A level chemistry

CCEA ADVANCED SUBSIDIARY

CHEMISTRY

MODULE 1

1.4 Atomic Size

Atomic radius

An atom or ion is not now regarded as a hard incompressible sphere. The modern wave mechanics picture shows the atom or ion to be a positively charged nucleus surrounded by a cloud of negative electron density. Since the electron cloud of an atom has no definite limit, the size of an atom can be defined in several ways.

Ionic Radii

The most useful model of an ion is to regard it as a uniformly charged sphere. This is a simple model in terms of your study of the wave mechanical picture of the atom and atomic orbitals but is adequate for your AS Level work.

If an ion is regarded as a sphere, then its radius is a convenient measure of its size.

Metallic radius

For metallic elements, half the distance between the nuclei in the metallic crystal lattice gives the atomic radius. The inter-nuclear distance is determined by X-ray diffraction. The results of X-ray diffraction experiments are often presented in the form of electron density maps. These are like the charge clouds of atomic orbitals you looked at, except that contour lines are used to indicate the most probable position of electrons.

Exercise 1

(a)  The figure below shows an electron density map for aluminium. Use the scale to find the metallic radius for aluminium.

[1nm. = 10^-9 m]

(b)  The ionic radius for Al³⁺ is 0.045 nm. (4.5 x 10^-11 m).why is this so much smaller than the metallic radius?

Ionic Radius

In sodium chloride, NaCl, the Na⁺ and Cl^- ions are packed together in a crystal lattice.

Exercise 2

Do you expect the radius of

(a)    a sodium ion, Na⁺, and

(b)   a chloride ion, Cl^-,

to be greater or smaller than the radius of the parent atom? Explain your answer.

In Exercise 2, we were thinking of atoms or ions in isolation. However, there is no way of measuring the size of isolated atoms or ions. What we can measure very precisely are the distances between nuclei in crystalline solids or molecules.

Exercise 3

(a)    Fig. 2 above shows two sodium ions and two chloride ions. Look at the electron densities, especially near the nuclei, to decide which are the chloride ions.

(b)   Does the map show precisely the boundaries between chloride ions and sodium ions?

(c)    Use a ruler and the map scale to obtain approximate values for the radii of sodium ions and chloride ions.

Trends in Ionic Radii

The table below shows some values for ionic radii of atoms.

NOTE:

·         The ionic radius of the cation (+ve ion) is less than that of the parent atom.

Na = 0.157 nm      Na⁺ = 0.098 nm

·         The ionic radius of an anion (-ve ion) is greater than that of the parent atom.

Br = 0.114 nm        Br^- = 0.196 nm

·         Ionic radii increase down a group

See table

·         Ionic radii decrease across a Period.

Na⁺ = 0.098 nm  Mg²⁺ = 0.065 nm  Al³⁺ = 0.045 nm  N^3- = 0.171 nm  O^2- = 0.146 nm  F^- = 0.133 nm

Covalent Radii of Atoms

Covalent bonds are formed by the overlapping of the outer orbitals of one atom with that of another and the atoms take up positions of minimum energy (i.e. maximum stability). The atomic radius can be taken as half the distance between the nuclei of identical atoms at closest approach.

For example in chlorine, Cl₂, there can be two different measures of the atomic radius- covalent radius and Van der Waals radius.

Covalent radius

The covalent radius refers to atoms covalently bonded together. The covalent radius for the  chlorine atom is 0.099 nm.

Van der Waals Radius

The Van der Waals radius refers to the situation when the atoms are adjacent but not bonded. The Van der Waals radius for chlorine is 0.180 nm.

Bond lengths

The lengths of single covalent bonds are the sum of the appropriate covalent radii.

In CCl₄ the C-Cl bond lengths can be experimentally determined as 0.177 nm. From other data it can be determined that the covalent radius for C = 0.077 nm and the covalent radius for Cl = 0.099 nm giving 0.176 nm for the bond length.

For multiple bonds the greater the number of bonds the shorter the bond length.

C-C = 0.154 nm           C=C = 0.133 nm           C≡C = 0.120 nm

The greater the number of bonds the larger is the electron density between the positive nuclei of the carbon atoms. Therefore there is a greater attraction towards the negative charge and shorter bond lengths.

Trends in Covalent Radii

·         Covalent radii increase down a Group.

F = 0.072 nm                    Cl = 0.099 nm             Br = 0.114 nm              I = 0.133 nm

·         Covalent radii decrease across a Period.

Li = 0.123 nm                    Be = 0.089 nm            B = 0.080 nm              C = 0.077 nm