State of matter

Matter is composed of tiny particles called atoms, molecules or ions. Matter is classified into three states ( solids, liquids, and gaseous states). The kinetic theory deals with how the arrangement of particles of a substance determines the properties that substance will possess and the state in which it is likely to be found under a given set of conditions.

Solid state

Substances in the solid state are made up of particles which are very closely packed and are held firmly together by forces of cohesion. The cohesive forces may be electrovalent, covalent, metallic or the very weak Vander Waals forces.

Liquid state

The particles in a liquid can move about because they have more kinetic energy than solid, and are not held in fixed position. A liquid, therefore, retains its volume but has no definite shape; it flows to assume the shape of a container in which it is placed

Gaseous state

They have more kinetic energy than those in a liquid. They are restricted only by the walls of the container. A gas has no definite shape.

Comparison of the properties of the three states of matter

Change of state

When a solid is heated, the particles acquire greater kinetic energy and vibrate more violently overcomes the cohesive forces and the crystalline structure collapses. The particles are no longer held in fixed positions but are free to move about and the liquid state is reached. 

Note the following:

Sublimation occurs when iodine molecules break away from the crystal and change directly into the vapour state when the solid is heated.

Evaporation is the process of vaporization of liquids at all temperatures.

Vapour pressure takes place when evaporating liquid is confined in a closed container, which makes the particle to accumulate in the space above the liquid colliding with one another and with walls of the container.

Boiling point of a liquid changes with changes in atmospheric pressure. If pressure is raised, the boiling point will be raised and if the pressure is lowered the boiling point will be lower.

Condensation is a process whereby a vapour loses some of its kinetic energy to a colder body and changes into the liquid state.

Kinetic theory of gases

The theory postulates the following for an ideal or perfect gas:

1. Gas molecules are in constant, rapid, straight motion and collide with one another and with the walls of the container.
2. The average kinetic energy of the gas molecules is a measure of the temperature of the gas molecules.
3. Gases consist of molecules widely in space
4. Collisions of gas molecules are  perfectly elastic.
5. The force of attraction (cohesive forces) between the gas molecules are negligible.

Boyle’s law

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

I.e., P = 1/v

      P = k/v

:. PV = K

Hence, P₁V₁ = P₂V₂……………P_nV_n

*Graphical representation of Boyle’s law

Source: www.commons.wikimedia.org 

Charles’ law

Charles ‘law states that the volume of a fixed mass of gas varies directly with the absolute (Kelvin) temperature, provided the pressure remains constant.

V = T (pressure constant)

V = KT

:. V/T = K

Hence, V₁ / T₁ = V₂ / T₂ ………… Vn/Tn

*Graphical representation of charles’ law

Source: www.google.com 

Note to convert a Celsius temperature (°c) to a Kelvin temperature (k); k= °c + 273

And to convert a Kelvin temperature to a Celsius temperature; °c = k – 273

*Comparison of the Kelvin, Celsius and Fahrenheit temperature scales

Source: www.google.com 

General Gas Equation

Boyle’s law and Charles’ laws are combined into a single expression known as the general gas equation and it states that the product of pressure and volume divided by the absolute temperature is constant for a fixed mass of gas :

PV/T = K

:. P₁V₁ / T₁ = P₂V₂ / T₂ …………. PnVn/Tn

Note that this expression shows the relationship between the three variables, i.e., volume, temperature and pressure.

Ideal gas equation

Is given as P₁V₁ / T₁ = P₂V₂ / T₂

For an ideal gas, PV/T is constant and equal 

volumes of all gases at the same temperature and pressure contain the same number of molecules. One mole of any gas occupies a volume of 22.4dm³ at S.T.P.

:. PV = nRT – (ideal gas equation) where R is the molar gas constant, P is in atm, V in dm³ and T in Kelvin.

      At s.t.p., for 1mole of a gas

      R= PV/ nT

        = (1atm)(22.4dm³)

            (1mol) (273k)

         = 0.082 atm dm³K^-1mol^-1

Dalton’s law of partial pressure

It states that, in a mixture of gases which do not react chemically together, the total pressure of a mixture of gases is equal to the sum of the partial pressure each gas would exert, if it alone occupies the whole volume of the container at the same temperature. 

P_Total = P_A + P_B + P_C + …………..On

P_A = (n_A / n_A + n_B + n_C) P_Total 

Gay lussac’s law of combining volumes 

Gay lussac’s law states that the volumes of gases which take part in a chemical reaction bear a simple whole number ratio to one another and to the volume of the products, if gaseous, when measured at constant temperature and pressure.

In the reaction, H_2(g) + Cl_2(g) > 2HCl_(g). Gay lussac’s discovered that one volume of hydrogen reacted with one volume of chlorine to produce two volumes of hydrogen chloride.

Avogadro’s law

It states that equal volumes of all gases under the same conditions of temperature and pressure contain equal numbers of molecules.

Relative vapour density of gases

The relative density of a gas is the number of times a given volume of gas is heavier than the same volume of hydrogen at a constant temperature and pressure.

V.d= mass of a given volume of the gas / vapour mass of an equal volume of hydrogen 

Graham’s law of diffusion

Graham’s law of diffusion states that, at a constant temperature and pressure, the rate of diffusion of a gas is inversely proportional to the square root of its density, i.e. R= 1/√d

                  R= k/√d (where k is constant)

(Diffusion) R₁ / R₂ = √d₂ / d₁

(Relative molecular mass M) R₁ / R₂ = √M₂ / M₁

(Rate of reciprocal of time) t₂ / t₁ = √m₂ / m₁

Past questions

1. The rate of diffusion of a gas Y is twice that of Z. If the relative molecular mass of Y is 64 and the two gases diffuse under the same conditions, find the relative molecular mass of Z. (Jamb 2013)

A. 8

B. 16

C. 32

D. 4

Answer: D

Solution: r_y / r_z =√M_z / √M_y ; 

       2/1 = √M_z / √64; 2=√M_z / 8

√M_z =2×8 √M_z = 16;  Mz= √16 Mz = 4

2. 200cm³ of a gas at 25°c exerts a pressure of 700mmHg. Calculate its pressure if its volume increases to 350cm³ at 75°c. (Jamb 2016)

A. 342.53mmhg

B. 1430.54mmhg

C. 467.11mmhg

D. 400.00mmhg

Answer: C

Solution:  V₁ = 200cm³, V₂ = 350cm³

T₁ = 25°c + 273=298k,  T₂ = 75^°c + 273 = 348k

P₁ = 700mmhg, P₂ = ?

P₁V₁ / T₁ = P₂V₂ / T₂ ; P₂ = P₁V₁ / T₂ × T₂ / V_2;

700×200×348 = 467.11mmHg

  298×350

3. Solids have definite volumes and shapes unlike liquids and gases because? ( Jamb 2017)

A. The intermolecular forces in them are negligible

B. The molecular forces in them are smaller than those of liquids and gases

C. Their atoms and molecules are loosely packed together

D. Their atoms and molecules are tightly packed together

Answers: D

4. The statement of Boyle’s law is based on? (Jamb 2017)

A. Pressure and volume

B. Pressure and temperature

C. Volume and number of moles 

D. Temperature and volume

Answer: A

5. P_total = P₁ + P₂ + P₃ + ……… P_n, where P_total is the pressure of a mixture of gases. The equation above is an expression of? (Wassce 2001)

A. Graham’s law

B. Gay-Lussac’s law 

C. Boyle’s law

D. Dalton’s law

Answer: D

6. State Graham’s law of diffusion. (Wassce 2005)

Answer: it states that, at a constant temperature and pressure, the rate of diffusion of a gas is inversely proportional to the square root of its density.

7. State Charles’ law. (Wassce 2006)

Answer: it states that the volume of a fixed mass of gas varies directly with the absolute (Kelvin) temperature, provided the pressure remains constant.

8. Which of the following bond types is responsible for the high boiling point of water? (Wassce 2013)

A. Metallic bond

B. Covalent bond 

C. Ionic bond

D. Hydrogen bond

Answer: D