Page 1 of 23
Gases
3.1 Kinetic theory of gases
States of matter
Solids
•
•
•
Strong forces of attraction between particles, particles are packed very closely
together in a fixed and regular pattern
Atoms vibrate in position but can’t change position or move
Solids have a fixed volume, shape, and high density
Liquids
•
•
•
Weaker attractive forces in liquids than in solids, particles are close together in
an irregular, unfixed pattern.
Particles can move and slide past each other which is why liquids adopt the
shape of the container they’re in and why they are able to flow.
Liquids have a fixed volume but not a fixed shape and have a moderate to
high density.
Gases
•
No intermolecular forces, particles are in random movement and so there is
no defined pattern
Updated August 2022 RC/AT/DB
Page 2 of 23
•
•
Particles are far apart and move quickly (around 500 m/s) in all directions,
they collide with each other and with the sides of the container (this is
how pressure is created inside a can of gas)
No fixed volume, since there is a lot of space between the particles, gases can be
compressed into a much smaller volume. Gases have low density.
The state of a substance at room temperature and pressure depends on its structure and
bonding.
Five types of structure are found in elements and compounds:
➢
➢
➢
➢
➢
simple atomic, e.g., helium
simple molecular, e.g., hydrogen
giant ionic, e.g., sodium chloride
giant metallic, e.g., copper
giant molecular, e.g., silicon (IV) oxide.
State Interconversions: Key terms and concepts
Melting: the process of converting from solid to liquid due to increase in temperature.
Melting point: the temperature at which a solid starts to melt, eg. ice melts at 0 °C.
Boiling: the process of converting from liquid to gas due to increase in temperature.
Also known as vaporisation.
Boiling point: the temperature at which a liquid starts to boil, eg. water boils at 100 °C.
Condensation: the process by which a gas turns to liquid.
Sublimation: the process by which a solid turns directly to gas without melting.
Solidification: the process by which a gas turns directly to solid.
Evaporation: the process by which a liquid turns to a gas below its boiling point.
Volatile: liquids that evaporate at room temperature.
Updated August 2022 RC/AT/DB
Page 3 of 23
Interconversions of solids, liquids and gases
Solid to Liquid
Heat solid until it melts. When a solid is heated the particles gain kinetic energy and
start to vibrate faster about their fixed position. When the temperature is high enough,
the vibration of particles becomes sufficient to overcome the forces of
attraction between them. The particles begin to break away from their regular pattern.
They can now slide past each other. The solid becomes a liquid.
Liquid to Solid
Cool liquid until it freezes. When a liquid is cooled, the particles lose their kinetic
energy. When the temperature is low enough, the particles no longer have the energy to
slide over each other. The forces of attraction can hold the particles together in a regular
pattern. The substance becomes solid.
Liquid to Gas
Heat the liquid until it boils. When a liquid is heated, the particles gain kinetic
energy and mover further apart. Eventually, the attractive forces in the liquid are
broken. Bubbles of gaseous particles escape from the liquid. The substance becomes
gas.
Gas to Liquid
Cool the gas until it condenses. When a gas is cooled, the particles lose kinetic
energy and the attractive forces become great enough to keep the particles closer
together as a liquid.
Solid to Gas
Heat the solid until it sublimes. The solid particles gain kinetic energy and vibrate
faster. Eventually, the forces of attraction between the particles are completely broken
and they escape from the solid as a gas.
Updated August 2022 RC/AT/DB
Page 4 of 23
Brownian motion
•
•
Brownian motion is defined as the random movement of particles in a liquid, or a
gas produced by large numbers of collisions with smaller, often invisible
particles
The observation of Brownian motion proves the correctness of the kinetic
particle theory.
Diffusion
•
•
•
•
This is the process by which different gases or different liquids mix and is due to
the random motion of their particles.
Diffusing particles move from an area of high concentration to an area of low
concentration.
Eventually the concentration of particles is even as they spread out to occupy all
of the available space.
Diffusion happens on its own and no energy input is required although it occurs
faster at higher temperatures.
This point will be dealt with in much more detail in the next topic: Bonding and
Structure.
The molar volume of a gas
Knowing how much gas is available for a dive is crucial
to a diver's survival. The tank on the diver's back is
equipped with gauges to indicate how much gas is
present and what the pressure is. A basic knowledge
of gas behaviour allows the diver to assess how long
they can stay underwater without developing
problems.
•
• 1 mole of any gas contains the same number of
molecules. (That comes from the definition of a mole.)
If you have the same number of molecules of any gas, they must occupy the same
volume at the same temperature and pressure.
The volume occupied by 1 mole of any gas is called the molar volume.
The molar volume varies with temperature and pressure, but at this level you will
almost always be given the value at room temperature and pressure (rtp) which is
taken to be about 20°C and 1 atmosphere pressure.
The number will usually be quoted as 24 dm3 per mole (dm3 mol-1), but you may find it
as 24000 cm3 per mole.
The cubic decimetre (dm3) isn't a common everyday unit of volume but is exactly the
same as the litre.
There are 1000 cm3 in 1 dm3.
Updated August 2022 RC/AT/DB
Page 5 of 23
Standard temperature and pressure (STP) is defined as 0oC (273.15K)
and 1atm pressure. The molar volume of a gas is the volume of one mole of a gas at
STP. At STP, one mole (6.02×1023 representative particles) of any gas occupies a volume
of 22.4dm3
Question 1: What volume of carbon dioxide (measured at rtp) would you get if you
added excess hydrochloric acid to 10 g of calcium carbonate?
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
Question 2: Hydrogen gas is produced when you drop lithium metal into water.
2Li + 2H2O
2LiOH + H2
Assuming you have an excess of water, what is the maximum mass of lithium you could
use to avoid over-filling a 100 cm3 gas syringe, collecting the gas at room temperature
and pressure?
(RAM: Li = 7, Molar volume = 24000 cm3 mol-1 at rtp.)
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
Updated August 2022 RC/AT/DB
Page 6 of 23
Question 3: At 0°C and 1 atmosphere pressure, the density of oxygen is 1.429 g dm-3.
Calculate the value for the molar volume of a gas at this temperature and pressure.
(RAM: O = 16)
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
Question 5: Calculate the volume of 1.42 g of chlorine, Cl2, at room temperature and
pressure. (RAM: Cl = 35.5. Molar volume = 24000 cm3 mol-1 at rtp.)
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
Question 6: Calculate the density of ammonia gas, NH3, in g dm-3 at room temperature
and pressure. (RAMs: H = 1; N = 14. Molar volume = 24 dm3 mol-1 at rtp.)
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
Self-Assessment Criteria
✓ Recall Avogadro’s Law
✓ Calculate the ratios of reactants and products in chemical equations using gas volumes.
Updated August 2022 RC/AT/DB
Page 7 of 23
Molecular speed distribution of gases according to temperature
In the mid-19th century, James Maxwell and Ludwig Boltzmann derived an equation for
the distribution of molecular speeds in a gas. Graphing this equation gives us
the Maxwell-Boltzmann distribution of speeds. The Maxwell-Boltzmann speed
distribution curve for N2 at 25ºC is shown below.
The speed that corresponds to the peak of the curve is called the most probable speed.
The area under any part of the curve equals the fraction of molecules in the
corresponding velocity range. The shaded area in the graph below is proportional to the
total number of molecules present in a system.
To determine the fraction of molecules that have velocities between 500 and 1000
m/sec, one needs to measure the area of the shaded region below.
Updated August 2022 RC/AT/DB
Page 8 of 23
The speed distribution curve shape will vary with both temperature and molar mass of
the gas.
At increasing temperature:
•
The Maxwell-Boltzmann curve spreads and flattens out.
•
The most probable speed increases (the peak shifts to the right).
•
The fraction of fast-moving molecules increases.
•
The fraction of slow-moving molecules decreases.
Updated August 2022 RC/AT/DB
Page 9 of 23
Maxwell-Boltzmann speed distribution for nitrogen at four different temperatures
Note: when the temperature goes up, the particles in a gas tend to move faster. As a
result, the entire distribution shifts to the right, toward higher speeds. When the
temperature increases, the most probable speed increases (the highest point on the
curve shifts to the right). In addition, the entire curve gets wider and lower: a wider
range of speeds results, but fewer molecules at the most probable speed.
Updated August 2022 RC/AT/DB
Page 10 of 23
When the temperature is raised, the fraction of molecules moving at high speeds
increases. E.g., from 25ºC to 300ºC, the fraction of molecules moving faster than 800
m/sec becomes larger.
Likewise, when the temperature is raised, the fraction of molecules moving
at low speeds decreases. E.g., from 25ºC to 300ºC, the fraction of molecules moving
slower than 800 m/sec becomes smaller.
Updated August 2022 RC/AT/DB
Page 11 of 23
Note: The profile of the curve depends on the molar mass of the gas. When the molar
mass increases:
➢
➢
➢
➢
The Maxwell-Boltzmann curve gets taller and narrower.
The most probable speed decreases (the peak shifts left).
The fraction of fast-moving molecules decreases.
The fraction of slow-moving molecules increases.
Activation Energy and the Maxwell-Boltzmann Distribution Curve
For a reaction to take place, the reactant particles need to overcome a minimum amount
of energy. This energy is called the activation energy (Ea)
Updated August 2022 RC/AT/DB
Page 12 of 23
The graph shows that only a small proportion of molecules in the sample have enough
energy for an effective collision and for a chemical reaction to take place
Changes in temperature
•
•
When the temperature of a reaction mixture is increased, the particles gain more
kinetic energy. The particles start to move around faster and more frequent
collisions result.
The proportion of successful collisions increases, meaning a
higher proportion of the particles possess the minimum amount of energy
(activation energy) to cause a chemical reaction.
Updated August 2022 RC/AT/DB
Page 13 of 23
Catalysis and the Maxwell-Boltzamnn Distribution curve
A catalyst increases the rate of a reaction by providing the reactants with an alternative
reaction pathway which is lower in activation energy than the uncatalysed reaction.
•
•
A Catalyst provides the reactants with another pathway which has a lower
activation energy Ea. A greater proportion of molecules in the reaction mixture
have sufficient energy for an effective collision
As a result of this, the rate of the catalysed reaction is increased compared to the
uncatalyzed reaction
Updated August 2022 RC/AT/DB
Page 14 of 23
Self-Assessment Criteria
✓ Sketch distribution diagrams showing the speed of gas molecules at different
temperatures.
✓ Relate these diagrams to the concept of activation energy of chemical reactions.
3.2 Ideal gases and the Ideal Gas Law
Background…
Charles’ Law
The volume of an ideal gas at constant pressure is directly proportional to the
temperature measured in kelvin.
V/T = k
Boyle’s Law
The pressure exerted by a gas (of a given mass, kept at a constant temperature) is
inversely proportional to its volume.
PV = k
Note: the absolute temperature is O Kelvin or -273oC.
Updated August 2022 RC/AT/DB
Page 15 of 23
Questions
A sample of gas occupies 360cm3 under a pressure of 625mm Hg. At constant
temperature what volume would the gas occupy at a pressure of 750mm Hg?
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
At 0oC and 5 atm a gas occupies 100cm3. If the gas is compressed to 30cm3 at constant
temperature what will be the final pressure of the gas?
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
If 200 L of a gas at 27°C is cooled to -33°C at a constant pressure, the volume will be?
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
The volume of a sample of a gas at 273 oC is 200 L. If the volume is decreased to 100 L at
constant pressure, what will be the new temperature of the gas?
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
Updated August 2022 RC/AT/DB
Page 16 of 23
The volume that a gas occupies depends on:
•
•
its pressure: Units - pascals, Pa
its temperature; Units - kelvin, K
Questions
A weather balloon has a volume of 105L at 0.97 atm when the temperature is 318K.
What is the volume at 293K and 1.05 atm?
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
Updated August 2022 RC/AT/DB
Page 17 of 23
If 10L of O2 at 273K and 1 atm is compressed to a 7L container at 250K, what is the new
pressure?
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
The Kinetic Theory of gases makes some assumptions:
➢ the gas molecules move rapidly and randomly
➢ the distance between the gas molecules is much greater than the diameter of the
molecules so the volume of the molecules is negligible
➢ there are no forces of attraction or repulsion between the molecules
➢ all collisions between particles are elastic – this means no kinetic energy is lost in
collisions (kinetic energy is the energy associated with moving particles
A theoretical gas that fits this description is called an ideal gas.
The ideal Gas equation… combines and obeys Charles’ Law and Boyle’s Law and follows
the assumptions written above.
pV = nRT
where…
p is the pressure in pascals, Pa
V is the volume of gas in cubic metres, m3 (1m3 = 1000dm3)
n is the number of moles of gas
R is the gas constant, which has a value of 8.31JK–1mol–1
T is the temperature in kelvin, K.
Note: Any given units in a question must be converted to the ones shown when using the
ideal gas equation!
Standard Temperature and Pressure (STP) refers to the internationally agreed-upon
standard of measurement for experiments in chemistry.
Updated August 2022 RC/AT/DB
Page 18 of 23
According to the International Union of Pure and Applied Chemistry (IUPAC), the
currently accepted values for standard temperature and pressure are 273.15 K (0
°C) and exactly 100kPa (0.986923 atm) (kPa = kilopascal). The purpose of STP is to
provide chemists with a common experimental baseline from which to interpret and
compare data.
Questions
Calculate the volume occupied by 0.500mol of carbon dioxide at a pressure of 150kPa and
a temperature of 19°C. (R = 8.31JK–1mol–1)
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
A flask of volume 5.00dm3 contained 4.00g of oxygen. Calculate the pressure exerted by
the gas at a temperature of 127°C.
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
Calculate the volume occupied by 272g of methane at a pressure of 250kPa and a
temperature of 54°C. (R = 8.31JK–1mol–1)
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
Updated August 2022 RC/AT/DB
Page 19 of 23
The pressure exerted by 0.25mol of carbon monoxide in a 10dm3 flask is 120kPa.
Calculate the temperature in the flask in kelvin.
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
A volume of 1.00dm3 is occupied by 1.798g of a gas at 298K and 101kPa. Calculate the
molar mass of the gas.
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
Krypton has a density of 3.44gdm-3 at 25OC and 1.01 X 105 Nm-2. Calculate its molar
mass. (Recall: density = mass / volume)
________________________________________________________
________________________________________________________
________________________________________________________
________________________________________________________
________________________________________________________
________________________________________________________
________________________________________________________
________________________________________________________
________________________________________________________
Updated August 2022 RC/AT/DB
Page 20 of 23
When 100cm3 of 1M hydrochloric acid are added to 8g of powdered calcium carbonate,
carbon dioxide is released. Calculate the volume of gas given off in cm3 at a pressure of
100kPa and a temperature of 32OC.
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
_____________________________________________________________________________________________________
Self-Assessment Criteria
✓ Recall the basic assumptions of the ideal gas model.
✓ Explain the Ideal Gas Law.
✓ Solve problems involving the ideal gas equation.
Updated August 2022 RC/AT/DB
Page 21 of 23
The origin of saturated vapour pressure
The evaporation of a liquid
The average energy of the particles in a liquid is governed by the temperature. The
higher the temperature, the higher the average energy. But within that average, some
particles have energies higher than the average, and others have energies lower than
the average.
Some of the more energetic particles on the surface of the liquid can be moving fast
enough to escape from the attractive forces holding the liquid together. They evaporate.
The diagram shows a small region of a liquid near its surface.
Notice that evaporation only takes place on the surface of the liquid. That's quite
different from boiling which happens when there is enough energy to disrupt the
attractive forces throughout the liquid.
The evaporation of a liquid in a closed container
Now imagine what happens if the liquid is in a closed container. Common sense tells you
that water in a sealed bottle doesn't seem to evaporate - or at least, it doesn't disappear
over time.
But there is constant evaporation from the surface. Particles continue to break away
from the surface of the liquid - but this time they are trapped in the space above the
liquid.
Updated August 2022 RC/AT/DB
Page 22 of 23
As the gaseous particles bounce around, some of them will hit the surface of the liquid
again and be trapped there. There will rapidly be an equilibrium set up in which the
number of particles leaving the surface is exactly balanced by the number re-joining it.
In this equilibrium, there will be a fixed number of the gaseous particles in the space
above the liquid.
When these particles hit the walls of the container, they exert a pressure. This pressure
is called the saturated vapour pressure of the liquid.
Self-Assessment Criteria
✓ Explain vapour pressure as evidence of the presence of a vapour in contact with
the evaporating liquid/solid.
✓ Explain saturated vapour pressure.
References:
✓
✓
https://www.savemyexams.co.uk/-/chemistry/
https://chem.libretexts.org/Courses/City_College_of_San_Francisco/Chemistry_101A/Topic_C%3A_Gas_Laws_and_Kineti
c_Molecular_Theory/05%3A_Gases/5.09%3A_Molecular_Speeds
Updated August 2022 RC/AT/DB
Page 23 of 23
Updated August 2022 RC/AT/DB