Particulate Nature Of Matter

Matter is anything that has weight and occupies weight. Matter is composed of discrete tiny particles was a point that was first put forward by the early Greeks.

An atom is the smallest indivisible particle of an element that takes part in chemical reactions. Matter exists in three states namely; solids, liquids and gases.

The particles in the solid state are closely packed and they vibrate about fixed positions. On heating the solid, the particles gain more kinetic energy and therefore vibrate faster about their fixed positions. When sufficient heat is supplied, the forces between solid particles are weakened and solid turns into liquid. This is called melting.

Melting point is a fixed temperature at which a solid turns into a liquid. The particles in liquids are far apart and free to move throughout the entire system and their movement is orderly. When heat is applied to the liquids, the particles gain more kinetic energy and move with greater velocity. When sufficient heat is applied, the forces of attraction are broken between the particles and the liquid turns into a gas. This process is called evaporation.

Evaporation is the change of a liquid to a gas at temperatures below the boiling point of the liquid.

Boling point is a fixed temperature at which saturated vapour pressure of a liquid becomes equal to the atmospheric pressure. At this temperature, the liquid changes to vapour.

Factors that affect boiling and melting points.

• Presence of impurities.

Increase the boiling point of liquids and decrease the melting point of a solid. This is because presence of impurities on the surface of the liquid reduces escaping tendency of liquid molecules into vapour phase. Since the liquid boils when its vapour pressure is equal to atmospheric pressure, more heat is required to vaporise the molecules and consequently increase in boiling point.

• Atmospheric pressure.

The higher the atmospheric pressure, the higher the boiling point and the lower the atmospheric pressure, the lower the boiling point. This is because when the atmospheric pressure is low, fewer vapour molecules are required to create vapour pressure equal to the reduced atmospheric pressure. Since a liquid boils when its vapour pressure is equal to atmospheric pressure, little heat thus low boiling point is required.

• Altitude.

The higher the altitude, the lower the boiling point and the higher the melting point. At very high altitude, a pressure is low therefore the boiling point is low and melting point is high.

Evidence For The Particulate Nature Of Matter.

Diffusion.

Is the movement of particles from a region of their high concentration to a region of low concentration even defying the law of gravity, until a uniform mixture is obtained.

It is one of the most striking characteristics of gases. The gases continue to diffuse until the available space or volume is occupied and a homogenous concentration is obtained. As compared to solids and liquids the rate of diffusion in gases is faster. A lighter gas would diffuse faster than a heavier one due to the size of the molecules of the two.

Graham’s law of diffusion.

It states that the rate of diffusion/effusion of a gas at constant temperature and pressure is inversely proportional to the square root of its density.

By comparing the rate of diffusion of two gases, A and B, it is possible to measure the density of one if that of the other is known; hence (equation).

From graham’s law, it can be deduced that when the density of a gas is high, less of the gas diffuses in a given time. Hence the rate is small. The same applies to R.F.M of the gas. When it is greater, the density is also greater.ie. The amount of a gas diffusing in a time T is inversely proportional to the square root of the density of the gas or the R.F.M of the gas.ie. (Equations).

*Examples.

Diffusion In Gases.

One of the most striking characteristics of gases is their ability to diffuse. It takes place in all directions even against gravity. The fact that a gas can move in all directions from a region of high concentration to a region of low concentration even defying the law of gravity is an indication that matter is composed of particles in constant random motion.

Diffusion in gases can be demonstrated by placing a gas jar full of air mouth to mouth with that containing bromine. With time, the brown colour of bromine vapour becomes evenly spread throughout the jars despite its being denser than air.

Diffusion In Solids.

Movement of solid particles is restricted but under suitable conditions they can be able to move from place to place. Those on the outside of a solid have more freedom of movement than those inside. Increase in thermal energy results to their leaving the main body of the solid.

Diffusion In Liquids And Dissolved Substances.

The slower diffusion of liquids compared to gases is explained by the closer packing of molecules and the greater frequency of collision whereas any two gases form a homogenous mixture as a result of diffusion. This happens with only certain liquids.

Brownian Motion.

This is a continuous random movement of microscopic solid particles when suspended in a fluid medium. It is a result of the collision of the solid particles with the continually moving molecules of the fluid. The smaller the particles, the more extensive the motion is. The effect is also visible in particles of smoke suspended in a still gas.

Uses of diffusion.

• Calculation of RFM/ density of a gas by carrying out diffusion experiments.
• Separation of isotopes.eg. Separation of uranium isotopes; 235 U and 238 U.
• Separation of gases.eg. Helium from natural gas.ie. Nitrogen.

Kinetic Theory Of Matter.

It states that matter is made up of particles that are in constant random motion and possesses kinetic energy.

The average amount of kinetic energy is proportional to absolute temperature and is independent of the nature of the gas.

This theory explains the physical properties of matter in terms of motions of its constituent particles. The following are five main assumptions made in the theory;

• The gas particles are assumed to be spherical.
• Collisions between gas particles are perfectly elastic.ie. There is no loss in momentum by gas molecules after collision.
• The volume of gas particles in a container is negligible compared to the volume of the container (this is so at high volume and low pressure. However at low volume and high pressure, he gas particle occupy an appreciable volume).
• Intermolecular forces of attraction between the gas particles are assumed to be negligible.
• Pressure of a gas in a container is due to the collisions of the gas molecules with the walls of the container. The higher the pressure, the larger the number of collisions and hence the higher the concentration of gas particles in the container.

Gas Laws.

These are laws relating pressure, temperature and volume of an ideal gas.

An ideal gas is a hypothetical gas that obeys the laws exactly.

Boyle’s law; the volume of a fixed mass of a gas at a constant temperature is inversely proportional to the pressure. (Graph)

Charles’ law; the volume of a fixed mass of a gas is directly proportional to absolute temperature at constant pressure.

(Graph)

Pressure law; the pressure of a fixed mass of a gas is directly proportional to absolute temperature so long as the volume is kept constant. (Equations).

Combining the three gas laws;

PV/T= constant.

PV/T=R.

For one mole of an ideal gas, and for n moles of an ideal gas .

Units of R.

When pressure is measured in Nm-2/Pa, volume in m3 and absolute temperature in kelvin and at standard temperature and pressure, then for one mole of a gas;

R= PV/T.

Examples.

Dalton’s Law Of Partial Pressures.

It states that in a mixture of gases which do not react chemically, the total pressure is the sum of the partial pressures of the constituent gases.ie. The sum of the pressures that each component would exert if it were present alone and occupied the same volume as the mixture of gases.

Strictly speaking, the principle is true only for ideal gases.ie. If gases A, B, C and D do not react chemically and a replaced in the same container, then the total pressure;

PT= PA + PB + PC + PD

Where PT pressure.

PA + partial pressure of component A.

NB: the total pressure of any gas is directly proportional to its mole fraction.

(Equations)

Examples.

Ideal And Real Gases.

A gas that obeys gas laws exactly at any conditions of temperature and pressure is an ideal gas. However it is difficult to find the ideal gas.

Real gases do not obey gas laws especially at high temperature and low temperature .Eg. Consider the Amagat’s curves showing that real or usual gases do not obey gas laws.

(Graph).

Why do real gases fail to obey gas laws/deviate from ideal behaviour/ what reasons account for van der Waal’s equation?

• At high pressure molecules are very close together at the volume they occupy is no longer negligible.
• When the pressure is high, the molecules become nearer each other and therefore attractions for one another Is no longer negligible. As a result, the velocity with which they strike the container decreases.

Van der Waal’s developed a new equation to take into consideration these deviations.ie. For one mole of a gas, and van der Waal’s modified it to become (equation)

Liquefaction Of Gases.

It is the conversion of a gaseous substance into a liquid. It is usually achieved by one of the four methods or by combination of two of them.

• By vapour compression provided that the substance is below its critical temperature.
• Refrigeration at constant pressure typically by cooling it with a colder fluid in a counter current heat exchanger.
• By making it perform work adiabatically against the atmosphere in a reversible cycle.
• By the joule-Thompson effect.

Critical temperature; it is the temperature above which a gas cannot be liquefied no matter what pressure is exerted.

Critical pressure; the pressure which is just enough to liquefy a gas at its critical temperature.

Critical volume; the volume occupied by one mole of a gas at its critical temperature and critical pressure.

The critical temperature, critical pressure and critical volume are called critical constants for any one gas but their values are different for different gases.

A graph showing pressure of a gas plotted against its volume at different temperatures- Isothermalsfor carbon dioxide.

Graph.

Explanation of the graph.

If then Boyle’s law is obeyed and therefore a plot of P against V will give a rectangular hyperbola graph. That is true for gases at high temperature but at low temperature the isothermals are discontinuous, continue to split up into three parts AB, BC and CD.

AB shows the effect of increased pressure in decreasing the volume of the gas. BC shows a large volume change with no change in pressure. This shows liquefaction of the gas. At C liquefaction is complete and CD indicates the effect of pressure on the volume of the liquid produced. Its stiffness as compared to AB shows that a liquid is much less compressible than a gas.

The ends of the horizontal portions of different isothermals form an appropriate parabola when joined together and the apex gives a point at which the horizontal portion of the dithermals just disappear. Point X represents critical point.eg. For carbon dioxide its critical temperature-31 degrees celsius, critical pressure-72.8 atm.

NB: the factors are involved in the liquefaction of a gas.

• Intermolecular attractions which tend to bring the molecules together.
• Thermal or kinetic energy of molecules which tends to keep them apart. It’s impossible to liquefy a gas above its critical temperature because the molecules have very high kinetic energy hence they move vigorously and are able to overcome intermolecular attractions.

Relative Atomic Masses.

Measurement of absolute mass of an atom is difficult because an atom is too tiny to be weighed but its mass can be compared with the mass of another atom or other atoms.

Relative atomic mass is the ratio of the average mass per atom of the naturally occurring form of the element to a twelfth of the mass of carbon-12 atom.ie (equation).

Since RAM is a ratio, it has no units.

Mass Spectrometer.

This is an instrument that is used to determine the mass numbers and the intensities of the different isotopes of some of the elements. It can also be used to determine R.M.M of gaseous organic substances. It measures charge to mass ratio.

Mass spectrometer consists of;

• An ion source (ionisation chamber)
• An electric field (analyser) 
  a magnetic field
• A collector (ion detector)
• Amplifier and recorder.

Schematic diagram for mass spectrometer.

(Diagram)

Analysis involving mass spectrometer is as follows;

The sample whose RFM is required is first vaporized to give gaseous particles (atoms/molecules).

The particles are then made to collide with a stream of fast moving electrons.

The electrons knock off an electron from each gaseous particle resulting into gaseous positive ions.

(Equations)

NB: positive ions can also be produced by passing an electric discharge through the gaseous form of the sample, whose RAM is required.

For isotopes, the produced positive ions move at different velocities and would have different charge to mass ratio. These ions are passed through the analyser which consists of an electric field at high voltage. Its function is to allow ions moving with nearly the same velocity move to the magnetic field at a time.

The purpose of the magnetic field is to separate/deflect ions into different areas of the collector according to their charge to mass ratio.

The lighter the ion, the more its deflected by the magnetic field and vice versa. Or the higher the charge to mass ratio, the more the deflection.

It must also be noted that the larger the charge on an ion, the more the ion will be deflected by the magnetic field.eg. Al3+ is deflected more than Al 2+ which is also deflected more than Al1+.

Consider isotopes of chlorine, Cl-35, Cl-37, where Cl-35 is three times more stable and abundant than Cl-37.ie. In every sample of chlorine atoms, ¾ of Cl-35 and ¼ are of Cl-37. When calculating the relative atomic mass of chlorine, the two isotopes are considered; Cl-35 contributing ¾ of the RAM and Cl-37, 1//4.

NB: the RAM of chlorine is not a whole number because chlorine exhibits isotopy/due to existence of two different isotopes in different ratios

Some other elements that also exhibit isotopy also have RAM which is not a whole number.

Consider the analysis of a molecule of chlorine in a mass spectrometer. Three different molecules arising from the different combination of the two isotopes are possible as follows;

Cl2 from35 Cl- 35Cl   70

Cl2 from35 Cl- 37Cl   72

Cl2 from37 Cl- 37Cl   74

Mass Spectrograph.

This has a photographic plate that is used to record a mass spectrum.ie. The beam of positive ions falls on photographic plate producing a series of lines known as a mass spectrum. The masses of the ions are then taken as the masses of the neutron-ions. The intensity of each line on the photographic plate gives an indication of the amount of each particle (ion) present.eg. A mass spectrum of lead is shown below.

Graphs

From the above spectrum;

• Lead has four isotopes.
• The mass numbers are 204, 206, 207 and 208.
• The most abundant isotope is 208, 206, 207 and 204.

Consider the following detailed results on such a mass spectrum.

Isotopic mass	intensity	% abundance
204	0.2	2
206	2.4	24
207	2.2	22
208	5.2	52
	= 10.0	=100

Equation.

Relative Formula Mass.

The ratio average mass per molecule of the naturally occurring form of an element or compound to a twelfth of the mass of the carbon-12 atom.

It is equal to the sum of the relative atomic masses of all the atoms that comprise a molecule.