CHEM 151 Lecture Notes PDF

CHEM 151: BASIC INORGANIC CHEMISTRY LECTURE 1  COURSE OUTLINE Atomic structure; qualitative wave mechanics Periodic table and periodicity, reactive parameters Chemical bonding – Molecular, – ionic – Covalent – Metallic – Van der waal’s bonding...

CHEM 151: BASIC INORGANIC CHEMISTRY LECTURE 1  COURSE OUTLINE Atomic structure; qualitative wave mechanics Periodic table and periodicity, reactive parameters Chemical bonding – Molecular, – ionic – Covalent – Metallic – Van der waal’s bonding 2  COURSE OUTLINE Forces within molecules – Bond strength – Bond energy – Polarity – Continuity of bonds Valence bond theory, resonance, multiple bond, shapes of molecules, hybridization of non- transition elements Crystal structures The principal types of unit cell space lattice 3  QUIZES AND EXAMINATIONS 1st Quiz: Form of exam: Written (30 marks) Mid-semester: Form of exam: Written (30 marks) End of Semester: Form of exam: Multiple choice (100 marks) 4  ATOMIC STRUCTURE Atom : An atom is the smallest particle of an element that retains the properties of that element. Original ideas on atomic structure consisted of a positively charged ‘cloud’ with embedded, negatively charged, particle-like electrons. This was superseded by the Rutherford’s model in which a central, positively charged nucleus, containing most of the mass of the atom, was surrounded or orbited by the much lighter electrons. 5  ATOMIC STRUCTURE The atom was viewed as a miniature solar system in which the nucleus was analogous to the sun and the electrons to the planets but this was a simple model. It was inconsistent with classical physics which predicted that the electrons in such an atom should spiral into the nucleus with concomitant emission of radiation. 6  ATOMIC STRUCTURE Observations in atomic spectroscopy showed that the electrons could have only certain orbits or energies. This observation provided a way around the problem but from a theoretical standpoint, this factor had to be introduced on a purely adhoc basis with no clear idea of why it should be so. The resulting picture formed the basis of the subsequent model proposed by Niels Bohr. 7  ATOMIC STRUCTURE This model was quite successful in explaining the observed spectroscopic properties of the hydrogen atom, the simplest of all atoms containing only a single electron. The model soon ran into problems with heavier atoms containing more than one electron. 8  ATOMIC STRUCTURE The French scientist Louis de Broglie had the curious idea that the same wave-particle duality, or combined wavelike and particle-like character, should apply to matter too. In 1924, he suggested that we should also think of an electron as having the properties of a wave. 9  ATOMIC STRUCTURE He proposed that every particle has wavelike properties, including a wavelength that is related to its mass m and speed υ by the De Broglie relation λ= 10  ATOMIC STRUCTURE According to this relation, a heavy particle travelling at high speed has a small wavelength λ. A small particle travelling at low speed has a large wavelength. Because of its wavelike character, we cannot say precisely where an electron is when it is travelling along a path. This is expressed numerically by the uncertainty principle discovered by Werner Heisenberg. 11  ATOMIC STRUCTURE Heisenberg found that the more precisely we know the position of a particle, the less we can say about its speed, and vice versa. More specifically, if we know the position of a particle of mass m to be within a range Δx, then its speed must be uncertain by at least an amount Δυ, where ℎ Δx× (m× ∆𝜐)≥ 4𝜋 12  ATOMIC STRUCTURE If Δx is zero (meaning we have perfect knowledge about the location), the only way this inequality can be satisfied is for Δν to be infinite (meaning we are totally ignorant about the speed). Similarly, if the speed is certain (Δν is zero), the position must be completely uncertain (Δx is infinite). The uncertainty principle implies that Bohr’s picture of electrons travelling in precise orbits cannot be valid, because an electron in such an orbit has a definite position and definite speed at every instant. 13  ATOMIC STRUCTURE An elegant solution to the problem was provided by Schrödinger in 1926. He proposed the electrons in atoms should be considered not as particles but as waves and that they could therefore be described by a suitable wave equation. The important conceptual breakthrough here was that the presence of only certain allowed electron energies is a direct and natural consequence of a wave treatment and no ad hoc assumptions are necessary. 14  ATOMIC STRUCTURE The Schrödinger wave equation is used to describe the behavior of electrons in atoms, – i.e. we treat electrons as waves such that only certain solutions to the wave equation, or energies for the electron, are possible and this quantization results directly from boundary conditions. Moreover, we obtain not one solution but a series of many possible solutions each with certain energy and each described by a certain set of quantum numbers. Each one of these solutions or wavefunctions (ψ) describes a possible state of the electron in the atom and this is called an orbital. 15  ATOMIC STRUCTURE The solutions or wavefunctions, ψ, refer to the amplitude of an electron wave. Of more physical significance is the square of this function (ψ2) which refers to the electron intensity (density) or more precisely a probability of finding an electron. 16  ATOMIC STRUCTURE Thus ψ2 at any particular point is the probability of finding the electron at that point. High values of ψ2 mean high probability, low values mean low probability; ψ2 equal to zero means zero probability. 17  Quantum Numbers Boundary conditions and the spherical, three- dimensional nature of the atom give rise to three quantum numbers and these are given the symbols n, l and ml. These can take only certain allowed values and a solution exists to the Schrödinger equation for certain allowed sets of these three numbers. 18  Quantum Numbers The names and symbols for these quantum numbers and the values which they can take are given below as follows: – n is the principal quantum number and this determines the radial part of the wavefunction. The energy of the orbital also depends on n but not on l and ml. The number n can take integral values 1, 2, 3, 4….∞ but we will be concerned only with the first few. – l is the subsidiary or angular momentum quantum number. This determines the shape of the orbital and can take values 0,1, 2, 3…n-1, i.e. the possible values of l are dependent on n. In fact, l determines the type or shape of the orbital and these are usually referred to by letters. 19  Quantum Numbers l=0 s orbital l=1 p orbital l=2 d orbital l=3 f orbital 20  Quantum Numbers Orbital are then labeled according to their value of n and the letter associated with l: n=1 l=0 1s n=2 l=0 2s n=2 l=1 2p n=3 l=0 3s n=3 l=1 3p n=3 l=2 3d Note that orbitals such as 1p and 2d are not allowed according to these rules. 21  Quantum Numbers ml is the magnetic quantum number and it takes values -l, -l+1,…0…, l-1, l, i.e. 2l+1 values for a given value of l. Thus for l=0, ml =0 and so there is only one type of s orbital for any given value of n, i.e. one 1s, one 2s etc. For l=1, ml=-1, 0, +1, i.e. three types of p orbital; three 2p, three 3p etc. For l=2, ml=-2, -1, 0, +1, +2, i.e. five types of d orbital. This quantum number specifies the orientation of the orbital. 22  Quantum Numbers When we look at these orbitals or wave functions in more detail we will see that they contain nodes and there are a few simple rules concerning nodes that are worth remembering. The total number of nodes in any orbital is given by n-1. Some of these are in the radial part of the wave function and some are in the angular part. 23  Quantum Numbers In the case of the hydrogen atom, the energy of an electron or orbital depends only on the value of n and so, for example, the 2s and 2p orbitals have the same energy and are said to be degenerate. The energy of the orbitals increases as n increases. The separation in energy is not constant but that the levels become closer together as n increases. Moreover, the energies are given negative values with n=∞ defined as zero energy. 24 The angular part of the wavefunction The angular part of the wavefunction reveals how the wavefunction varies as a function of angle from the origin of some suitably chosen coordinate systems and thus determines the shape of the orbital. It is dependent on the quantum number l and we can label the types of orbitals according to this quantum number or more usually with the letters s, p, d, f, etc. The number of nodes in the angular part of the wavefunction for a given orbital is equal to l. Thus, s orbitals (l = 0) have no angular nodes. Moreover, since there is no angular dependence, the orbital is spherical and this is true for all s orbitals; 1s, 2s, 3s, etc. 25 The angular part of the wavefunction For p orbitals, l=1 and there is one angular node. This is planar and divides the orbital into two lobes of opposite sign. There are three possible orientations for orbitals of this type (three values of ml) which lie along the axes x, y and z, and these are usually designated as px, py and pz. All p orbitals have this shape and there are always three for any given value of n, i.e. three 2p, three 3p etc. 26 The angular part of the wavefunction For d orbitals, l=2 and there are therefore two nodes associated with these orbitals. These are perpendicular and each orbital has four lobes. There are five d orbitals which are given the labels dxy, dxz, dyz, dx2-y2 and dz2. Figure: diagrams of angular part of the wavefunction for selected orbitals 27  The radial part of the wavefunction The radial part of the wavefunction tells us how the wavefunction varies with distance, r, from the nucleus, i.e. the effective size of the orbital. Atomic orbitals depend on an exponential function 𝑒 −𝐵𝑟 where B is some constant and r is the distance from the nucleus. This means that ψ falls away exponentially at large r values. 28  The radial part of the wavefunction For a 1s orbital, a standard expression is ψ=A𝑒 −𝐵𝑟 and if we plot this function as a graph, we obtain a curve shown in figure below. We can see that there is a maximum value of ψ at r = 0 or at the nucleus. 29  The radial part of the wavefunction The probability of finding an electron on a particular surface rather than at a point along a line from the nucleus is of interest at this stage. Considering the 1s orbital, we can imagine a spherical surface expanding from the nucleus and it will be useful to know the probability of finding an electron at some point on this surface as a function of distance from the nucleus. 30  The radial part of the wavefunction The greater the distance from the nucleus, the more points on a sphere and so the function we want will be proportional to the surface area of the sphere or 4𝜋𝑟 2. We can therefore plot a probability that an electron is at a certain distance r according to the function 4𝜋𝑟 2. 𝜓 2. This is called the radial probability function (RPF). 31  The radial part of the wavefunction The graphs of RPFs of 1s, 2s, 2p, 3s, 3p and 3d orbitals are shown in Figure 2. When r = 0, the RPF is also 0 and so for all orbitals, the function is zero at the centre of the nucleus. The graph has a maximum, i.e. there is a distance at which we are most likely to find an electron, ro. 32 The radial part of the wavefunction Figure 2 Graphs of RPFs of 1s, 2s, 2p, 3s, 3p and 3d orbitals 33