Fundamentals of inorganic chemistry, Lecture note PDF

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Fundamentals of Inorganic Chemistry (Chem1011): Lecture Note, 12-14-2015 Unit One Fundamental Laws of Chemical Combinations 1. Introduction 1.1. Development of atomic theory Atomic theory is the study of atoms and the force which hold them together.  Philosophers and scientists did not arrive at th...

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Fundamentals of Inorganic Chemistry (Chem1011): Lecture Note, 12-14-2015

Unit One Fundamental Laws of Chemical Combinations 1. Introduction 1.1. Development of atomic theory Atomic theory is the study of atoms and the force which hold them together.  Philosophers and scientists did not arrive at the atomic theory alone. It is the contribution of each succeeding persons would build the concept from a previous ideas.  The nature of matter stated by Arstotile, is that solid body can be divided and subdivided into smaller pieces without limit. This view is known as the continuous theory of matter.  The Greek philosopher, Democritus, suggested that matter is made of up of particles so small and indestructible that they can`t be divided into anything smaller. This view is known as discontinuous theory of matter. Democritus called such indestructible particles as atoms: from Greek word indivisible or indestructible.  The English man, Robert Boyle (17th century), who did research on the behavior of gases, provided clear evidence for the atomic make up of matter. He defined an element as a substance that cannot be chemically broken down further. He believed that a number of different elements might exist in nature. 1.1.1. Dalton’s Atomic Theory (DAT) Thus the main postulates of Dalton’s Atomic Theory can be stated as follows:  Matter is discrete (discontinuous) and made up of very small particles called atoms. An atom is the smallest indivisible particle of an element which can take part in a chemical change.  Atoms are neither created nor destroyed during chemical reaction. Chemical reactions only rearrange the way that atoms are combined; the atoms themselves are unchanged.  Atoms of the same element are identical in all respects, having the same size, shape and structure, and especially mass. Atoms of different elements have different properties and different masses. By: Bezabih Kelta(M.Sc. Inorg. Chem) -1- Department of Chemistry, Wolaita Sodo University

Fundamentals of Inorganic Chemistry (Chem1011): Lecture Note, 12-14-2015 

Atoms of different elements can combine in a fixed ratio of small whole numbers to form compounds.

Drawbacks of Dalton's theory In light of the current state of knowledge in the field of Chemistry (according to the modern atomic theory), Dalton’s theory had a few drawbacks. According to Dalton’s postulates: An atom is the smallest indivisible particle of an element. However, it is now known that atoms can further be subdivided into elementary particles like electrons, protons, and neutrons.  Atoms of the same element are identical in all respects, having the same size, shape and structure, and especially mass. Today, we know that atoms of the same element can have slightly different masses. Such atoms are called isotopes. Atoms of different elements have different properties and different masses. However, different elements do exist whose atoms have the same mass. Such atoms are called isobars. Activity 1.1 1. Briefly discuss the difference between isotopes, isobars and isotones and give two examples for each. 2. What are the importances of Dalton’s atomic theory? Discuss briefly.

1.2. Laws of Chemical Combination a) The law of conservation of mass (Lavoisior, 1789) – states that in chemical reaction, the mass of the system (reactants and products) remains constant. Hence matter is neither created nor destroyed in a chemical reaction. Example: Hydrogen + oxygen 2H2

+

O2

water 2H2O

2 molx2 g/mol + 1 molx32 g/mol 4 g + 32 g 36 g

= 2 molx18 g/mol = 36 g = 36 g

b) The law of definite (constant) proportions (Proust, 1799) - This law states that, in a pure chemical substance, the elements are always present in definite proportions by mass.

By: Bezabih Kelta(M.Sc. Inorg. Chem) -2- Department of Chemistry, Wolaita Sodo University

Fundamentals of Inorganic Chemistry (Chem1011): Lecture Note, 12-14-2015 Example: In the substance sodium chloride (NaCl), for instance, the ratio of the mass of sodium to the mass of chlorine is always 23:35.5, regardless of the source of the salt. c) The law of multiple proportions (Dalton, 1805).  When two elements combine to form more than one compound, the mass of one element that combine with a fixed mass of the other element are in the ratio of small whole number. Example: H2O  2: 16 or 1: 8

H2O2 2:32 or 1: 16

The two masses of oxygen are simple whole numbers ratio, 8:16 1:2 Review Activity 1. Silicon dioxide (SiO2), made up of elements silicon and oxygen, contains 46.7% by mass of silicon. With what mass of oxygen will 10g of silicon combine? 2. 2.16 g of mercuric oxide gave on decomposition 0.16 g of oxygen. In another experiment 16 g of mercury was obtained by the decomposition of 17.28 g of mercuric oxide. Show that these data conform to the law of constant composition. 3. In an experiment 34.5 g oxide of a metal was heated so that O2 was liberated and 32.1 g of metal was obtained. In another experiment 119.5 g of another oxide of the same metal was heated and 103.9 g metal was obtained and O2 was liberated. Calculate the mass of O2 liberated in each experiment. Show that the data explain the law of multiple proportions.

By: Bezabih Kelta(M.Sc. Inorg. Chem) -3- Department of Chemistry, Wolaita Sodo University

Fundamentals of Inorganic Chemistry (Chem1011): Lecture Note, 12-14-2015

Unit Two Structure of Ionic Solids 2.1. Introduction In crystalline solids the atoms or ions are arranged in a periodic fashion and have long range order. By translating atoms or group of atoms in three dimensions, a crystal structure is formed. The crystal structure of a material is based on the crystal lattice, which is an imaginary point in space. This array of points are not arbitrary but follows a set of rotational and translation rules. Unit cell – is the smallest group of lattice points that displays the full symmetry of the crystal structure. The unit cell has all the properties found in the bulk crystal.

Fig.2.1 The three dimensional unit cell  Ionic compound has a giant ionic structure in which there are strong ionic bonds between cations (positively charged ions) and anions (negatively charged ions).  Common ionic compounds include: salts, oxides, hydroxides, sulphides and the majority of inorganic compounds, which are held together by the electrostatic force of attraction between the positive and negative ions.  The attractive force becomes maximum when each ion is surrounded by the greatest possible number of oppositely charged ions.  The number of ions surrounding any particular ion is called the coordination number(CN). The possible geometry and CN of ionic solids can be predicted by radius ratio calculation. 2.2 Radius Ratio Rule An ionic solid should achieve maximum electrostatic stability when: (i) each ion is surrounded by as many as possible ions of opposite charge, By: Bezabih Kelta(M.Sc. Inorg. Chem) -4- Department of Chemistry, Wolaita Sodo University

Fundamentals of Inorganic Chemistry (Chem1011): Lecture Note, 12-14-2015 (ii) the anion cation distance is as short as possible.  The cation-anion radius ratio is the ratio of the ionic radius of the cation to the ionic radius of the anion in a cation-anion compound. This is simply given by:Radius ratio= r+/r- , where: r+ = radius of cation & r- = radius of anion Table 2.1The radius ratio values with their respective geometrical arrengments Radius ratio(r+/r-)

CN

Geometry

Example

n1

R is Rydberg’s constant =109,678cm-1 = 1.097x107 m-1

Series

n1

n2

Spectrum region

Lyman

1

2,3,4,…

Ultraviolet

Balmer

2

3,4,5,…

Visible

Paschen

3

4,5,6,…

Infrared

Brackett

4

5,6,7,…

Far IR

Pfund

5

6,7,8….

Far IR

Table 4.2: Various series in atomic hydrogen emission spectrum By: Bezabih Kelta(M.Sc. Inorg. Chem) -27- Department of Chemistry, Wolaita Sodo University

Fundamentals of Inorganic Chemistry (Chem1011): Lecture Note, 12-14-2015 Examples: Calculate the wavelengths of the radiations by a hydrogen atom when an electron makes the following transitions:

a) n2 = 2 to n1 = 1

b) n2 = 4 to n1 = 2

Solution a) 1/ = R(1/n12 – 1/n22)

b) 1/ = R(1/n12 – 1/n22)

1/ = R(1/12 – 1/22)

1/ = R(1/22 – 1/42)

1/ = 109678cm-1(1 – 1/4)

1/ = 109678(1/4 – 1/16)

1/ = 109678(3/4)

1/ = 109678(3/16)

 = 4/3x109678

 = 16/3x109678

=

 = 3.65x10-5 cm

6.38x10-6 cm

Activity 1. Calculate the wavelengths of the radiations by a hydrogen atom when an electron makes the following transitions. a) n2 = 3 to n1 = 2

b) n2 = 4 to n1 = 1

c) n2 = 5 to n1 = 2 2. The wavelength of which of the above transitions is (are) in the visible region? 3. Discuss in groups about the limitations of Rutherford’s atomic model

4.3.3 Postulates of Bohr In 1913, Niels Bohr proposed a theory of hydrogen atom which not only explained the origin of hydrogen spectrum but also led to an entirely new concept of atomic structure. The three postulates on which Bohr model was based are described:

1. In a hydrogen atom, the electrons revolve around the nucleus in certain definite circular paths called orbits, or shells.

By: Bezabih Kelta(M.Sc. Inorg. Chem) -28- Department of Chemistry, Wolaita Sodo University

Fundamentals of Inorganic Chemistry (Chem1011): Lecture Note, 12-14-2015

2. The atom does not radiate energy while in one of its stationary states. That is even through it violates the idea of classical physics the atom does not change energy while the electrons moves with in an orbit. Each shell or orbit corresponds to a definite energy.

3. The electrons present in an atom can move from a lower energy level (E lower) to a level of higher energy (Ehigher) by absorbing the appropriate energy. Similarly, an electron can jump from a higher energy level (Ehigher) to a lower energy level (Elower) by losing the appropriate energy. The energy absorbed or lost is equal to the difference between the energies of the two energy levels, i.e., ΔE=hv= E higher - Elower The state of atom with the lowest energy is called is ground state. The states with higher energies are called excited states. Thus the energy of a hydrogen atom in the ground state is - 13.6 eV and in the first excited state = -3.4eV.

Fig 4.4 Energy level diagram for the electron in the hydrogen atom

By: Bezabih Kelta(M.Sc. Inorg. Chem) -29- Department of Chemistry, Wolaita Sodo University

Fundamentals of Inorganic Chemistry (Chem1011): Lecture Note, 12-14-2015 Activity Using the Fig 4.4 and the previous concepts do the following questions. a) Calculate the frequency of electromagnetic radiation emitted by the hydrogen atom in electron transition from n = 4, to n = 3. b) The first line of the Lyman series of the hydrogen atom emission results from a transition from the n = 2 level to then = 1 level. What is the wavelength of the emitted photon? Using figure 4.2 describe the region of the electromagnetic spectrum in which this emission lies. c) What is the difference in energy between the two levels responsible for the ultraviolet emission line of the magnesium atom at 285.2 nm? d) Calculate the shortest wavelength of the electromagnetic radiation emitted by the hydrogen atom in undergoing a transition from the n = 6 level. Limitations of Bohr’s model

i.

The only 'success' was with the hydrogen atom and similar atoms i.e. those with one electron like: He+, Li++ etc. Thus, it does not explain the properties of multi electronic atoms.

ii.

It does not show conformity to the uncertainty principle, which states that it is not possible to know precisely both the energy and position of the electron at the same time. If the energy is known, the position cannot be determined with certainty. He used the classical physics concepts to determine the electrons around the nucleus of an atom and considered an electron as macro objects. The Energy states of Hydrogen Atom

A very useful result from Bohr`s work is an equation for calculating the energy levels of an atom: ΔE = Efinal-Einitial = -2.18x10-28J

Note that if we combine the above equation with plank`s expression for the change in an an atom`s energy, we obtain the Rydberg’s equation: ΔE = hυ =

= -2.18x10-28J

By: Bezabih Kelta(M.Sc. Inorg. Chem) -30- Department of Chemistry, Wolaita Sodo University

Fundamentals of Inorganic Chemistry (Chem1011): Lecture Note, 12-14-2015 Therefore, =

-2.18x10-28J

= 

=



=

Where nfinal = n2, ninitial = n1 and 1.097x107m-1 is the Rydberg’s constant. Activity The line spectra in H-atom has wavelength of 1212.7Ao (use 1Ao = 10-10 m). The line result from transition to n2 = 2. Then determine n1. (Use R= 1.097 X10-7 m-1)

4.4 Quantum numbers 

Quantum numbers designate main energy levels, shapes of sub-shells, orbitals, and spins of electrons.



A total of four quantum numbers were developed to better understand the electronic structure of an atom.



Each quantum number indicates an electron's trait within an atom, which satisfies to explain the movement of electrons as a wave function, described by the Schrodinger equation.



Each electron in an atom has a unique set of quantum numbers; no two electrons can share the same combination of four quantum numbers. Quantum numbers are very significant because they can determine the electron configuration of an atom and a probable location of the atom's electrons. They can also aid in graphing orbitals.



Quantum numbers can help to determine other characteristics of atoms, such as ionization energy and the atomic radius.

There are a total of four quantum numbers: 

the principal quantum number (n)



the angular momentum quantum number (ℓ)



the magnetic quantum number (mℓ)



and the electron spin quantum number (ms) By: Bezabih Kelta(M.Sc. Inorg. Chem) -31- Department of Chemistry, Wolaita Sodo University

Fundamentals of Inorganic Chemistry (Chem1011): Lecture Note, 12-14-2015

1. The principal quantum number (n) -

n can be any positive integer values (1,2,3…etc)

-

The principal quantum number, n, designates or describes the principal electron shell (the main energy levels). i.e n=1=K , n=2=L , n=3=M ….etc.

-

It also describes the most probable distance of the electrons from the nucleus, the larger the number n is, the farther the electrons are from the nucleus, the larger the size of the orbital, and the larger the atom is.

-

n can be starting at 1, as n=1 designates the first principal shell (the innermost shell). The first principal shell is also called the ground state, or lowest energy state.

n = 3 designates the third principal shell, n=4 designates the fourth

principal shell, and so on. n=1, 2, 3, 4… -

As energy of the electron increases, so does the principal quantum number.

-

The maximum number of sub-shells permitted for a particular shell is equal to n2.

-

The maximum number of electrons permitted in a particular shell is equal to 2xn2.

-

This explains why n can’t be 0 or any negative integer, because there exists no atoms with zero or a negative amount of energy levels/principal shells.

2. The Angular momentum quantum number (azimuthal quantum number) (ℓ)  ℓ describes the shape of the orbital. Orbitals have shapes that are best described as spherical (l = 0), polar (l = 1), or cloverleaf (l = 2).  The quantum number that designates the “sub-shell” an electron occupies. By: Bezabih Kelta(M.Sc. Inorg. Chem) -32- Department of Chemistry, Wolaita Sodo University

Fundamentals of Inorganic Chemistry (Chem1011): Lecture Note, 12-14-2015  It is an indicator of the shape of an orbital in the sub-shell. Each value of ℓ indicates a specific s, p, d, f subshell (each unique in shape.)  It has integer values from: 0 to n-1. i.e. ℓ = 0, 1, 2, 3, …, n – 1  The value of ℓ is dependent on the principal quantum number n. Unlike n, the value of ℓ can be zero. It can also be a positive integer, but it cannot be larger than one less than the principal quantum number (n-1): i.e. ℓ = 0 to (n-1)

3. Magnetic quantum number (mℓ)  There is only one way in which a sphere (l = 0) can be oriented in space. Orbitals that have polar (l = 1) or cloverleaf (l = 2) shapes, however, can point in different directions.  The magnetic quantum number (m), to describe the orientation in space of a particular orbital. (It is called the magnetic quantum number because the effect of different orientations of orbitals was first observed in the presence of a magnetic field.)  It is an integer from –  through o to +  .  The possible numbers of an orbital magnetic quantum numbers are set by its azimutal quantum number (that is,  determines mℓ).  The possible permitted values of mℓ for a particular sub-shell (ℓ) is equal to 2ℓ + 1.

By: Bezabih Kelta(M.Sc. Inorg. Chem) -33- Department of Chemistry, Wolaita Sodo University

Fundamentals of Inorganic Chemistry (Chem1011): Lecture Note, 12-14-2015

Activity 1) List the values of n,  , and mℓ in the following sub-shell. i) 3d

ii) 4s

iii) 3p

iv) 4f

v) 6d

vi) 7d

2) What is the maximum number of electrons that can be present in the following expressions? a) n =3,  = 2, ml =0. b) n= 3,  = 2

c) n = 5,  = 1

d) n = 2,  = 0

e) n =4,  = 3

3) Give the notation for the sub-shells denoted by the following quantum numbers. i) n = 3,  = 1

ii) n = 4,  = 2

iii) n = 4,  = 0

iv) n = 5,  = 3

4. Spin Quantum Number (ms)

 Unlike n, ℓ , and mℓ, the electron spin quantum number ms does not depend on another quantum number.  It designates the direction of the electron spin and may have a spin of +1/2, represented by↑, or –1/2, represented by ↓. This means that when ms is positive the electron has an upward spin, which can be referred to as "spin up." When it is negative, the electron has a downward spin, so it is "spin down." ms = +1/2 or ms = 1/2  The significance of the electron spin quantum number is its determination of an atom's ability to generate a magnetic field or not.

By: Bezabih Kelta(M.Sc. Inorg. Chem) -34- Department of Chemistry, Wolaita Sodo University

Fundamentals of Inorganic Chemistry (Chem1011): Lecture Note, 12-14-2015 Now we can write a set of four quantum numbers for any electron in the ground state of any atom. Example Boron atom has a total of five electrons. Write the four quantum numbers for each of the five electrons in the ground state. Solution Start with n = 1, so  = 0 , a sub shell corresponding to the 1s orbital. This orbital can accommodate a total of two electrons. Next, n = 2, and .  may be either 0 or 1. The  = 0 sub shell contains one 2s orbital, which can accommodate a total of two electrons. The remaining one electron is placed in the .  =1 sub shell, which contains three 2p orbitals. The o...