Kinetics

Question 1

Advection Vs. Diffusion

Answer 1

Advection:
Physical movement of a system containing the species.
Examples: river flow, magma rising from the mantle.
Composition remains identical during movement.
Diffusion:
Movement of species without the host phase moving.
Examples: sediment pore water, crystal growth in a melt.
Involves random movement without overall transport.

Question 2

Diffusion Process

Answer 2

Diffusion in a Box:
Ions move randomly in water.
Flux depends on concentration differences.
Equation - Fick’s 1st Law:
Flux (J) is proportional to concentration gradient (dc/dx).
Negative sign indicates movement from high to low concentration.
Real World Example - Oxygen Flux:
Sediment cores with ash layers.
Oxygen depletion due to reactive Fe^(2+).
Calculation of flux across sediment-water interface.
Fick’s 2nd Law:
Describes how concentration changes with time.
Rate of change proportional to diffusion coefficient and second derivative of concentration with respect to distance.
Concentration Profile Evolution:
Linear gradient → Constant flux.
Non-linear profile → Changing flux over time.
Approach to equilibrium as concentration evens out.

Question 3

thin film problem

Answer 3

Scenario:
Rapid deposition of substance on sediments.
Substance diffuses into sediments over time.
Solution - Fick’s 2nd Law:
Concentration at a fixed distance and time.
Initial concentration in the thin film (C0).
Diffusion coefficient (D).
Concentration peak decreases and spreads laterally with time.
Example - Error Function:
Unusual mathematical expression.
Used for initial step function in concentration.
Calculates how concentration profiles change with time.

Question 4

Thermodynamics and reaction direction

Answer 4

Energy Exchange in Reactions:
Energy exchange determines the direction of a reaction.
Calculation of equilibrium constants based on energy exchange.
Sophisticated calculations for redox diagrams.
pH Prediction for Metal Solubility:
Prediction of pH for minimum solubility of metals.
Understanding environmental influences.
Example reaction: organic carbon with oxygen forming CO2 and water.
Challenge to Thermodynamic Predictions:
Despite negative change in free energy, some reactions don’t proceed as predicted.
Focus on reaction speed (kinetics) as the determining factor.
Illustration with organic carbon and oxygen reaction.

Question 5

Kinetics and Reaction speed

Answer 5

Earth’s Atmosphere Reactions:
Illustration with cosmic rays generating free nitrogen atoms.
Reaction of free nitrogen atoms with oxygen to form free oxygen atoms and nitrogen oxide.
Importance of the reaction in ozone formation.
Kinetic factors affecting reaction rates.
Activation Energy (EB):
Neutral species interaction requires overcoming electrostatic repulsion.
Activation energy (EB) defined as the energy barrier.
Need for sufficient energy to overcome repulsion.
Example: gamma rays breaking molecular nitrogen.

Question 6

Activation Energy and Gas molecules

Answer 6

Interaction of Gas Molecules:
Similar reaction between two gas molecules.
Carbon monoxide and nitrogen dioxide forming carbon dioxide and nitrogen monoxide.
Intermediate species (activated complex) with higher energy.
Overcoming energy barrier for the reaction.
Catalysts and Reaction Speed:
Catalysts speed up reactions by lowering EB.
Examples in chemistry for reaction acceleration.
Role of catalysts in lowering activation energy.
Vital role of catalysts in biological processes (e.g., nitrogen-fixing bacteria).

Question 7

Temperature and reaction rate

Answer 7

ffect of Temperature on Reaction Rate:
Higher temperatures provide energy boost to reactants.
Reaction rate expressed as k in chemistry.
Definition of terms: A (constant), EB (activation energy), kB (Boltzmann constant), T (temperature in Kelvin).
Thermodynamic favorability does not guarantee observable reactions on human timescales.
Example: Temperature Impact on Reaction Rates:
Plot of dissolution rates of alumina-silicate minerals vs inverse temperature.
Logarithmic representation of moles of oxygen atoms released during dissolution per square centimeter per second.
Higher temperatures significantly increase dissolution rates.
Similar temperature dependence for various minerals indicates a common mechanism.