Elementary Geochemistry: July 2011

What is Geochemistry?

Geochemistry is the study of the distribution of elements on and within the Earth, its atmosphere and hydrosphere, and other planets. It involves the chemical and physical processes and reactions that the Earth as a system has undergone and is still undergoing, producing the dynamic equilibrium that we observe today.

Victor Goldschmidt

Modern Geochemistry started when Victor Goldschmidt classified the elements according to their affinities to Oxygen (Lithophiles), Sulphides (Chalcophiles), Iron (Siderophiles), or their tendency to form gases (Atmophiles).

Goldschmidt’s Classification, in effect, determines the distribution of elements within the Earth system. Lithophiles are found on the crust as they have high tendency to bond with the silicate structure. Chalcophiles form sulphides that are denser than common rock-forming minerals; hence, these are depleted on the Earth’s crust. Siderophiles that form strong metallic bonds with iron are abundant in the core. Atmophiles occur as gases and so are depleted on the Earth itself. This distribution has started since the Earth’s differentiation (Historical Geology).

The Rock Cycle

In Petrology, we learn that The Rock Cycle is the transformation of rocks from and into Igneous, Metamorphic and Sedimentary, as conditions are changed (especially Temperature and Pressure) for the systems to achieve equilibrium. In Geochemistry, we are more concerned with the processes involved in the cycle, rather than the rock types. This simple illustration shows the rock cycle. Note that the presentation of the rock cycle may vary depending on the illustrator’s interpretation.

Thermodynamics

Thermodynamics is the study of effects of changes in heat, work and energy on a system. It predicts and measures the reaction of a body or system as conditions are changed, in order to gain dynamic equilibrium.

How do we apply thermodynamics in Geochemistry?

Zeroth Law

Zeroth Law of Thermodynamics states that if System A is in thermodynamic equilibrium (there is balance in the transfer of heat, work and energy; note that it does not mean that there is no transfer – static vs. dynamic equilibrium) with System B, and System B is in thermodynamic equilibrium with System C, then System A is in thermodynamic equilibrium with System C.

The concept of Temperature may be derived from the Zeroth Law.

First Law

The First Law of Thermodynamics states that if heat is added or subtracted from a system, an equivalent amount of work will be done by or to the system, respectively. The reverse is also true, when work is done to or by the system, an equivalent amount of heat will be released or absorbed by the system, respectively.

It can be written as dU = ΔQ –ΔW

Where:

U is the internal energy of the system

Q is the amount of heat; and

W is the amount of work

This law observes the Law of Conservation of Energy where energy is neither created nor destroyed, rather it is only transformed.

Second Law

The Second Law of Thermodynamics states that all systems tend to gain entropy when it undergoes spontaneous reactions (reactions that don’t need work). It also explains irreversible reactions.

It is mathematically written as dS = ΔQ/ T

Acid-Base Reactions

Neutralization is the reaction between an acid and a base. A neutralization reaction usually produces water, a salt, and the remainder of an acid or base.

Definitions of Acids and Bases

Arrhenius

Acids are substances that form hydrogen ions H⁺ while bases are substances that form hydroxide ions OH^-.

Bronsted-Lowry

Acids are proton donors and bases are proton acceptors.

Lewis

Acids are electron pair acceptors and bases are electron pair donors.

pH is the negative logarithm of the concentration of hydrogen ions in molars

Why are felsic rocks often referred to as acidic and mafic rocks as basic?

Redox Reactions

Redox (for this discussion as we will not discuss as far as oxidation numbers) is a pair of two-reactions, Oxidation and Reduction, that occur simultaneously.

The following mnemonic is commonly used: LEOGER

Spelled out:

Loss of electron/s is oxidation (and the reactant that loses an electron is called the reducing agent); and

Gain of electron/s is reduction (and the reactant that gains electron is called the oxidizing agent.

Structural Chemistry

Structural chemistry is a branch of science closely related to crystallography and solid-state physics, that deals with arrangement of ions, atoms and molecules (as usually observed macroscopically).

The most basic structure is that of NaCl, which has a coordination number of six. This means that every Na+ ion is surrounded by six Cl^- ions (above, below, front, back, left and right). Connecting the Cl^- ions with lines will form an octahedron. This is why NaCl is said to have n octahedral structure (in contrast to cubic habit).

Ionic Bonding

NaCl is a product of a purely ionic bond. NaCl is a bond between Na⁺ cation and Cl^- anion. In this bonding, there is complete transfer of electron from sodium to chlorine, forming sodium and chloride ions.

In solid NaCl (halite) and in all crystals, these ions are arranged to have the closest packing (octahedral structure of salt discussed above). This arrangement is determined by the radius ratio of Na⁺ and Cl^- ions.

Radius ratio is simply the radius of the cation divided by the radius of the anion.

For ionic bonds, these generalizations are calculated based on geometry:

If the radius ratio is between 0.41 and 0.73, the pattern of closest packing has each ion surrounded by 6 ions of the opposite sign (coordination number of 6). e.g. NaCl, with radius ratio of 0.64.
If the radius ratio is between 0.73 and 1.0, closest packing would have a coordination number of 8 (each ion is surrounded by 8 ions of the opposite sign). e.g. CsCl, with radius ratio of 1.03
If the radius ratio is between0.22 and 0.41, the coordination number is 4 (each ion is surrounded by 4 ions of the opposite sign). e.g. ZnS₂, with radius ratio of 0.43

These generalizations, however, are not always observed because most minerals are not formed purely of ionic bonds.

Covalent Bonds

Covalent bonds, in contrast to ionic bonds, is equal sharing of electrons (remember that ionic bond is complete transfer). Covalent bonds are usually weaker than ionic bonds, hence, softer substances. Diamond which is formed by covalent bonds is an exception. Substances formed by ionic bonds more easily dissolve in polar solutes (e.g. water).

Polar Bonds

Most substances are not formed by purely ionic bonds or purely covalent bonds. Polar bonds are intermediate between ionic and covalent bonds. There is unequal sharing of electrons. This means that the resulting molecule will have slightly positive and slightly negative poles.

The following are general rules observed about bond types:

For a given cation and two different cations, the bond with the larger anion is more covalent
For a given anion and two different cations, the bond with the smaller cation is more covalent
For ions of similar size and different charge, the one with the highest charge form the most covalent bonds
Ions of metals in the middle of the long periods of the periodic table form more covalent bonds with anions than do ions of similar size and charge in the first two or three groups of the table

Silicate Structures

The silicate tetrahedron, as the name implies, has a structure with four faces. These faces can be drawn connecting four oxygen atoms surrounding a single silicon atom (refer to figure below). This is the basic unit of most common rock-forming minerals (silicates).

As we know from Petrology, there is a diversity of silicate structures from a single tetrahedron to a framework structure. This is due to the properties of silicon that are intermediate to that of metals and nonmetals. The size of a silicon ion is intermediate between the smallest common metal ions and the largest nonmetal ions.

Here are the common silicate structures:

Nesosilicates – independent tedrahedral groups. Common example is olivine.

Sorosilicates – two to six tetrahedral linked to form larger independent anions. Example is hemimorphite.

Inosilicates – tetrahedra linked to form chains of indefinite length. e.g. pyroxene (single chain) and amphibole (double chain).

Phyllosilicates – three oxygens of each tetrahedron are linked with adjacent tetrahedral, forming flat sheets of indefinite extent. e.g. biotite and muscovite.

Tektosilicates – three-dimentional framework. e.g. quartz

Isomorphism

General statements regarding isomorphism:

Two compounds are said to be isomorphous if they have the same, or nearly the same, crystal form.
The general requirement for isomorphism is that the two compounds contain ions of approximately the same size, or at least the same relative size.
A pair of isomorphous compounds may show solid solution. i.e. homogenous crystals may form containing two end members in various ratios. e.g. fayalite and forsterite forming solid solutions of olivine.
Solid solution is not possible for isomorphous compounds that only have relative similar ionic sizes. e.g. halite and galena
Ionic size is the most important but not the sole determiner of isomorphism.

Substitution

Ions may substitute for another ion in a given crystal structure provided that they have approximately the same ionic size (among other properties, such as charge). Example would be the substitution of Fe and Mg in olivine, making a solid solution with ratios of fayalite and forsterite. Trace elements usually proxy for other more common elements without having to change the structure.

Polymorphism

Polymorphs are crystals that have the same chemical formula but different structures. This means that the ions making up the compound may be arranged in two or more different patterns. e.g. calcite and aragonite (CaCO₃).

Elementary Geochemistry

Homework 1: Ternary Diagrams

Lesson 1: Introduction

Course Outline