# Jamb Chemistry Tutorials S01

## INTRODUCTION

Welcome to the first series of this Jamb chemistry tutorial we will be starting of this Jamb Chemistry tutorial series by first looking at KINETIC THEORY OF GAS AND GAS LAWS. This is probably the question you will see first before any other. Check out jamb chemistry hot topics jamb, these are topics jamb set almost every year by clicking here.

Grab your writing material (Biro and jotter). Also, make sure you get a glass of chilled fruit drink or water to refresh yourself as we start up with this Jamb chemistry tutorial series.

Do you find it hard to concentrate while reading click here to see the steps you can take to discipline yourself to study well.

In this Jamb Chemistry Tutorial series one we will achieve the following objectives:

• Why kinetic theory of gas and gas laws
• Kinetic theory of gases explained
• Assumptions made for the ideal gas law theory
• Boyle’s law
• Using kinetic theory to explain boyle’s law
• Charle’s law
• Using Kinetic theory to explain charle’s law
• Pressure law
• General gas law
• Ideal gas law
• Gay lussac law of combining volume
• Dalton’s law of partial pressure
• Grahams law of diffusion

#### WHY KINETIC THEORY OF GAS AND GAS LAWS

Kinetic theory of gas and gas laws are one of the rudimentary topics in chemistry. This is also because Jamb set questions from this topic every year.

Moreover, kinetic theory of gas and gas laws are topics that exposes student on the behaviour of gases, how they combine with one another, how they dissove in liquids and other substances. This should be one topic student should try as much as possibe to grasp.

### Kinetic Theory of Gases EXPLAINED

The kinetic theory of gases describes a gas as a large number of microscopic particle which might be atoms or molecules. The kinetic theory of gases also posits that the gas molecules are in constant random motion colliding perfectly with each other and with the walls of the container.

It is the collision that constitute the gas pressure.Kinetic theory of gases explains the macroscopic properties of gases, such as temperature, pressure, viscosity, and volume, by considering their molecular composition and motion. The theory also states that gas pressure results from particles’ collisions with the walls of a container at different velocities.

#### Assumptions made on the theory of an ideal gas

• The gas consists of very small particles known as atoms or molecules.
• The size of the atoms or molecules are so small that the total volume of the individual gas molecules is negligible when compared with the volume of their container.
• The distance separating each gas molecule from the other is so large when compared with the size of the molecules.
• These particles have the same mass.
• The number of molecules is so large that statistical treatment can be applied.
• The gas molecules are in constant random motion colliding elastically with one another and with the wall of the containing vessel.
• The molecules are considered to be perfectly spherical in shape and elastic in nature.
• Except during collisions, the interaction among molecules are negligible. (That is, they exert no attractive or repulsive force on one another.)
• The average kinetic energy of the gas particles depends only on the absolute temperature of the system.
• The elapsed time of a collision between a molecule and the container’s wall is negligible when compared to the time between successive collisions.
• The gravitational forces on the gas molecules are negligible.

### GAS LAWS

#### BOYLE’S LAW

Boyle’s law states that the pressure of a fixed mass of gas is inversely proportional to the volume occupied by the gas provided that the temperature of the gas remains constant.

###### Using the Kinetic theory to explain boyle’s law

If the pressure of a gas remains constant, the pressure of a container is determined by the number of times gas molecules strike the container walls.

If the gas is compressed to a smaller volume, then the same number of molecules will strike against a smaller surface area; the number of collisions against the container will increase, and, by extension, the pressure will increase as well.

However, if the gas is expanded to a larger volume, lesser number of molecules will strike a given surface area. This will make the number of collision against the container to reduce, thus reducing the pressure as well.

Mathematical derivation of the boyle’s law;

from the law, pressure is inversely proportional to volume;

P $\alpha$ $\frac{1}{V}$

Introducing K as a constant of proportionality;

P = $\frac{K}{V}$……eq(i)

from eq(i) P*V = K

Proceeding further, K = ${P_{1}}*{V_{1}} = {P_{2}}*{V_{2}}$

Finally we have our boyle’s law equation as;

${P_{1}}*{V_{1}} = {P_{2}}*{V_{2}}$

#### CHARLE’S LAW

Charle’s law states that the volume of a fixed mass of gas is directly proportional to the absolute temperature of that gas provided the pressure of the gas remains constant.

###### Using the Kinetic theory to explain charle’s law

According to Kinetic Molecular Theory, an increase in temperature will increase the average kinetic energy of the molecules. As the particles move faster, they will likely hit the entire body of the container more often. Since pressure is to remain constant according to the charle’s law, they must stay farther apart, and an increase in volume will compensate for the increase in particle collision with the surface of the container.

However, a decrease in temperature wil decrease the average kinetic energy of the molecules. As the particle moves slower, the will likely hit the entire body of the container less often. Since the pressure must be constant according to charle’s law, they must stay closer and therefore, a reduction in volume will compensate for the reduction in particle collision with the container.

Mathematical derivation of the charles law;

Volume directly proportional to absolute temperature

$V \alpha T$

Introducing the constant of proportionality;

V = K*T….eq(i)

from eq(i)

$\frac{V}{T} = K$....eq(ii)

eq(ii) can be written as $\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$ or $\frac{T_{1}}{V_{1}} = \frac{T_{2}}{V_{2}}= K$

Finally; $\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$

#### PRESSURE LAW

This Law states that the pressure of a fixed mass of gas is directly proportional to its absolute temperature provided the volume of the gas remains constant.

Most textbooks do not list this laws among the gas laws but this law is as important as the others . It was postulated by Gay lussac.

###### Using the Kinetic theory to explain pressure law

According to Kinetic Molecular Theory, an increase in temperature will increase the average kinetic energy of the molecules. As the particles move faster, they will likely hit the entire body of thereby increasing the pressure of the container since the volume is to remain constant according to the pressure law,

However, a decrease in temperature wil decrease the average kinetic energy of the molecules. As the particle moves slower, the will likely hit the entire body of the container less often thereby reducing the pressure exerted on the vessel since the volume of the vessel must be constant according to pressure law.

mathematical derivation of the pressure law;

Pressure directly proportional to absolute temperature at constant volume

$P \alpha T$

Introducing the constant of proportionality;

P = K*T….eq(i)

from eq(i)

$\frac{P}{T} = K$….eq(ii)

eq(ii) can be written as $\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}$ or $\frac{T_{1}}{P_{1}} = \frac{T_{2}}{P_{2}}= K$

Finally; $\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}$

#### GENERAL GAS LAW

The general gas law combine Boyle’s,Charle’s and Pressure law to form one law. If i am to state the general gas law, I will states it as follow;

That the product of the Pressure and Volume of a fixed mass of gas is directly proportional to its absolute temperature

Mathematically,

P*V $\alpha$ T

Therefore, $\frac{P*V}{T}$ = K

Giving us the final equation as

$\frac{P_{1}*V_{1}}{T_{1}} = \frac{P_{2}*V_{2}}{T_{2}}$

#### IDEAL GAS LAW

This law is also known as general gas equation because it is very much like with the general gas law.

The ideal gas law combines Boyle’s law, Charle’s law, Pressure law and Avogadro’s law to take its definition. The ideal gas law equation also represent the equation of state of a hypothetical ideal gas.

Ideal Gas Equation or the general gas equation;

P*V = n*R*T

The Avogadro’s law otherwise known as Avogadro’s hypothesis or Avogadro’s principle is a an experimental laws that gives the relationship between the number of moles of a substance and its volume

Avogadro’s law states that equal volume of all gases at the same temperature and pressure contains the same number of molecules.

Alternatively. it states that For a given mass of an ideal gas the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant.

Simple put if ammonia gas at 100k and 2 bar contains 120 molecules it simply means that oxygen gas or any other gas at 100k and 2 bar will also contain 120 molecules. That is what Avogadro is trying to say.

Mathematically;

$V \alpha n$

introducing the constant

V = n*K

final equation:

$\frac{V_{1}}{n_{1}} = \frac{V_{2}}{n_{2}}$

#### GAY LUSSAC LAW OF COMBINING VOLUME

This Law was postulated by Sir Gay lussac for the purpose of bringing out a law or a pattern that gases follow during their combination.

It should be noted that this law is only applicable when both the procuct and the reactant of a chemical equations are all gases

This law states that when gases combine, they do so in volume which bear simple ratios with one another and to the volume of their products at constant temperature and pressure.

Consider the equation below;

$N_{2} + 3H_{2} = 2NH_{3}$

we can write the mole ratio as;

1 :  3 = 2

according to Gay lusac law of combining volume, the mole ratio is the same as the volume ratio so that;

1 vol : 3 vol = 2 vol

Therefore, from the above equation, it can be said that;

1 vol of Nitrogen gas react with 3 vol of Hydrogen gas to give 2 vols of ammonia.

#### DALTON’S LAW OF PARTIAL PRESSURE

In chemistry and physics, Dalton’s law (also called Dalton’s law of partial pressures) states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressure of the individual gases.

mathematically;

$P_{total} = P_{1} + P_{2} + P_{3} + P_{4} + …….+ P_{n}$

#### GRAHAM’S LAW OF DIFFUSION

Graham law of diffusion of gases states that the rate of diffusion of a given mass of gases is inversely proportional to the square root of the gas  density.

Graham postulated that the lighter gases will diffuse faster than the heavier gases. A quick check is to look at the molar mass of any gas to know its performance when it comes to diffusion.

mathematically;

$\frac{r_{1}}{\sqrt{M_{1}}}$$\frac{r_{2}}{\sqrt{M_{2}}}$

##### IMPORTANT NOTE

Please note that this Jamb Chemistry tutorial will be continued in the next series. In the next Jamb chemistry tutorial series, we will look at how to tackle calculations from each of the gas laws, we will solve questions explicitly and exhaustively from Jamb past question. DO NOT MISS OUT!!!!

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