. Relating liquid height and pressure
What is the height of a column of water that gives the same pressure as a column of mercury
76.0 cm high?
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Gas Pressure
One of the most obvious characteristics of gases is that they exert a measurable pressure on the
walls of their container. A gas pressure is a large collection of particles moving at random
throughout a volume that is primarily empty space. Collisions of randomly moving particles with
the walls of the container exert a force per unit area that we perceive as gas pressure. The
pressure of gas is usually measured indirectly, by comparing it with a Liquid pressure
Barometric Pressure
Chemists have traditionally used other two units of pressure, based on the mercury barometer. A
barometer is a device for measuring the pressure of atmosphere. It consists of a glass tube about
one meter long filled with mercury and inverted into a dish of the same liquid metal. The
downward pressure of the mercury in the column is exactly balanced by the outside atmosphere
pressure that presses down on mercury in the dish and pushes it up the column.
The height of mercury in a barometer, called the barometric pressure varies with atmospheric conditions
and with altitude.
Standard Condition of Temperature and Pressure (STP)
The standard atmosphere (atm) at sea level is defined as the pressure exerted by a mercury
column of exactly 760 mm in height when the density of the mercury = 13.5951 g/cm3 (0°C) and
the acceleration due to gravity g = 9.80665 ms-2, exactly.
1 atm = 760 mmHg
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The millimeter of mercury is also called torr.
Knowing the density of mercury and the acceleration due to gravity, it’s possible to calculate the
pressure exerted by the column of mercury 760mm (0.76m) in height. Thus,
P = (0.76m) x 1.35951x 104 kg/m3 x 9.80665 ms-2 = 101,325 Pa
1 atm = 760 mmHg = 101,325 Pa
Manometers
A manometer is a device that measures the pressure of a gas or liquid in a vessel. Gas pressure
inside a container is often measured using an open-end manometer.
E.g. An oil whose density is 0.775g/mL was used in a open-end manometer to measure the
pressure of a gas in a flask, as shown in figure (b). If the height of the oil column is 7.68cm and
Pbar = 760.0mmHg. What is the pressure of the gas in the flask in mmHg?
II The Simple Gas Laws
One of the characteristic properties of gas is its compressibility. The compressibility of gas is
first study by Robert Boyle. Imagine that you have a sample of gas inside a cylinder with a
movable piston at one end. What would happen if you push the piston partway down?
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E.g. Consider the 50.0L tank of O2. The pressure of gas in the tank is 15.7 atm at 21°C. What
volume of O2 can we get from the tank at 21°C if the atmospheric pressure is 1.00atm?
Charles’s Law
Imagine that you again have a sample of gas inside a cylinder with a movable piston at one end.
What would happen if you were to raise the temperature of the sample while letting the piston
move freely to keep the pressure constant?
E.g. A gas at 25C and 0.987atm is confined in a cylinder by a piston. When the cylinder is
heated, the gas volume expands from 0.250L to 1.65L. What is the new temperature of gas,
assuming the P remains constant.
Avogadro’s Law: the relationship between volume and amountIn 1808 Gay-Lussac
concluded from experiments on gas reaction that the volumes of reactant gas as a given P and T
are in ratios of small whole # (the law of combing volumes)
2H2(g) + O2(g) 2H2O(g)
2 volume 1 vol
2 vol
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Later Avogadro’s interpreted it as following :
1 Equal volumes of different gases compare at the same temperature and pressure contain equal
numbers of molecules.
2 Equal numbers of molecules of different gases compared at the same temperature and pressue
occupy equal volumes.
Lead to Avogado’s Law (only apply to gases)
E.g. A 128g of solid carbon dioxide (dry ice) sublimes into CO2(g). How many liters of gas are
formed at STP? molar gas volume = 22.4 L/mol
III The Ideal Gas Law
1 Bolye’s : PV = a at constant n and T
2 Charles’s Law : V = bT at constant n and P3 Avogadro’s law: V/n = c at constant T and
P.Combine this three law into a single equation-the ideal gas law-that includes all four gas variable:
V, P, T and amount of gas.
V nT
and
V = RnT
P
P
PV=nRT R = gas constant (has the same value for all gases)
Since 1 mol of an idea gas occupies a volume of 22.414L at 0°C(273.15K) and 1 atm pressure,
the gas constant is
A gas whose behavior confirms to the ideal gas equation is called an ideal gas.
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E.g. How many moles of air are in the lungs of an average adult with a lung capacity of 3.8L?
Assume that the person is at 1.00atm and has a normal body temperature of 37°C
The general Gas Equation
Sometimes a gas is described under two set of conditions. Here we have to apply the idea gas
twice, to an initial condition and a final condition.
E.g. A 1.00mL sample of N2(g) at 36.2C and 2.14 atm is heated to 37.8C and the pressure
change to 1.02 atm. What volume does the gas occupy at the final temperature and pressure?
IV Molar mass determination
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E.g. What is the molar mass of He(g) in a 5.00L storage tank filled with helium at 10.5atm
pressure at 30.0°C?
Gas Density
E.g. What is the density of oxygen, O2, in grams per liter at 25°C and 0.85atm? Assume O2 is an
idea gas.
Gases in Chemical Reactions
When the reaction involve gases as reactant or product, we can handle information about gases in
terms of V, P, T as well as by mass and amount in mole.
E.g. Consider the following reaction 


Cl
s

Cl(s) + 3O2(g)


n 
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
Suppose we heat 0.0100 mol of potassium chlorate in a teat tube. How many liters of O2 can we
produce at 25°C and 1.02 atm?
Law of Combining VolumesThe volumes of reactant gas as a given P and T are in ratios of
small whole number.
So, if the reactants and products involved in a stoichiometric calculation are gases, we can use
the simple approach
consider
E.g. If all gases are measured at the same T and P, What volume of NH3(g) is produced when
225L of H2 is consumed in the reaction?
Dalton’s law of Partial Pressure
The simple gas laws and idea gas law apply to individual gases as well as to a mixture of
nonreactive gases.
What is responsible for the pressure in a gas mixture?
Since the pressure of pure gas at constant V and T is proportional to its amount (P=nRT/V), the
pressure contribute from each individual gas in a mixture is also its amount in the mixture.
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In other words, the total pressure exerted by a mixture of gases in a container at constant V and T
is equal to the sum of the partial pressure of each individual gas in the container, a statement
known as Dalton’s law of partial pressure
Ptot = PA + PB+ PC….at constant V and T
Where PA, PB, PC …. refer to the pressure each individual gas would have if it were alone.
The pressure exerted by a particular gas in a mixture, PA, PB, PC is called partial pressure and
refer to the pressure each individual gas would exert if it were alone in the container. That is,
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E.g. A 1.00L sample of dry air at 25°C and 786mmHg contains 0.925g of N2, plus other gases.
(a) What is the partial pressure of N2 in the air sample? (b) What is the mole fraction and mole
percent of N2 in the air?
Collecting a gas over water
A gas collected in a pneumatic trough filled with water is said to be collected over water. It is a
mixture of gases that contains the desired gases and water vapor. The partial pressure of water
vapor in the gas mixture in the collection tube depends only on the temperature. This partial
pressure of water vapor is called the vapor pressure.
Ptot = Pbar = Pgas + PH2O
E.g. In the following reaction:
2Al(s) + 6HCl(aq) 2AlCl3(aq) + 3H2(g)
If 35.5mL of H2(g) is collected over water at 26C and a barometric pressure of 755mmHg, how
many moles of HCl must have been comsumed? (The vapor pressure of water at 26C is
25.2mmHg)