React Conceptual Model

Equilibrium in Multicomponent Systems The “basis” Secondary species Mass action Mass balance

— Important Point — Bulk vs. Free Quantities Bulk quantities describe overall composition in terms of the amount of a component distributed throughout the system. For example, the analytical concentration of Na (perhaps in mg/kg) describes the total amount of sodium present in all Na species. Free quantities describe the actual amount or activity of a species, mineral, or gas. For example, the free concentration of Na + includes just the sodium present as the free ion. Example: the bulk amount of quartz in a system would include the mineral plus the amount of silica in solution. The free amount of quartz is the number of moles, grams, or cm 3 of the mineral itself. Commonly used bulk constraints are fluid compositions determined by chemical analysis. Common free constraints are the amounts of minerals in the system, pH, Eh, and gas fugacities.

Tracing a Reaction Path  = 0Initial composition, initial temperature, initial fugacities Solve for equilibrium state  =  Incremental changes in composition, temperature, fugacity Solve for equilibrium state  = 2  Further increment of changes Solve for equilibrium state  = 1Further composition, temperature, fugacities Solve for equilibrium state

Reaction Path Examples — (1) Titration Path Define an initial system on Basis pane Set species to be titrated on Reactants pane This mass of reactant will be added over reaction path

Reaction Path Examples — (2) Polythermal Paths Go to Basis pane Access “temperature” pulldown to see options You can set a sliding temperature path or a mixing path. Or, add a heat source on the Medium pane

Reaction Path Examples — (3) Sliding Activity/Fugacity Paths Define an initial system on Basis pane Set species to slide on Reactants pane CO 2 fugacity will slide from initial value to one

Task 1 — Buffers in Solution Titrate HCl into two alkaline solutions. Consider NaCl and Na 2 CO 3 solutions. How does pH change?

pH CO 3 −− + H +  HCO 3 − HCO 3 − + H +  CO 2 (aq) + H 2 O HCl reacted (moles) NaCl solution Na 2 CO 3 solution

HCl reacted (mmol/kg) Species concentration (mmol/kg) CO 3 −− HCO 3 − NaHCO 3 NaCO 3 − CO 2 (aq)

–1 +1 Slopes-of-the-Lines Method Species concentration (mmol/kg).83 CO 3 −− +.17 NaCO 3 −− + H + .83 HCO 3 − +.17 NaHCO 3.83 HCO 3 − +.17 NaHCO 3 + H +  CO 2 (aq) +.17 Na + + H 2 O HCl reacted (mmol/kg) CO 3 −− HCO 3 − CO 2 (aq) NaCO 3 − NaHCO 3

pH CO 2 (aq) CO 3 -- HCO 3 - NaCO 3 - NaHCO 3 Species concentration (mmol/kg)

Task 2 — Coexisting Minerals as Buffers Pyrite and Hematite in equilibrium. How do pH and oxidation state change when exposed to oxygen? Project reaction trace on Act2 diagram.

O 2 reacted (mmol/kg) FeCl + H+ HSO 4 − Pyrite Hematite Species concentration (mmol/kg) Mineral concentration (mmol/kg) O 2 (aq) Fe ++ SO 4 −−

Fe ++ Hematite Pyrite Troilite Fe +++ FeOH O Fe H 2 O Fe 2 O H O 2 + Pyrite + H 2 O Fe HSO O 2 + Pyrite + H 2 O Fe SO H + 100°C

Task 3 — Gas Buffers Gas reservoir buffers chemistry of natural waters. Consider exhaustible and infinite buffers.

NaOH reacted (moles) pH Fixed CO 2 fugacity Closed system

CO 2 (aq) CO 3 NaCO 3 − 2− Species concentration (mmol/kg) NaOH reacted (moles) Closed System

CO 3 2− NaCO 3 − HCO 3 − NaHCO 3 − NaOH reacted (moles) Fixed CO 2 Fugacity Species concentration (mmol/kg)

Craig M. Bethke and Brian Farrell © Copyright 2016 Aqueous Solutions LLC. This document may be reproduced and modified freely to support any licensed use of The Geochemist’s Workbench® software, provided that any derived materials acknowledge original authorship.