APPLICATIONS OF GAS LAWS

DEPARTMENT OF PHYSICS AND BIOCHEMICAL SCIENCES

PBS-CHE-122

MR. B. MALIMUSI
 Objectives

By the end of this topic, students should be able to;

Identify the elements that exist as gases.
Understand the origins of gas pressure.
Understand the measurement of gas pressure.
Apply the gas laws in different gas P-V-n-T problems.
Differentiate absolute zero from absolute temperature.
Compare and contrast real and ideal gases.
Calculate the density and molar mass of various gaseous substances.
Understand and apply Dalton’s law of partial pressures.
Solve gas stoichiometry problems.
Differentiate gas diffusion from gas effusion.
Explain real life applications of the gas laws.
 Substances That Exist as Gases

• Air is all around us.

• Air’s composition by volume is roughly 78 percent , 21 percent , and 1 percent other
gases, including
 Substances That Exist as Gases

• Only 11 elements are gases under normal atmospheric conditions.

• Normal atmospheric conditions are defined as 25˚C and 1 atmosphere (atm) pressure.
 Substances That Exist as Gases

• The noble gases (the Group 8A elements) are monatomic species; Helium (He), Neon
(Ne), Argon (Ar), Krypton (Kr), Xenon (Xe), and Radon (Rn).
• The other elements exist as diatomic molecules; and .
• Ozone (), an allotrope of oxygen, is also a gas at room temperature.
 Physical Properties of Gases

Gases assume the volume and shape of their containers.

Gases are the most compressible of the states of matter.
Gases will mix evenly and completely when confined to the same container.
Gases have much lower densities than liquids and solids.
 Pressure of a Gas
Units of Pressure
 Gases exert pressure on the walls of
their container due to the constant
collisions of gas particles with the
container walls.
Gases exert pressure on any surface
with which they come in contact,
because gas molecules are constantly in
motion.
Gas pressure is the force exerted per
unit area by gaseous molecules as they
collide with the walls of their container.
Gas pressure is expressed in several
units (See the table on the right).
 Atmospheric Pressure and Pressure at Sea Level

Atmospheric pressure is the force per

unit area exerted by an atmospheric
column (that is, the entire body of
air above the specified area).
Atmospheric pressure is the pressure
exerted by Earth’s atmosphere.
The pressure exerted on an object in a
fluid comes from all directions—
downward and upward, as well as from
the left and from the right.

Atmospheric column of air

 Atmospheric Pressure and Pressure at Sea Level

Atmospheric pressure is commonly measured

using a barometer.
A simple barometer consists of a long glass tube,
closed at one end and filled with mercury.
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 of the tube.
• 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 (Hg)
exactly 760 mm (or 76 cm) high at 0˚C at sea level.
That is; A simple Mercury Barometer
Atmospheric Pressure and Pressure at Sea Level
 Example - Cabin Pressurization

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. If the barometer reading is 688 mmHg, calculate the pressure in the
cabin
i. In atmospheres,
ii. In Torr,
iii. And in Pascals.

Solution;
i. The required conversion factor is; or ,
Therefore; .
 Example - Cabin Pressurization

Solution Cont’d;
ii. The required conversion factor is; or ,
Therefore; .

iii. Given pressure in mmHg, we can convert it to pressure in atm, then we can convert
the pressure in atm to pressure in pascals.
The required conversion factors are; and .
 The Manometer
A manometer is a device used to measure the pressure of gases other than the atmosphere.
Two types of manometers exist; The open-tube manometer and the closed-tube
manometer.
The open-tube manometer is generally used for measuring pressures equal to or greater
than atmospheric pressure.
The closed-tube manometer is normally used to measure pressures below atmospheric
pressure.
Most manometers (and nearly all barometers) use mercury (Hg) as the working fluid, despite
its toxicity.
 The reason is that mercury has a very high density (13.6 g/mL) compared with most other liquids.
 The higher the liquid density in a column, the shorter the liquid column since atmospheric or gas
pressure will have to be sufficiently high in order to induce a unit rise of the liquid in the column.
 Therefore, mercury allows for construction of manageably small barometers and manometers.
 If liquids of lower density were used, we would need very long columns to accommodate high gas or
atmospheric pressure measurements.
 The Manometer

Closed-tube manometer Open-tube manometer

 The Gas Laws

1) Boyle’s Law
Proposed by British chemist Robert
Boyle.
Boyle noticed that when temperature is
held constant, the volume (V) of a fixed
amount of a gas decreases as the total
applied pressure (P)—atmospheric
pressure plus the pressure due to the
added mercury—is increased.
Mathematically, the pressure is inversely
proportional to the volume of the gas.
 Boyle’s Law

Boyle’s law states that the pressure of a fixed amount of gas, maintained at constant
temperature, is inversely proportional to the volume of the gas.
Mathematically, Boyle’s law can be stated as;

To change the proportionality symbol ( to an equals sign, we shall introduce a constant
of proportionality, ;

Such that;
Alternatively, Boyle’s law states that the product of the pressure (P) and the volume
(V) of a fixed amount of gas, maintained at constant temperature, is constant.
 Boyle’s Law

According to Boyle’s law, if the temperature is kept constant, the product of P and V
of a fixed amount of gas, at state 1, is the same as P×V at state 2, which is also the
same as P×V at state 3, and so on.
This can be represented mathematically as;

Or simply;

Where are the gas pressure and volume, respectively, at state 1. Such that are the
gas pressure and volume, respectively, at state 2.
 Boyle’s Law - Examples
Example 1
A gas occupying a volume of 725 mL at a pressure of 0.970 atm is allowed to expand at
constant temperature until its pressure reaches 0.541 atm. What is its final volume?
Solution;
Given; Constant T, , and .
According to Boyle’s law;

Or

Hence the final volume of the gas is 1299.9 mL or 1.3 L

 Boyle’s Law - Examples
Example 2
At 46˚C a sample of ammonia gas exerts a pressure of 5.3 atm. What is the pressure
when the volume of the gas is reduced to one-tenth (0.10) of the original value at the
same temperature?
Solution;
Given; Constant T, , and
As per Boyle’s law;
 The Gas Laws

2) Charles’ Law
Jacques Charles, a French physicist,
discovered in the 1780s that heating a
gas (increasing its temperature) causes
it to expand (increase in volume).
At constant pressure, the volume of a
gas sample expands when heated and
contracts when cooled.
In the animation on the right, the two
weights (in green) above the moveable
piston (in red) in conjunction with
atmospheric pressure, represent the
constant pressure exerted on the gas
system.
 The Gas Laws

2) Charles’ Law
Charles’ law states that the volume (V) of
a fixed mass of gas is directly proportional
to the absolute temperature (T) of the gas
when pressure is kept constant.
Mathematically;
Or , where is the proportionality constant.
Also;
Charles’ law states that at constant
pressure, the ratio of the volume (V) of a
fixed mass of gas to the absolute
temperature (T) of the gas is always
constant.
 The Gas Laws

2) Charles’ Law

Or simply;

Where are the gas volume and absolute temperature, respectively, at state 1. Such
that are gas volume and absolute temperature, respectively, at state 2.
 Absolute Zero & Absolute Temperature

At any given pressure, the plot of volume

versus temperature yields a straight line
according to Charles’ law.
All gases ultimately condense (become liquids)
if they are cooled to sufficiently low
temperatures.
The solid (not-dashed) portions of the lines
represent the temperature region above the
condensation point.
By extrapolating (the dashed portions) the lines
to zero volume, we find the same intercept on
the temperature axis for all the lines and it is at
a temperature of - 273.15˚C.
 Absolute Zero & Absolute Temperature

Scottish physicist Lord Kelvin identified

-273.15˚C as absolute zero.
Absolute zero is the lowest theoretically
attainable temperature.
Lord Kelvin proposed a new temperature
scale with absolute zero as the starting
point.
He called this temperature scale the
absolute temperature scale. Nowadays it
is called the Kelvin temperature scale.
Absolute temperature is the
temperature measured using the Kelvin
temperature scale where the starting
point (the zero point) is absolute zero.
 Absolute Temperature Scale (K) and the Celsius
Temperature Scale (˚C)
When performing calculations involving gas laws, always use the absolute
temperature.
Given temperature in ˚C, always convert it to K, before substituting it into the gas laws
equations.
Use the following formula to convert temperature in ˚C to temperature in K.
 Charles’ Law Example

A 36.4 L volume of methane gas is heated from 25˚C to 88˚C at constant pressure. What
is the final volume of the gas?
Solution;
In all gas law calculations, temperature must be expressed in kelvins (K) !!!.
Given;
Using Charles’ law, we can determine the final volume () ;
or
Such that;

As expected, the volume of gas should increase due to the increase in the temperature.
 The Gas Laws

3) Gay-Lussac’s Law
Gay-Lussac’s law states that at
constant amount of gas and constant
volume, the pressure (P) of gas is
directly proportional to the absolute
temperature (T) of the gas.
Mathematically;
Or
Such that;
 The Gas Laws

4) Avogadro’s Law
Avogadro’s law states that at constant pressure and constant temperature, the
volume (V) of a gas is directly proportional to the number of moles (n) of the gas
present.
Mathematically, we can write;
Or;
The greater the number of moles of gas, the greater the volume they occupy at
constant temperature and pressure.
 The Ideal Gas Law

The four gas laws can be summarized as follows;

Boyle’s law; , at constant n and T.
Charles’ law; , at constant n and P.
Gay-Lussac’s law; , at constant n and V.
Avogadro’s law: , at constant T and P.
Combining these gas laws implies that;

or; , where R is the proportionality constant.

 , is the ideal gas equation
 What is an Ideal Gas?

An ideal gas is a hypothetical gas whose pressure-volume-temperature behavior can

be completely accounted for by the ideal gas equation.
An ideal gas has the following characteristics;
i. The molecules of an ideal gas do not attract or repel one another.
ii. The volume of the molecules of an ideal gas is negligible compared with the volume of the
container.
 Real Gases vs Ideal Gases

In real life there is no such thing as an ideal gas.

Only under certain conditions, the behaviour of real gases can be approximated as
that of ideal gases.
Real gases generally exhibit ideal gas behaviour at sufficiently low pressures. At very
high pressures, real gases exhibit significant deviations from ideal gas behaviour.
For example, at Standard Temperature and Pressure (STP) conditions many real
gases behave like an ideal gas.
Standard temperature and pressure (STP) refers to the conditions at 0˚C and 1 atm.
Hence, at STP,
 Real Gases vs Ideal Gases

Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L.

If we make R subject of the formula in the ideal gas equation, we obtain;

For for an ideal gas at STP; .

Such that;

R is called the ideal gas constant or simply the gas constant.

 Examples

Example 1
Calculate the volume (in liters) occupied by 2.12 moles of nitric oxide (NO) at 6.54 atm
and 76˚C.
Solution;
Given;
Assuming ideal gas behaviour;
 Examples

Example 2
What is the volume (in liters) occupied by 49.8 g of HCl at STP?
Solution;
We know that at STP, 1 mole of an ideal gas occupies 22.4L. We can make use of this
fact if we assume ideal gas behaviour for HCl at STP.

Converting mass of HCl to number of moles yields;

Hence ;
 The Combined Gas Law

Starting from , and noting that R is a constant. We can compare the Pressure (P),
Volume (V), number of moles (n) and the temperature (T) for a given sample of gas at
two different states.
We can write;

Moreover if the amount of gas is kept constant, i.e.

The equation above is called the combined gas law.

 The Combined Gas Law

PRACTICE!
1. A gas initially at 4.0 L, 1.2 atm, and 66˚C undergoes a change so that its final volume
and temperature are 1.7 L and 42˚C. What is its final pressure? Assume the number of
moles remains unchanged.
2. An ideal gas originally at 0.85 atm and 66˚C was allowed to expand until its final volume,
pressure, and temperature were 94 mL, 0.60 atm, and 45˚C, respectively. What was its
initial volume?
3. A gas evolved during the fermentation of glucose (wine making) has a volume of 0.78 L
when measured at 20.1˚C and 1.00 atm. What was the volume of this gas at the
fermentation temperature of 36.5˚C and 1.00 atm pressure?
 Density and Molar Mass of a Gaseous Substance

Consider the ideal gas equation; or

Rearranging it yields;

Recall that; number of moles (n) is equal to mass (m) divided by molar mass (M), i.e.;

Hence;

Rearranging this equation yields;

Density (d) equals mass (m) divided by volume (V). Such that;
 Example

The density of a gaseous organic compound is 3.38 g/L at 40˚C and 1.97 atm. What is its
molar mass?
Solution;
Given;
We know that;

Hence;
 Density and Molar Mass of a Gaseous Substance

PRACTICE
1. A quantity of gas weighing 7.10 g at 741 torr and 44˚C occupies a volume of 5.40 L.
What is its molar mass?
2. A volume of 0.280 L of a gas at STP weighs 0.400 g. Calculate the molar mass of the
gas.
3. Calculate the density of hydrogen bromide (HBr) gas in grams per liter at 733 mmHg and
46˚C.
 Dalton’s Law of Partial Pressures
Dalton’s law of partial pressures states that the total pressure of a mixture of gases is just the
sum of the pressures that each gas would exert if it were present alone.
Where partial pressures are the pressures of individual gas components in the mixture.
Given a mixture of three different gases A, B and C. The partial pressure exerted by each gas is;
, and
According to Dalton’s law of partial pressures, the total gas pressure ( is;
+

)
where
Such that depends only on the total number of moles of gas present, not on the nature of the
gas molecules.
 Dalton’s Law of Partial Pressures

The partial pressure of any gas in a mixture of gases is related to the total gas pressure by
the following equation;

Where; is the partial pressure of gas , is the mole fraction of gas and is the total gas
pressure.
In general, the mole fraction of gas in a mixture of gases is given by;

Where; is the mole fraction of gas , is the number of moles of gas and is the total
number of moles of gas.
 Dalton’s Law of Partial Pressures

Example
A mixture of gases contains 4.46 moles of neon (Ne), 0.74 mole of argon (Ar), and 2.15
moles of xenon (Xe). Calculate the partial pressures of the gases if the total pressure is 2.00
atm at a certain temperature.
Solution;
Given;
The mole fraction of each gas will be given by;

Hence; Using , we obtain;

 Dalton’s Law of Partial Pressures

PRACTICE
1. Assuming that air contains 78 percent Nitrogen gas, 21 percent Oxygen gas, and 1
percent Argon gas, all by volume, how many molecules of each type of gas are
present in 1.0 L of air at STP?
2. A sample of natural gas contains 8.24 moles of methane (), 0.421 mole of ethane (,
and 0.116 mole of propane (). If the total pressure of the gases is 1.37 atm, what are
the partial pressures of the gases?
 Gas Stoichiometry

Example 1
The equation for the metabolic breakdown of glucose is the same as the equation for the
combustion of glucose in air:

Calculate the volume of produced at 37˚C and 1.00 atm when 5.60 g of glucose is used up
in the reaction.
Solution;
Firstly, we need to determine the number of moles of glucose in 5.60 g of glucose ;
 Gas Stoichiometry

Example Cont’d
Now we shall determine the volume occupied by 0.186 moles of at 37˚C and 1.00 atm.

Where; ;
 Gas Stoichiometry

Example 2
Sodium Azide () is used in some automobile air bags. The impact of a collision triggers the
decomposition of as follows:

The nitrogen gas produced quickly inflates the bag between the driver and the windshield and
dashboard. Calculate the volume of generated at 80˚C and 823 mmHg by the decomposition of 60.0
g of .
Solution;
 Gas Stoichiometry

Example 2 Cont’d
Using the ideal gas law;

Where;
;
Hence;
 Gas Diffusion

Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by
virtue of their kinetic properties.
Graham’s law of diffusion states that under the same conditions of temperature and
pressure, rates of diffusion for gases are inversely proportional to the square roots of their
molar masses.

Where; and are the diffusion rates of gases 1 and 2, while and are their molar masses,
respectively.
 Gas Effusion

Gas effusion is the process by which a gas under pressure escapes from one
compartment of a container to another by passing through a small opening.
Although effusion differs from diffusion in nature, the rate of effusion of a gas has the same
form as Graham’s law of diffusion.
In the diagram below, Gas molecules move from a high-pressure region (left) to a low-
pressure one through a pinhole.
 Applications of The Gas Laws in Everyday Life

1. Cooking using a pressure cooker

A pressure cooker is a sealed pot with a valve
that controls the steam pressure inside.
As the liquid inside the cooker heats up
(increasing T), steam is produced, and the
pressure (P) inside the cooker increases
according to Gay-Lussac’s law.
At higher pressure, water’s boiling point is
increased.
Because the boiling point of water is higher
inside a pressure cooker, the temperature of
the steam and water is also higher.
Higher cooking temperatures mean that food Pressure Cookers
cooks faster.
 Applications of The Gas Laws in Everyday Life

2. Hot Air Balloons

In hot air balloons, heating the air
(increasing T) inside the balloon
causes it to expand (increase in
volume) and become less dense
than the cooler air outside,
allowing the balloon to rise.
Hot air balloons operate based on
the principles of Charles’ law.

Hot air balloons

 Applications of The Gas Laws in Everyday Life

3. Breathing
When you inhale, your diaphragm
contracts, increasing the volume of
your lungs and decreasing the pressure
inside them, allowing air to flow in.
Conversely, when you exhale, the
diaphragm contracts, decreasing lung
volume and increasing pressure,
pushing air out.
This is an application of Boyle’s law.

Boyle’s law during breathing