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## Matter

Chemistry studies the properties of matter and the interaction of different kind of matter with each other. Matter is everything that occupies mass and space and is in one of three physical states: solid, liquid, gas. The properties and interactions of matter were mainly discovered accidentally, but had a very important contribution to the ability of humans to manufacture the world around them. About 400 B.C. Greek philosophers tried to explain the properties and interaction of matter. They assumed that all matter was composed of four fundamental substances: fire, earth, water, and air, and that the properties of matter resulted directly from the properties of the microscopic building blocks, called 'atoms', of matter. Although we currently know that there are much more fundamental substances, the main ideas of what we now call an atom remained.

In chemistry we classify matter into pure substances and mixtures. A pure substance has a fixed composition and unique set of properties. A pure substance consists of either elements or compounds. An element is a substance that cannot be decomposed into simpler substances. A compound is a substances of two or more elements united chemically in definite proportions by mass. A mixture is a substance consisting of two or more pure substances. A homogeneous mixture, called solution, is uniform throughout the sample. A heterogeneous mixture, is not uniform throughout the sample.

Properties can be classified into physical and chemical. Physical properties describe changes of a substance without changing the identity of the substance. Examples: physical state, color, boiling point, melting point, electrical conductivity, thermal conductivity. Chemical properties describe the reactiveness of a substance with another substance. Examples: reactivity with water, oxygen, acids, toxicity.

Changes that affect the physical appearance of matter, but not its composition, are physical changes. Changes that alter the composition of matter are called chemical changes. Iron rusting, wood burning, and bread baking are three examples of chemical changes.

## Atomic theory of matter

In 1808 Dalton published A New System of Chemical Philosophy, in which he presented his theory of atoms.

• Each element is made up of tiny particles called atoms.
• The atoms of a given element are identical; the atoms of different elements are different in some fundamental way or ways.
• Chemical compounds are formed when atoms combine with each other. A given compound always has the same relative numbers and types of atoms.
• Chemical reactions involve reorganization of the atoms—changes in the way they are bound together. The atoms themselves are not changed in a chemical reaction.

In the view of Dalton atoms were spheres, like billiard balls. The British physicist J.J. Thomson studied cathode rays, the rays that are emitted when a high voltage is applied between two electrodes in an evacuated glass tube. He concluded in 1897 that these rays are streams of charged particles emitted from the atoms in the negatively charged electrode, which is called the cathode. These particles were named electrons. He found that these particles were the same for each material he used for the cathode and with a constant ratio of charge/mass. Robert Millikan developed an oil-drop experiment and found the charge of the electron to be $e=1.602 \times 10^{-19}\mathrm{C}$. Based on the charge/mass ratio found by Thomson the mass of the electron could be derived as $9.1 \times 10^{-31}\mathrm{kg}$

As the electron has a negative charge and the atom as a whole is electrically neutral the atom must also contain positively charged particles that balance the negative charge of electrons. Rutherford together with two of his students, Hans Geiger and Ernest Marsden, conducted an experiment by shooting $\alpha$ particles toward a piece of platinum foil. The results of the experiment were astonishing. Almost all of the particles passed through and were deflected only very slightly. The results of this experiment suggested a model of an atom in which there is a dense point like center of positive charge surrounded by a large volume of mostly empty space. Rutherford called this center the atomic nucleus. The particle with the positive charge is called the proton.

In 1932, Chadwick demonstrated the existence of the neutron, a nuclear particle having no charge but with nearly the same mass as a proton.

According to the current nuclear model the atoms consists of electrons distributed throughout the space around the nucleus. The nucleus consist of neutrons ans protons. The negative charge of the electrons in the atom is balanced by the positive charge of the protons. The neutrons are electrically neutral.

### Properties subatomic particles

#### Mass (kg)

Electron $\mathrm{e}^{-1}$ $-\mathrm{e}=-1.602 176 53(14) × 10^{–19}$ $\mathrm{m}_e=9.109 3826(16) × 10^{–31}$
Proton $\mathrm{p}^+$ $\mathrm{e}=1.602 176 53(14) × 10^{–19}$ $\mathrm{m}_p=1.672 621 71(29) × 10^{–27}$
Neutron $\mathrm{n}^0$ $\mathrm{e}=0$ $\mathrm{m}_n=1.674 927 28(29)×10^{-27}$

Atoms of different elements differ by the number of protons in the nucleus. This number is called the atomic number. The sum of the number of protons and neutrons is called the mass number. Atoms of the same element, but with a different number of neutrons are called isotopes. The atomic number is denoted by $Z$ and the mass number by $A$ in the notation of an element as follows: $\ce{^{A}_{Z}X}$

Scientists have established a standard for the measurement of atomic mass by assigning the carbon-12 atom a mass of 12 atomic mass units (amu). Thus, 1 amu is equal to 1/12 the mass of a carbon-12 atom. The atomic masses of many elements are not whole numbers. The reason for this is that many elements occur in nature as a mixture of isotopes—isotopes with different masses. The atomic mass of an element given in the table is a weighted average of the atomic masses of the naturally occurring isotopes of the element.

## Elements

In 1869, the Russian chemist Dmitri Mendeleev noted that when the known elements were placed in order of increasing atomic mass, their properties repeated in a regular pattern—a periodic pattern. The elements are arranged in the periodic table in order of increasing atomic number in 7 horizontal rows called periods. Because the pattern of properties repeats in each new row of elements, the elements in a column have similar properties and are called a group or family of elements. There are 18 groups. The groups are designated with a number and the letter A or B. Groups 1A through 8A are called the main group or representative elements. The group B elements are called the transition elements.

Elements are divided into three main classes—metals, metalloids, and nonmetals. As you can see from the periodic table, the majority of the elements are metals. Metals are generally shiny solids and are good conductors of heat and electrical current. Some groups of elements have names. For example, the first two groups of metals, groups 1A and 2A, are called the alkali metals and the alkaline earth metals, respectively. Most of the elements to the right of the heavy stair-step line in the periodic table are nonmetals, which are generally either gases or brittle solids at room temperature. Group 7A elements are commonly called halogens, and group 8A elements are the noble gases. Many of the elements that border the stair-step line are metalloids, which have some of the characteristics of both metals and nonmetals.

## Compounds

Each compound is an electrically neutral substance that is uniquely defined by two or more different elements and consists of a definite ratio of masses of these elements. The atoms are bonded to one another in a specific way: either molecular or ionic. A molecule is a discrete group of atoms bonded together in a specific arrangement. An ion is a positively or negatively charged atom or molecule. A positively charged ion is called a cation and a negatively charged ion an anion. The result of this bonding of elements is a compound with definite chemical and physical properties different from those of the elements that form it. There are two major classes of compounds: organic which contains the element carbon and usually hydrogen too, and inorganic which consists of all other compounds.

Chemical analysis is the process of discovering the elements that make up a compound. Chemical synthesis is the process of combining elements to produce compounds or converting compounds into other compounds.

In general binary compounds of nonmetals are molecular, whereas binary compounds of a nonmetal with a metal are ionic.

### Molecular compounds

Some of the elements exist in molecular form. Except for the noble gases all the elements that are gasses at ordinary temperatures are diatomic molecules, like $\ce{H2}$ and $\ce{O2}$. All the halogens exists as diatomic molecules. Solid sulfur exists as $\ce{S8}$ and phosphorus as $\ce{P4}$.

We describe a molecule with a chemical formula. A chemical formula of a compound represents the composition in terms of chemical symbols for the elements and subscripts to show the number of atoms of each element present in the smallest unit that is representative of the compound. There are many different ways to represent a chemical formula. For molecular compounds it is common to give a molecular formula which represent all elements with the number of atoms as subscript, like for benzene $\ce{C6H6}$ or sometimes an empirical formula $\ce{CH}$. An empirical formula is the simplest positive integer ratio of atoms of each element present in a compound.

To indicate how the atoms are linked in a molecule a structural formula is used. Each line in a structural formula represent a chemical link between two atoms and each symbol an atom.

Structural formulas are clear, but cumbersome. So chemists write the structural formula in a more condensed form, with the molecular formula $\ce{CH3CH2OH}$, the symbols with subscripts represents atoms connected to the preceding element in the formula. A group of atoms attached to another atom in the molecule is set of with parentheses.

A carbon atom can form four single bonds, two double bonds, or any combination that results in four bonds. Organic chemists have found a way to draw these potentially very complex molecular structures, by not showing the $\ce{C}$ and $\ce{H}$ atoms. A line structure represents a chain of carbon atoms by a zigzag line, where each short line indicates a bond and the end of each line represents a carbon atom. Atoms other than $\ce{C}$ and $\ce{H}$ are shown by there symbols. Double bonds are represented by a double line, and triple bonds by a triple line. As each carbon atom can form 4 bonds we mentally substitute $\ce{H}$ atoms to fill the gaps.

Another way to represent molecules is graphically by space-filling models which shows the geometrically shape of molecules. Still another graphical method of presentation is the ball-and-stick method which shows clearly the bond length and angles.

### Ionic compounds

An ionic compound consists of a large number of cations and anions stacked together in a regular three dimensional formation. The ions bond together by the attraction of there opposite charge. Ions are formed by gaining or losing electrons.

The periodic table can help us decide what type of ion an element forms and what charge to expect the ion to have. One major pattern is that metallic elements (toward the left of the periodic table), typically lose electrons and form cations. Nonmetallic elements (toward the right of the periodic table) gain electrons and form anions.So in general an ionic compound consists of a metal and a nonmetal.

For the elements in Groups 1 and 2 the charge of the cation is equal to the group number. The transition metals (groups 3-11) and the metals in groups 12,13,14 form a wide variety of cations. The charge of the anions of the nonmetals follows from their distance from group 18: N -18. The rule is that atoms lose or gain electrons until they have the same number of electrons as the nearest noble gas atom. Notice that most polyatomic ions are oxoanions (contains $\ce{0}$). Ammonium is a polyatomic cation and forms ionic compounds consisting of nonmetals, like ammonium sulfate $\ce{(NH4)2SO4}$.

The chemical formula of an ionic compound shows the ratio of the numbers of ions present in the compound by adding subscripts to the ions. When a subscript has to be added to a polyatomic ion, the ion is written within parentheses as in $\ce{(NH4)2SO4}$. All ionic compounds are electrically neutral. So the total charge of the ions in the chemical formula of an ionic compound must be zero.

To analyse the structure of atoms chemists use the electromagnetic radiation they emit. This branch of chemistry is called spectroscopy. A ray of electromagnetic radiation consists of oscillating electric and magnetic fields that travel though empty space at the speed of light $c=3.00 \times 10^8 m.s^{-1}$. An electromagnetic field exerts an oscillating force on charged particles in the field. The number of cycles per second is called the frequency $\nu$ of radiation with unit 1 hertz ($1 \mathrm{Hz}=1 s^{-1}$). Electromagnetic radiation spreads through space like a wave. The amplitude is the maximum height of the wave, the wavelenght $\lambda$ is thye peak-to-peak distance.

The different forms of radiation form a spectrum.

There seems to be no upper or lower limit to the spectrum, although modern theories suggest that the concept of space breaks down on a scale of $10^{-34}$.

As the speed for all electromagnetic radiation is the same, $c$, we have the following relation: $$\lambda\nu=c$$

Experiments studying the intensity of radiation emitted by a heated black-body at different wavelengths and temperatures showed a contradiction with the existing classical theories in late 19th century. Maxwell electromagnetic theory explained radiation as a wave phenomenon. but the experimental facts did not fit with classical theory.

Classical theory based on Maxwell equations modelled the black-body radation by Rayleigh-Jeans Law as $R_v(T) \sim Tv^2$ which results in an ultra-violet catastrophy with infinite total radiated energy since $\sum_{v=1}^n \nu^2\sim n^3 \to \infty \text{ as } n\to \infty$. Experiments showed however two laws which theory had to incorporate.

• Stefan-Boltzmann's law $$R(T)=\sigma T^4$$ where $R(T)$ is the total radiated energy per unit surface area, $T$ the temperature in degrees Kelvin and $\sigma=5.67\times10^{-8}\mathrm{W.m^{-2}.K^{-4}}$ Stefan-Boltzmann's constant.
• Wien's law $$\lambda_{\mathrm{max}}T=b$$
• where where $\lambda_{\mathrm{max}}$ is the peak wavelength, $T$ is the absolute temperature of the black body, and $b$ is a constant of proportionality called Wien's displacement constant, equal to $2.8977685(51)\times10^{-3}\mathrm{m·K}$

The suggestion that resolved the problem came in 1900 from the German physicist Max Planck. He proposed that the interaction between matter and radiation must occurs in quanta, or packets, of energy. He postulated that an atom oscillating at a frequency $\nu$ can exchange energy with its surroudings only in quanta of magnitude: $$E=h\nu=\frac{hc}{\lambda}$$ where $h=6.626\times10^{-34}\mathrm{J.s}$ is Planck's constant. Remember $\mathrm{E=P\times t}$ with the unit of $P$ measured in Watts ($1\mathrm{W}=1\mathrm{J.s}^{-1}$). The release of energy will be detected as radiation of frequency $\nu=E/h$. This assumption explained why high frequency radiation is not emitted by low temperatures, simply because this requires an high amount of energy (temperature) from the oscillating black-body.

Another phenomenon where classical theory also failed to explain the experimental outcomes is the photoelectric effect, the ejection of electrons from a metal when its surface is exposed to ultraviolet radiation. The experimental observations are as follows:

• No electrons are ejected unless the radiation has a frequency above a certain threshold value characteristic of the metal.
• Electrons are ejected immediately, however low the intensity of the radiation.
• The kinetic energy of the ejected electrons increases linearly with the frequency of the incident radiation.

Albert Einstein found a n explanation of these observations, he postulated that electromagnetic radiation consists of particles, which were later called photons. Each photon can be regarded as a packet of energy related to the frequencyof the radiation: $E=h\nu$. The intensity of the radiation relates to the number of photons present.

With this particle view of electromagnetic radiation the photoelectrical effect is easily explained. If the incident radiation has frequency $\nu$, then the energy of the protons is $E=h\nu$.These particles collide with the electrons in the metal. The required energy to remove an electron from the surface of a metal is called the work function $\Phi$. If the energy of a photon is less than $\Phi$ then no electrons will be ejected. However if the energy is greater than $\Phi$ the electron is ejected with a kinetic energy $E_k=\tfrac{1}{2}m_ev^2$ and equal to $h\nu-\Phi=\frac{hc}{\lambda}-\Phi$.

The black-body radiation and the photoelectric effect caused physicists to use a particle view of radiation. However other phenomenon such as diffraction requires the behaviour of radiation as waves. So in modern physics we have to accept the wave-particle duality of electromagnetic radiation. In the wave model the intensity is proportional to the square of the amplitude and in the particle model to the number of photons.

In 1925 the French scientist Louis de Broglie proposed that all particles should also be regarded as having wavelike properties and formulated the following equation for its wavelenght, currently known as de Broglie relation: $$\lambda=\frac{h}{p}$$ where $p=mv$ is called the linear momentum. The wavelengths of matter are extremely small.

## References

• [1]    Peter Atkins & Loretta Jones, Chemical Principles, Third Edition 2005, Freeman and Company.