Molecular Theory of Matter

Fundamental assumptions of molecular theory


Subject: Physics
Theme: Energy Quantization And Duality Of Matter
Topic: Molecular Theory of Matter
Sub Topic: Fundamental assumptions of molecular theory
Date: dd/mm/yyyy
Class: S.S.S 2
Duration: 40 Minutes
No of Learners: 40



Learning Objectives: By the end of the lesson learners should be able to:

1. Explain the Molecular Nature Of Matter - Dalton's Atomic Theory

The atom is the most fundamental unit of matter that is, all things are made up of small fundamental units termed as atoms making up everything that we see around us. It is extremely small, measuring in at less than 0.1 to 0.5 nanometers.
Dalton suggested in his findings that an atom is the smallest unit of matter, which cannot be divided any further.

Also, according to Dalton's Atomic Theory, atoms of one element are identical but differ from those of the other elements and a few atoms of each element combine to form a molecule of the compound.

The discovery of electrons, protons, and neutrons suggested that atoms comprise these three units in different proportions. It was proven that atoms are not individual units but the elementary units of matter. They consist of a nucleus and electrons and the nucleus is made up of protons and neutrons. Further findings suggest that the neutrons and protons also have further division, as they consist of smaller units termed as quarks.

2. Defined what kinetic theory of gases is

The kinetic theory of gases (also known as kinetic-molecular theory) explains the behavior of a hypothetical ideal gas. It is a theoretical model that describes the molecular composition of the gas in terms of a large number of submicroscopic particles, which include atoms and molecules.

3. Explain the Kinetic Theory of Gases Assumptions

The continuous collision of the molecules of the gas with the walls of the containing vessel and their reflection from the walls results in the change of momentum of the molecules. According to Newton's second law of motion (F=dp/dt), the rate of change of momentum per unit area of the wall surface corresponds to the force exerted by the gas per unit area. The force per unit area measures the pressure of the gas. Implications of these assumptions are as follows:

Collisions of Gas Particles
(i) Particles: Gas is a collection of a large number of atoms or molecules.
(ii) Point Masses: Atoms or molecules making up the gas are very small particles like a point (dot) on a paper with a small mass.
(iii) Negligible Volume Particles: Particles are generally far apart such that their inter-particle distance is much larger than the particle size, and there is large free unoccupied space in the container. Compared to the volume of the container, the volume of the particle is negligible (zero volume)
(iv) Nil Force of Interaction: Particles are independent. They do not have any (attractive or repulsive) interactions among themselves.
(v) Particles in Motion: The particles are always in constant motion. Because of the lack of interactions and the free space available, the particles randomly move in all directions but in a straight line.
(vi) Volume of Gas: Because of motion, gas particles occupy the total volume of the container, whether it is small or big, and hence the volume of the container is to be treated as the volume of the gases.
(vi) Mean Free Path: This is the average distance a particle travels to meet another particle.
(vii) Kinetic Energy of the Particle: Since the particles are always in motion, they have average kinetic energy proportional to the temperature of the gas.
(viii) Constancy of Energy/Momentum: Moving particles may collide with other particles or containers. But the collisions are perfectly elastic. Collisions do not change the energy or momentum of the particle.
(ix) Pressure of Gas: The collision of the particles on the walls of the container exerts a force on the walls of the container. Force per unit area is the pressure. The pressure of the gas is thus proportional to the number of particles colliding (frequency of collisions) in unit time per unit area on the wall of the container.

4. Explain the Kinetic Theory of Gases Postulates

The kinetic theory of gas postulates is useful in understanding the macroscopic properties from the microscopic properties.

(i) The gas is composed of small indivisible particles called molecules. The properties of the individual molecules are the same as that of the gas as a whole.
(ii) The distance between the molecules is large as compared to that of a solid or liquid and hence the forces of intermolecular attraction is negligible.
(iii) The are continuously in motion with varying velocities and the molecules move in a straight line between any two consecutive collisions. The collisions do not alter the density of gas.
That is, the Same numbers in unit volume and no accumulation.
(iv) The size of the molecules is infinitesimally small as compared to the average distance traversed by a molecule between any two consecutive collisions is called free path and the average distance is called mean free path. The mean free path is dependent on the pressure of the gas. If the pressure is high the mean free path is less and if the pressure is low the mean free path is more.
(v) The time of impact is negligible in comparison to the time taken to traverse to the free path.
(vi) The molecules are perfectly hard elastic spheres and the whole of the energy is kinetic.

Rationale:

The behaviour of gases is studied by considering the small-scale action of individual molecules or by considering the large-scale action of the gas as a whole. The large-scale action of the gas can be easily studied and measured, however, to study the action of the gas molecules a theoretical model needs to be used. This theoretical model is known as the kinetic theory of gases. In this article let us discuss the kinetic theory of gases and the assumptions considered for the theory.

Prerequisite/ Previous knowledge:

Application of light wave, musical instruments.

Learning Materials:

Tunning fork, guitar strings, drumheads, and tuning fork, vocal cords.

Reference Materials:

1. New School Physic for Senior Secondary Schools, by M. W. Anyakowa.
2. Lamlas's SSCE and UTME, by O. Ajaja and H. B. Olaniyi.
3. Okeke P.N and etal (2011), Macminian, Senior Secondary School Physics, New Edition.
4. Farinde E.O and etal (2015), Essential Physics. 6th Edition,
5. New System Physics by Dr. Charles Chow.


When gas temperature increases, gas pressure increases due to increased force and frequency of molecular collisions.
Amonton's law

When volume decreases, gas pressure increases due to increased frequency of molecular collisions.
Boyle's law

When the amount of gas increases at a constant pressure, volume increases to yield a constant number of collisions per unit wall area per unit time.
Avogadro's law




Lesson Development:
STAGE TEACHER'S ACTIVITY LEARNER'S ACTIVITY LEARNING POINTS
STEP I: PREVIOUS KNOWLEDGE
full class session		 The teacher asks learners questions based on previous knowledge.

1. State Dalton’s Atomic Theory

2. Dalton's atomic theory says that atoms are indivisible. Is this statement still valid? Give reasons for your answer.

3. State the law of conservation of mass. Give one example to illustrate this law.

4. State the law of constant proportions. Give one example to illustrate this law.

5 (a) State the various postulates of Dalton’s atomic theory of matter.
(b) Which postulate of Dalton’s atomic theory can explain the law of conservation of mass?
(c) Which postulate of Dalton’s atomic theory can explain the law of constant proportions? 

 Learners' response to teacher's question.

1. According to Dalton’s Atomic Theory, atoms, which are indestructible and indivisible building blocks, make up all substances. Unlike other elements, which have atoms of different sizes and weights, an element’s atoms have all the same size and mass.
Dalton proposed that the concept of atoms could be used to explain the laws of conservation of mass and definite proportions. He proposed that atoms, which he described as “solid, massy, hard, impenetrable, moving particle(s)”, are the smallest, indivisible units of matter.

(i) The matter is made up of indivisible particles known as atoms.
(ii) The properties of all the atoms of a given element are the same, including mass. This can also be stated as – all the atoms of an element have identical mass and chemical properties; atoms of different elements have different masses and chemical properties.
(iii) Atoms of different elements combine in fixed ratios to form compounds.
(iv) Atoms are neither created nor destroyed. The formation of new products (compounds) results from the rearrangement of existing atoms (reactants) in a chemical reaction.
(v) The relative number and kinds of atoms are constant in a given compound.

2. Dalton's atomic theory states that atoms are indivisible. This statement is not valid as atoms can be further divided into electrons, protons and neutrons. This is one of the major drawbacks of Dalton's atomic theory of matter.


3. Antonie Lavoisier proposed the Law of conservation of mass, which states that ‘Mass can be neither created nor destroyed’, so in a chemical reaction, the total mass of reactants must be equal to the total mass of products.

For example, 100gs of calcium carbonate decomposes to produce 56gms of calcium oxide and 44gms of carbon dioxide

Mass of reactant = 100gm

Mass of Product = 56+44gm = 100gm

Since the mass of the reactant is equal to the mass of the product, there is no change in the chemical reaction.


4. Joseph Proust put forward the law of proportion in 1779. This law states that the chemical compound always consists of the same elements combined together in the same proportion by mass.

It means a pure chemical compound is always made up of the same elements in the same percentage.

For example, Carbon dioxide exists in nature in different forms and can be chemically produced in different ways. Yet, all the different samples of carbon dioxide will always contain the same elements. i.e. carbon and oxygen is in the same proportion by mass 3:8.


5 (a)  Postulates of Dalton’s atomic theory:

1)  All the matter is made up of very small particles called ‘atoms’.

2)  Atoms cannot be divided.

3)  Atoms can neither be created nor destroyed.

4)  Atoms are of various kinds. There are as many kinds of atoms as are elements.

5)   All the atoms of a given element are identical in every respect, having the same mass, size and chemical properties.

6) Atoms of different elements differ in mass, size and chemical properties.

7) The ‘number’ and ‘kind’ of atoms in a given compound are fixed.

8) During chemical combination, atoms of different elements combine in small whole numbers to form compounds.

(a) Atoms of the same elements can combine in more than one ratio to form more than one compound.


(b) The postulate “The elements consist of atoms and that atoms can neither be created nor destroyed” can be used to explain the law of conservation of mass.


(c) The postulate “The elements consist of atoms having fixed mass, and that the number and kind of atoms of each element in a given compound is fixed” can be used to explain the law of constant proportions.

 Confirming previous knowledge.
STEP II: INTRODUCTION
full class session		 The teacher introduce the topic for discussion.

Understanding Gas Laws of Ideal Gases
(i) Pressure α Amount or Number of Particles at Constant Volume: The collision of the particles on the walls of the container creates pressure. Larger the number of the particle (amount) of the gas, the more the number of particles colliding with the walls of the container.
At constant temperature and volume, the larger the amount (or the number of particles) of the gas, the higher will be the pressure.

(ii) Avogadro’s Law {N α V at Constant Pressure: When there is a greater number of particles, it increases the collisions and the pressure. If the pressure is to remain constant, the number of collisions can be reduced only by increasing the volume.
At constant pressure, the volume is proportional to the amount of gas.

(iii) Boyle’s Law {P α 1/V at Constant Temperature}: At a constant temperature, the kinetic energy of particles remains the same. If the volume is reduced at a constant temperature, then the number of particles in unit volume or area increases. If there is an increased number of particles in the unit area, then it increases the frequency of collisions per unit area.
At constant temperature, the smaller the volume of the container, the larger the pressure.

(iv) Charles’s Law {V α T at Constant Pressure}: The change of temperature changes proportionately to the pressure. If the pressure also has to remain constant, then the number of collisions has to be changed proportionately. At constant pressure and a constant amount of substance, collisions can be changed only by changing the area or volume.
At constant pressure, volume changes proportionally to temperature.

(v) Graham Law of Diffusion {V α √(1/M)}: Two gases with molecular weights, M1 and M2, will have the same kinetic energy at the same temperature. Then,
1/2 × (M1V21) = 1/2 × (M2V22)
or
M1V21 = M2V22
or
V21 / V22 = M2 / M1
or
V1 / V2 = √(M2 / M1)
The velocity of the molecules is inversely proportional to their molecular weights.

(iv) Dalton’s Law {P = P1 + P2 + P3 ...
PV = nRT}: Because of the large distances between them, the molecules of one gas in a mixture bombard the container walls with the same frequency whether other gases are present or not.
The total pressure of a gas mixture equals the sum of the (partial) pressures of the individual gases.

(v) Amonton’s Law {P α T at Constant Volume}: The kinetic energy of the particle increases with temperature. When the volume is constant, with increased energy, particles move fast and increase the frequency of collisions per unit time on the walls of the container and hence the pressure.
At constant volume, the higher the temperature, the higher will be the pressure of the gas.



Molecules that make up a solid are thought to be very relatively tightly packed molecules. These molecules will gently sway in place without changing physical locations. In general, they are not affected by the shape or volume of the container that is holding them.

Liquids have a bit more space in-between each molecule than solids. Liquid molecules also move a bit faster than solids, and they will simply flow past other molecules within the container. As a result, liquids will tend to take the shape of the container which holds them, but the volume of a liquid is not typically affected by the container.

Gas molecules have the most space in-between molecules. These molecules also move the fastest out of the three phases (the three phases being solid, liquid, and gas). With the speed at which gas molecules move, they are able to overcome any attractive forces that would hold the molecules together in close proximity. As a result, gases move about wildly and take on both the shape and volume of the container that holds them

The five main points of the kinetic molecular theory are:

(i) Gases are composed of particles that are in random, constant motion.

(ii) Gases move in a straight line until they collide with something.

(iii) Gas molecules are not attracted to one another or the container.

(iv) Collisions that occur between gas molecules are thought of as being perfectly elastic.

(v) The average kinetic energy of a collection of gas particles depends only upon the temperature of the gas.

Learners listen to teacher, ask questions and make contribution. Developing the idea of the topic.

STEP III: EXPLORATION
Grouping		 The teacher presents the instructional material to the students and divides them into four groups. The representative of a group is asked to discuss the uses of the material. Aim is to explain the Kinetic Theory of Gases.

The teacher leads the students into the discussion from the observations gathered from the exploration, the Students equally gives their contribution's and the teacher gives the students note on the topic.		 Learners' expected answer
The students carry out the instructions accordingly and state their observations.

The kinetic theory of gases explains the macroscopic properties of gases, such as volume, pressure, and temperature.

Scientists James Clark Maxwell, Rudolph, and Clausius developed the kinetic theory of gases in order to explain the behaviour of gases. The theory explains gas as a collection of tiny, hard spheres that interact with each other and with the surface of the wall. The spheres represent the gas molecules, and they behave according to the laws of motion developed by Newton in the 17th century. It describes how molecules influence gas characteristics such as temperature and pressure. It also explains why gases follow Boyle’s law.
We have learned that the pressure (P), volume (V), and temperature (T) of gases at low temperature follow the equation:
PV=nRT
Where, n = number of moles in the gas
R = gas constant having value 8.314 JK-1mol-
Any gas which follows this equation is called an ideal gas. Hence, the equation is known as the ideal gas equation. But there are certain assumptions that we consider for describing ideal gas behaviour

 Kinetic theory explains the behaviour of gases based on the idea that gas consists of rapidly moving atoms or molecules. This is possible as the interatomic forces between the molecules are neglected in gas.

STEP IV: DISCUSSION The teacher guides learners to explain the Assumptions of Kinetic Theory of Gases.
The teacher leads the students into the discussion from the observations gathered from the exploration, the Students equally gives their contribution's and the teacher gives the students note on the topic.		 The students listen to teacher, ask questions and make contribution.
The following are the kinetic theory of gases assumptions:
1. All gases are made up of molecules that are constantly and persistently moving in random directions.
2. The separation between the molecules is much greater than the size of the molecules.
3. When a gas sample is kept in a container, the molecules of the sample do not exert any force on the walls of the container during the collision.
4. The time interval of a collision between two molecules, and between a molecule and the wall is considered to be very small.
5. All the collisions between molecules and even between molecules and walls are considered to be elastic. 6. All the molecules in a certain gas sample obey the laws of motion.
7. If a gas sample is left for a sufficient time, it eventually comes to a steady state. The density of molecules and the distribution of molecules are independent of position, distance, and time.		 Assumptions of Kinetic Theory of Gases.
STEP V: APPLICATION The teacher guides learners to explain the Postulates of Kinetic Theory of Gases.
The teacher leads the students into the discussion from the observations gathered from the exploration, the Students equally gives their contribution's and the teacher gives the students note on the topic.		 The students listen to teacher, ask questions and make contribution.
The following are the kinetic theory of gases postulates:
1. The space-volume to molecules ratio is negligible.
2. There is no force of attraction between the molecules at normal temperature and pressure. The force of attraction between the molecules builds when the temperature decreases and the pressure increases.
3. There is a large space between the molecules resulting in continuous motion.
4. The free movement of molecules results in a collision which is perfectly elastic.
5. The molecules have kinetic energy due to random movement. But the average kinetic energy of these molecules differs with temperature.
6. Molecules exert pressure on the walls of the container.

STEP VI: EVALUATION The teacher asks the learners questions.
(a) What is Kinetic-Molecular Theory?
(b) What are the assumptions of kinetic theory of gas?
(c) Explain the Kinetic Theory of Gases Assumptions related to Ideal Gases.
(d) Explain the Kinetic Theory of Gases Assumptions related to Pressure and Temperature Relationship.
(e) What are the three main components of the kinetic theory of gases?
(f) What are the assumptions made in the kinetic theory of gases?		 The learners expected answers.
(a) The kinetic-molecular theory is a model that helps explain the behavior of gases. It is based on several key assumptions about the nature of gas particles. The kinetic-molecular theory explains the behavior of gases based on the idea that gas particles are in constant, random motion. It posits that the temperature of a gas is directly related to the average kinetic energy of its particles, which helps to describe how gases expand, compress, and exert pressure.

(b) The assumptions of kinetic theory of gases are:-
1. A gas consists of a very large number of molecules which should be elastic spheres and identical for a given gas.
2. The molecules of a gas are in a state of continuous rapid and random motion.
3. The size of gas molecules is very small as compared to the distance between them.
4. The molecules do not exert any force of attraction or repulsion on each other.
5. The collisions of molecules with one another and with walls of the vessel are perfectly elastic.

(c) Assumptions of Ideal Gases: The kinetic-molecular theory is built on several key assumptions about ideal gases, gas particles are considered to have negligible volume, they do not attract or repel each other, and they collide elastically, meaning that energy is conserved in collisions. These assumptions simplify the complex interactions in real gases, allowing for easier calculations and predictions.

(d) Pressure and Temperature Relationship: According to the kinetic-molecular theory, pressure is a result of collisions between gas particles and the walls of their container. As temperature increases, the kinetic energy of the particles increases, leading to more frequent and forceful collisions, which in turn raises the pressure. This relationship is fundamental in understanding gas behavior under varying conditions.

(e) The three main components of the kinetic theory of gases are:
1) When molecules collide with each other, no energy is gained or lost.
2) The space occupied by the molecules of gas in a container is very negligible.
3) These molecules always have linear motion.

(f) 1) All gases are made up of molecules that are constantly and persistently moving in random directions.
2) All the collisions between molecules and even between molecules and walls are considered to be elastic.
3) All the molecules in a certain gas sample obey Newton’s laws of motion.		 Ask the learners questions to assess the achievement of the set objectives.

CONCLUSION

The teacher concluded the lesson with the students.
The kinetic molecular theory states that the motion of molecules is predictable based upon measurable traits such as the temperature, volume, and pressure of the atmosphere. There are between 4-6 key thoughts used to describe the motion of molecules depending on how the statements are listed. Kinetic Molecular Theory is most often referenced in relation to the behavior of gases, but it could also be applied to solids and liquids.

Through the use of kinetic molecular theory, a few different laws have been created to help quantify the relationship between the measurable characteristics of gases. The three laws are called the ideal gas law, Charles' law, and Boyle's law. These three laws relate the pressure, volume, temperature, and amount of a gas.

 The students listen and make contribute Kinetic Molecular Theory.

ASSIGNMENT The teacher gives learners a take home. 1. Who developed the kinetic theory of gases?
2. What is the main basis of the kinetic theory?
3. What are real gases and ideal gases?
4. What are the three main points of the kinetic model?		 Improving their level of understanding on Kinetic Theory of Gases.



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