Gases
All matter exists in three states as gas, liquid and solid under certain conditions
of pressure and temperatures. Water for examples, can be solid ice, liquid water,
steam, or water vapour. The physical properties of a substance often depend on
its state. Gases are simpler than liquids and solids in many ways. Molecular
motion in gases is totally random and the forces of attraction between gas
molecules are so small that each molecule moves freely and essentially
independently of other molecules. When subjected to change in temperature
and pressure, it is easier to predict the behaviour of gases.
A gas consists of molecules separated wide apart in empty space. The molecules
are free to move about throughout the container.
A liquid has molecules touching each other. However the intermolecular space,
permit the movement of molecules throughout the liquid.
A solid has molecules, atoms or ions arranged in a certain order in fixed positions
in the crystal lattice. The particles in solids are not free to move about but
vibrate in their fixed positions.
General characteristics of gases
1. Expansibility: gases have limitless expansibility. They expand to fill the
entire vessel they are placed in. I,e Gases assume the volume and shape
of their containers.
2. Compressibility: gases are easily compressed by application of pressure to
a movable piston fitted in the container, i.e Gases are the most
compressible of the states of matter.
3. Diffusibility: gases can diffuse rapidly through each other to form a
homogeneous mixture. i.e Gases will mix evenly and completely when
confined to the same container.
4. Pressure: Gases exert pressure on the walls of the container in all
directions.
5. Effect of heat: when gas, confined in a vessel is heated, its pressure
increases. Upon heating in a vessel fitted with a piston, volume of the gas
increases.
6. Gases have much lower densities than liquids and solids.
Parameters of A gas
A gas can be described in terms of four parameters (measurable properties)
a. The volume, V of the gas
b. Its pressure, P
c. Its temperature, T
d. The number of moles, n, of gas in the container.
The volume, V
The volume of the container is the volume of the gas sample. It is usually given
in liter (L) or milliliters (mL)
1 𝑙𝑖𝑡𝑟𝑒 = 1000 𝑚𝐿
1 𝑚𝐿 = 10−3 𝐿
One millilitter is practically equal to one cubic centimeter (cc). actually
1 𝑙𝑖𝑡𝑟𝑒 = 1000.028 𝑐𝑐
The SI unit for volume is cubic meter (m3) and the smaller unit is decimeter
(dm3).
The pressure, P
Temperature, T
The temperature of a gas may be measured in centigrade degrees (oC) or Celsius
degrees. The SI units of temperature is kelvin (K) or absolute degree. The
centigrade degrees can be converted to kelvins by using the equation.
0
𝐾= C + 273
The kelvin temperature or absolute temperature) is always used in calculations
of other parameters of gases.
The moles of a Gas sample, n
The number of moles, n, of a sample of a gas in a container can be found by
dividing the mass, m, of the sample by the molar mass, M (molecular mass).
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑔𝑎𝑠 𝑠𝑎𝑚𝑝𝑙𝑒 (𝑚)
𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝑔𝑎𝑠 (𝑛) =
𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑔𝑎𝑠 (𝑀)
Substances That Exist as Gases
We live at the bottom of an ocean of air whose composition by volume is roughly
78 percent N2 21 percent O2, and 1 percent other gases, including CO2.
The elements that are gases under normal atmospheric conditions is shown in
fig. 3. Note that hydrogen, nitrogen, oxygen, fluorine, and chlorine exist as
gaseous diatomic molecules: H2, N2, O2, F2, and Cl2. An allotrope of oxygen, ozone
(O3), is also a gas at room temperature. All the elements in Group 8A, the noble
gases, are monatomic gases: He, Ne, Ar, Kr, Xe, and Rn.
Figure 1:Elements that exist as gases at 25oC and 1 atm. The noble gases (the Group 8A elements) are monatomic species;
the other elements exist as diatomic molecules. Ozone (O3) is also a gas.
Ionic compounds do not exist as gases at 25°C and 1 atm, because cations and
anions in an ionic solid are held together by very strong electrostatic forces; that
is, forces between positive and negative charges. To overcome these attractions,
we must apply a large amount of energy, which in practice means strongly
heating the solid. Under normal conditions, all we can do is melt the solid; for
example, NaCl melts at the rather high temperature of 801°C. In order to boil it,
we would have to raise the temperature to well above 1000°C.
The behaviour of molecular compounds is more varied. Some—for example, CO,
CO2, HCl, NH3, and CH4 (methane)—are gases, but the majority of molecular
compounds are liquids or solids at room temperature. However, on heating they
are converted to gases much more easily than ionic compounds. In other words,
molecular compounds usually boil at much lower temperatures than ionic
compounds do.
Note that, the stronger the attractive forces among the molecules, (called
intermolecular forces), the less likely a compound can exist as a gas at ordinary
temperatures.
Table 1:Some substances found as gases at 1 atm and 25oC
Of the gases listed in Table 1, only O2 is essential for our survival. Hydrogen
sulphide (H2S) and hydrogen cyanide (HCN) are deadly poisons. Several others,
such as CO, NO2, O3, and SO2, are somewhat less toxic. The gases He, Ne, and Ar
are chemically inert; that is, they do not react with any other substance. Most
gases are colourless. Exceptions are F2, Cl2, and NO2. The dark brown colour of
NO2 is sometimes visible in polluted air. All gases have the following physical
characteristics:
Pressure of a Gas
Gases exert pressure on any surface with which they come in contact, because
gas molecules are constantly in motion. The pressure of a gas is defined as the
force exerted by the impacts of its molecules per unit surface area in contact.
The pressure of a gas sample can be measured with the help of a mercury
manometer (fig 1). Similarly, the atmospheric pressure can be determined with
a mercury barometer (fig. 2)
The pressure of air that can support 760 mmHg column at sea level, is called one
atmosphere (1 atm). The unit of pressure, millimetre of mercury, is also called
torr.
SI Units of Pressure
Pressure is one of the most readily measurable properties of a gas. In order to
understand how we measure the pressure of a gas; it is helpful to know how the
units of measurement are derived. We begin with velocity and acceleration.
Velocity is defi ned as the change in distance with elapsed time; that is,
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑚𝑜𝑣𝑒𝑑
𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 =
𝑒𝑙𝑎𝑝𝑠𝑒𝑑 𝑡𝑖𝑚𝑒
The SI unit for velocity is m/s, although we also use cm/s.
Acceleration is the change in velocity with time, or
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 =
𝑒𝑙𝑎𝑝𝑠𝑒𝑑 𝑡𝑖𝑚𝑒
Acceleration is measured in m/s2 (or cm/s2).
The second law of motion, formulated by Sir Isaac Newton in the late
seventeenth century, defines another term, from which the units of pressure
are derived, namely, force. According to this law,
𝑓𝑜𝑟𝑐𝑒 = 𝑚𝑎𝑠𝑠 × 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛
In this context, the SI unit of force is the newton (N), where
1𝑁 = 1𝑘𝑔𝑚𝑠 −1
Finally, we define pressure as force applied per unit area:
𝑓𝑜𝑟𝑐𝑒
𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 =
𝑎𝑟𝑒𝑎
The SI unit of pressure is the pascal (Pa), ‡ defined as one newton per square
meter: 1𝑃𝑎 = 𝑁𝑚2
Atmospheric pressure is the pressure exerted by Earth’s atmosphere. The
actual value of atmospheric pressure depends on location, temperature, and
weather conditions.
At the molecular level, air pressure results from collisions between the air
molecules and any surface with which they come in contact. The magnitude of
pressure depends on how often and how strongly the molecules impacts the
surface.
The barometer is probably the most familiar instrument for measuring
atmospheric pressure. A simple barometer consists of a long glass tube, closed
at one end and filled with mercury.
Figure 2: mercury barometer
If the tube is carefully inverted in a dish of mercury so that no air enters the
tube, some mercury will flow out of the tube into the dish, creating a vacuum at
the top (Figure 2). The weight of the mercury remaining in the tube is supported
by atmospheric pressure acting on the surface of the mercury in the dish.
Standard atmospheric pressure (1 atm is equal to the pressure that supports a
column of mercury exactly 760 mm (or 76 cm) high at 0°C at sea level. In other
words, the standard atmosphere equals a pressure of 760 mmHg, where mmHg
represents the pressure exerted by a column of mercury 1 mm high. The mmHg
unit is also called the torr, after the Italian scientist Evangelista Torricelli, † who
invented the barometer. Thus,
1 𝑎𝑡𝑚 = 760 𝑚𝑚𝐻𝑔 = 760 𝑡𝑜𝑟𝑟
1 𝑡𝑜𝑟𝑟 = 1 𝑚𝑚𝐻𝑔
The SI unit of pressure is the Pascal (Pa). the relation between atmosphere, torr
and pascal is
1 𝑎𝑡𝑚 = 760 𝑡𝑜𝑟𝑟 = 1.01325 × 105 𝑃𝑎
1000 Pa = 1 k𝑃𝑎(𝑘𝑖𝑙𝑜𝑝𝑎𝑠𝑐𝑎𝑙)
1 𝑎𝑡𝑚 = 1.01325 × 102 𝑘𝑃𝑎
The unit of pressure ‘Pascal’ is not in common use.
The pressure outside a jet plane flying at high altitude falls considerably below
standard atmospheric pressure. Therefore, the air inside the cabin must be
pressurized to protect the passengers. What is the pressure in atmospheres in
the cabin if the barometer reading is 688 mmHg?
Solution
1 𝑎𝑡𝑚 = 760 𝑚𝑚𝐻𝑔
1 𝑎𝑡𝑚
𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑎𝑏𝑖𝑛 = 688 𝑚𝑚𝐻𝑔 ×
760 𝑚𝑚𝐻𝑔
𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑎𝑏𝑖𝑛 = 0.905 𝑎𝑡𝑚
Practice: convert 749 mmHg to atmospheres.
The atmospheric pressure in San Francisco on a certain day was 732 mmHg.
What was the pressure in kPa?
1 𝑎𝑡𝑚 = 760 𝑚𝑚𝐻𝑔
1 𝑎𝑡𝑚
𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑎𝑏𝑖𝑛 = 688 𝑚𝑚𝐻𝑔 ×
760 𝑚𝑚𝐻𝑔
𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑎𝑏𝑖𝑛 = 0.905 𝑎𝑡𝑚
Example 2
The atmospheric pressure in San Francisco on a certain day was 732 mmHg.
What was the pressure in kPa?
1 𝑎𝑡𝑚 = 1.01325 × 105 𝑃𝑎 = 760 𝑚𝑚𝐻𝑔
1.01325 × 105 𝑃𝑎
𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑖𝑛 𝑠𝑎𝑛 𝐹𝑒𝑎𝑛𝑐𝑖𝑠𝑐𝑜 = 732 𝑚𝑚𝐻𝑔 ×
760 𝑚𝑚𝐻𝑔
𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑖𝑛 𝑠𝑎𝑛 𝐹𝑒𝑎𝑛𝑐𝑖𝑠𝑐𝑜 = 9.76 × 104 𝑃𝑎
𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑖𝑛 𝑠𝑎𝑛 𝐹𝑒𝑎𝑛𝑐𝑖𝑠𝑐𝑜 = 97.6𝑘𝑃𝑎
Practice Exercise Convert 295 mmHg to kilopascals.
A manometer is a device used to measure the pressure of gases other than the
atmosphere.
Figure 3 Two types of manometers used to measure gas pressures. (a) Gas pressure is less than atmospheric pressure. (b) Gas
pressure is greater than atmospheric pressure.
The principle of operation of a manometer is like that of a barometer. There are
two types of manometers, shown in Figure 3. The closed-tube manometer is
normally used to measure pressures below atmospheric pressure [ Figure 3 (a)],
whereas the open-tube manometer is better suited for measuring pressures
equal to or greater than atmospheric pressure [ Figure 3 (b)].
Nearly all barometers and many manometers use mercury as the working fluid,
even though it is a toxic substance with a harmful vapor. The reason is that
mercury has a remarkably high density (13.6 g/mL) compared with most other
liquids.
The Gas Laws
The volume of a given sample of gas depends on the temperature and pressure
applied to it. Any change in temperature or pressure will affect the volume of
the gas. The relationships, which describe the general behaviour of gases, are
called the gas laws.
The Pressure-Volume Relationship: Boyle’s Law
In 1660, Robert Boyle, investigated the pressure-volume relationship of a gas
sample. He notes that as the pressure (P) is increased at constant temperature,
the volume (V) occupied by a given amount of gas decreases. Conversely, if the
applied pressure is decreased, the volume the gas occupies increases. This
relationship is now known as Boyle’s law, which states that the pressure of a
fixed amount of gas at a constant temperature is inversely proportional to the
volume of the gas.
The Boyle’s law may be expressed mathematically as
1 (𝑇, 𝑛 𝑎𝑟𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡)
𝑉∝
𝑃
1
𝑉=𝑘×
𝑃
Where k is a constant called the proportionality constant
𝑃𝑉 = 𝐾
If P1V1 are the initial pressure and volume of a given sample of gas and P2, V2 the
changed pressure and volume, we can write.
𝑃1 𝑉1 = 𝑃2 𝑉2
The relationship is useful for the determination of the volume of a gas at any
pressure, if its volume at any other pressure is known.
Graphically Boyle’s law can be expressed in the following ways:
Figure 4: Graphical representation of Boyle's law
The Temperature-Volume Relationship: Charles’s and Gay-Lussac’s Law
In 1787 Jacques Charles and Joseph Gay-Lussac, investigated the effect of
change of temperature on the volume of a fixed amount of gas at constant
pressure. Their studies showed that, at constant pressure, the volume of a gas
sample expands when heated and contracts when cooled.
He established a generalisation which is called the Charles’ Law. which states
that the volume of a fixed amount of gas maintained at constant pressure is
directly proportional to the absolute temperature of the gas.
Charles’s Law may be expressed mathematically as
𝑉∝𝑇 (P, n are constant)
𝑉 = 𝑘𝑇
𝑉
=𝑘
𝑇
Where k is a constant.
If V1, T1 are the initial volume and temperature of a given mass of a gas at
constant pressure and V2, T2 be the new values, we can write
𝑉1 𝑉2
=𝑘=
𝑇1 𝑇2
𝑉1 𝑉2
=
𝑇1 𝑇2
Graphically, Charles’s law can be represented as
Figure 5: Graphical representation of Charle's law.
The Volume-Amount Relationship: Avogadro’s Law
The Italian scientist Amedeo Avogadro complemented the studies of Boyle,
Charles, and Gay-Lussac. In 1811 he published a hypothesis stating that at the
same temperature and pressure, equal volumes of different gases contain the
same number of molecules (or atoms if the gas is monatomic). It follows that
the volume of any given gas must be proportional to the number of moles of
molecules present; that is,
𝑉∝𝑛 P,T constant
𝑉 = 𝑘𝑛
where n represents the number of moles and k 4 is the proportionality constant.
Avogadro’s law, states that at constant pressure and temperature, the volume
of a gas is directly proportional to the number of moles of the gas present.
The Ideal Gas Equation
The simultaneous effect of change of pressure and temperature of a gas can be
studied by combining Boyle's law and Charles' law. The derived new equation is
called combined gas law or ideal gas equation.
𝐵𝑜𝑦𝑙𝑒’𝑠 𝑙𝑎𝑤: 1 (𝑇, 𝑛 𝑎𝑟𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡)
𝑉∝
𝑃
𝐶ℎ𝑎𝑟𝑙𝑒𝑠′ 𝑙𝑎𝑤 𝑉∝𝑇 (𝑃, 𝑛 𝑎𝑟𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡)
𝐴𝑣𝑜𝑔𝑎𝑑𝑟𝑜’𝑠 𝑙𝑎𝑤 𝑉∝n (𝑃, 𝑇 𝑎𝑟𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡)
We can combine all three expressions to form a single master equation for the
behaviour of gases:
nT
𝑉∝
𝑃
nT
𝑉=𝑅
𝑃
𝑃𝑉 = 𝑛𝑅𝑇 (𝑖𝑑𝑒𝑎𝑙 𝑔𝑎𝑠 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛)
where R, the proportionality constant, is called the gas constant. The ideal gas
equation describes the relationship among the four variables 𝑃, 𝑉, 𝑇, and 𝑛. An
ideal gas is a hypothetical gas whose pressure-volume-temperature behaviour
can be completely accounted for by the ideal gas equation.
Examples
Sulphur hexafluoride (SF6) is a colourless, odourless, very unreactive gas.
Calculate the pressure (in atm) exerted by 1.82 moles of the gas in a steel vessel
of volume 5.43 L at 69.5oC.
𝑃𝑉 = 𝑛𝑅𝑇
𝑛𝑅𝑇
𝑃=
𝑉
(1.82 𝑚𝑜𝑙𝑒𝑠) × (0.0821𝐿𝑎𝑡𝑚𝐾 −1 𝑚𝑜𝑙𝑒𝑠 −1 ) × (69.5 + 273)𝐾
𝑃=
5.43 𝐿
𝑃 = 9.42 𝑎𝑡𝑚
Calculate the volume (in litres) occupied by 2.12 moles of nitric oxide (NO) at
6.54 atm and 76oC.
