Learning Objectives - Geochemistry - Lecture Slides, Slides of Geochemistry

In these Lecture Slides, the Lecturer has put emphasis on following key points : Learning Objectives, Thermodynamics, Geochemistry, Mass Flux, Thermodynamic Models, Phase Diagrams, Visualize, Minerals, Aqueous, Interpretations

Typology: Slides

2012/2013

Uploaded on 07/25/2013

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Learning Objectives and Fundamental Questions
What is thermodynamics and how are its concepts
used in geochemistry?
How can heat and mass flux be predicted or
interpreted using thermodynamic models?
How do we use phase diagrams to visualize
thermodynamic stability of minerals and aqueous
solutions?
How do kinetic effects affect our interpretations
from thermodynamic models? - We will address
this later in the class.
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Learning Objectives and Fundamental Questions

  • What is thermodynamics and how are its concepts

used in geochemistry?

  • How can heat and mass flux be predicted or

interpreted using thermodynamic models?

  • How do we use phase diagrams to visualize

thermodynamic stability of minerals and aqueous

solutions?

  • How do kinetic effects affect our interpretations

from thermodynamic models? - We will address

this later in the class.

What is Thermodynamics?

• Thermodynamics: A set of of mathematical

models and concepts that allow us to describe the

way changes in the system state (temperature,

pressure, and composition) affect equilibrium.

  • Can be used to predict how geological systems ( e.g.

melts-minerals; solutes in aqueous solutions) will

respond to changes in state

  • Invert observed chemical compositions of minerals and

melts to infer the pressure and temperature conditions

or origin

Thermodynamic Systems - Definitions

Isolated System: No matter

or energy cross system

boundaries. No work can be

done on the system.

Open System: Free exchange

across system boundaries.

Closed System: Energy can be

exchanged but matter cannot.

Adiabatic System: Special case

where no heat can be exchanged

but work can be done on the

system (e.g. PV work).

Thermodynamic State Properties

• Extensive: These variables or properties

depend on the amount of material present

(e.g. mass or volume).

• Intensive: These variables or properties DO

NOT depend on the amount of material

(e.g. density, pressure, and temperature).

Spontaneous Reaction Direction

Energy and Work

  • Energy: commonly defined as the capacity to do work ( i.e.

by system on its surroundings); comes in many forms

  • Work: defined as the product of a force (F) times times a

displacement acting over a distance (d) in the direction

parallel to the force

work = Force x distance

Example: Pressure-Volume work in volcanic systems.

Pressure = Force/Area; Volume=Area x distance;

PV =( F/A)(Ad) = Fd = w

Heat Capacity Defined

An increment of heat, Δq, transferred into a body produces a

proportional incremental rise in temperature, ΔT, given by

Δq = Cp * ΔT

where Cp is called the molar heat capacity of J/mol-degree

at constant pressure; similar to specific heat, which is based

on mass (J/g-degree).

1 calorie = 4.184 J and is equivalent to the energy necessary

to raise 1 gram of of water 1 degree centigrade. Specific heat

of water is 1 cal /g °C, where rocks are ~0.3 cal / g °C.

First Law of Thermodynamics

The increase in internal energy as a result of

heat absorbed is diminished by the amount of

work done on the surroundings:

dE

i

= dq - dw = dq - P d V

By convention, heat added to the system, dq,

is positive and work done by the system, dw,

on its surroundings is negative.

This is also called the Law of Conservation of Energy

Reaction Deltas

Thermodynamics uses well established formalism. One

of the most widespread shorthands is the reaction delta.

the example below is for molar volume change, but it

can be extended to other molar properties and state variables.

Reaction Notation: ΔV = V

final

  • V initial

aA + bB + … = mM + nN + …

r

V = mM + nN + … - aA - bB - …

r

V = V

Al2O3*3H2O

  • V Al2O - 3V H2O

Note that the r subscript

is added to show that

the Δ

r

V corresponds

to a chemical reaction.

The ° superscript is

added to show that the

thermodynamic data are for

standard state conditions.

r

V

°

= V

Al 2 O 3 " 3 H 2 O °

# V

Al 2 O 3 °

# 3 V

H 2 O °

We will do an example on the board.

Additivity of State Variables

State variables may be added or subtracted in order to

calculate the value for a particular reaction, mineral, etc.

C + O 2 = CO 2 !r H ° = "393.509 kJmol

  • 1 CO + 1 2 O 2 = CO 2 !r H ° = "282.984 kJmol
  • 1 Subtracting the reactions - this means reverse the 2nd reaction and change the sign of !r H ° , we get C + 1 2 O 2 = CO !r H ° = "110.525 kJmol
  • 1 This allows us to calculate the enthalpy of formation for CO from C and O 2 , a reaction that is impossible to complete in the lab. The method is extensible to other state variables and molar properties. This of course is appropriate because the thermodynamic state variable’s value, for example the enthalpy of formation ONLY depends on the “state” of the system and not the “path” to reach some specific state.

More on Heat Capacities

Heat capacity is defined

by the amount of heat

that may be absorbed

as a result of

temperature change at

constant pressure.

The concept

can be extended to

enthalpies of formation,

reaction, etc.

dH dT ! "

$ % & P = Cp BASIC FORMAL DEFINITION d'H dT ! "

$ % & P = ' Cp DELTA RULES APPLY d' r H ° dT ! "

$ % & P = ' rCp ° STANDARD STATE RXN MAIER-KELLY EQUATION - T dependence of Cp Cp = a + bT ( cT ( 2 ' rCp ° = ' r a + ' rbT ( ' r cT ( 2

Enthalpy of Melting

580°C