Thermodynamics and solutions

Question 1

Reaction Thermodynamics

Answer 1

Reaction of Carbonic Acid:
Dissociates into protons and bicarbonate.
Known enthalpies and entropies at standard conditions.
Calculations:
Determine reaction direction and energy changes.
Utilize heat capacities and molar volumes.
Equilibrium Constant (K):
Expressions based on activities.
Predicts reactant and product amounts.
Free Energy Changes:
Linked to equilibrium constant.
ΔG = -RT ln(K) or ΔG = -2.303RT log(K).
Gas Constant (R):
Absolute value varies based on calculations.
For gases: J replaced by m³ and Pascals or atmospheres.
Rearrangement for K:
Depending on log base, rearrange equations.
ΔG negative → Reaction proceeds to the right.
ΔG more negative → K increases, favoring products.

Question 2

Calculating K

Answer 2

Reaction:
Proton reacts with HS- anion to form hydrogen sulfide.
Common in marine sediments and hydrothermal fluids.
Steps:
Write equilibrium constant expression.
Calculate ΔG for the reaction.
Rearrange ΔG = -RT ln(K) for K.
Substitute values and units correctly.
Verify dimensionless result.
Interpret K: High value → H2S dominates at equilibrium.

Question 3

Pe-pH Diagram Basics

Answer 3

Coordinate System:
Axes: pH (activity of protons) and pe (activity of electrons).
pH defined as minus the log of proton activity.
pe analogous to pH, representing electron activity.
Reduction and Oxidation Conditions:
Low pe: Reducing conditions, tendency to gain electrons.
High pe: Oxidizing conditions, tendency to lose electrons.
Stability Field of Water:
Area between two diagonal lines.
Above upper line: Oxygen gas formation.
Below lower line: Hydrogen gas formation.

Question 4

geochemical behaviour predictions

Answer 4

Applications of Pe-pH Diagrams:
Predict species speciation under varying pH-pe conditions.
Understand the behavior of elements sensitive to oxidation or reduction.
Example Scenarios:
Prediction of iron species in acidic mine waters (Fe3+) and bog waters (Fe2+).
Temperature Influence:
Diagrams expressed as Eh versus pH for hydrothermal fluids.
Species fields change with temperature; considerations for temperature and pressure in calculations.

Question 5

Aqueous Systems and stability limits

Answer 5

nterest in Water Stability Region:
Focus on pe-pH region where water is stable.
Grey area on the diagram denotes this stability.
Upper Limit: Oxygen Gas Reduction:
Defined by oxygen gas reduction to oxygen in water.
Equations balancing electrons, protons, and oxygen partial pressure.
Equilibrium Constants:
Similar writing to other redox reactions.
Activities of electrons and protons squared; pO2 to the power of 0.5.
Conversion to log functions in equilibrium constant expressions.

Question 6

solid phases and mineral stability

Answer 6

Determining if magnetite or hematite precipitate from iron-bearing solutions.
Equilibrium expression with log K (-5.77).
Sloping red line separates ‘magnetite + water’ and ‘hematite + water’.
Upper stability limit of water shown as a straight line with a slope of -1 and an intercept of 20.78.

Question 7

Dissolution and reduction of Magnetite

Answer 7

Equilibrium Expression:
Shows that the activity of dissolved Fe2+ influences the stability field of magnetite.
Position of line between ‘magnetite + water’ and ‘Fe2+’ varies with the activity of dissolved Fe2+.
Larger stability field for higher Fe2+ activity.
Influence of Concentration:
Solid phases precipitate more readily from concentrated solutions.
Calculations involve assuming or measuring the activity of dissolved Fe in the solution.

Question 8

Lower stability limit for water

Answer 8

Equilibrium Expression:
Describes the reduction of H+ in water to hydrogen gas.
Activity of pure H2 is 1 (log zero).
Change in free energy is zero.
Rearranging the equation to relate pe and pH.