7/8) Activity of aqueous species & Solubility and saturation states

what are the standard states defined as?

298.15K and 1 bar

gas: 1 atm ideal gas
liquid: pure liquid
solid: pure solid (not a solid solution)
solvent (liquid or solid): pure solvent
solute: 1 mol/kg (rarely do we have 1 mol of anything)

these are ideal conditions

when y=1 and x=1

what are the reference states defined as?

where the activity coefficient is equal to unity (unity=1) (y=1)

liquid: pure liquid
solid: pure solid
solvent (liquid or solid): pure solvent
solute: infinitely dilute 1m solution (as if activity coefficient is 0

the solute reference state is by definition impossible, you can’t be infinitely dilute (have nothing in solution) and also have 1 molal. it’s done to make the math easier (divide by 1 instead of nanomolals)

what can cause activity to not equal concentration?

electrostatic shielding

aqueous complexes

what does electrostatic shielding depend on? how is it accounted for?

ionic strength of solution and the size/charge of the ion itself

tiny and high charge = significant interactions with other ions

accounted for by activity coefficients

what do aqueous complexes depend on? how are they accounted for?

strength of the complexes and concentration of the complexing agent

if you have a ton of sodium and chlorine in solution, more of them will be in complexes just because there is a larger concentration of them in solution

accounted for by speciation

explain distance of closest approach

how close ions can get to other ions

caused by water molecules orienting themselves around a charged ion due to their polar nature. and much more water than ions in a solution (96%)

causes decrease in effective charge and increase in apparent size (hydrated radius)

higher charge _____?

higher charge attracts more solvent

increased hydrated radius ___?

reduces ability of ions to interact with each other, lowers the activity of an ion in solution

results in less solvent attracted (charge is more diffuse)

what is activity in simple terms

what proportion of the ion is actually doing reactions

what is activity coefficient

a translator between activity and concentration
thermodynamics speaks in activities, but we can only measure concentrations

varies between 1 and 0
as concentration decreases, the solution becomes more ideal (because we defined the reference solution to be infinitely dilute

what is ionic strength?

equation

what most influences ionic strength?

measure of total charge in a solution

I = ½ sum of all molar concentrations*charge²

charge really really affects ionic strength

details of variables in B-dot (DH) equation

Ay and By are calculated from physical constants (to do with water)

Anaught: distance of closest approach

Bdot: temperature dependent correction factor to allow debye-huckel to work in solutions with elevated ionic strength

DH works better at higher temps

explain the matlab example of different charges

higher charges decrease in activity much quicker than lower charges

if Anaught (distance of closest approach) is smaller, then H+ has lots of water guarding it, so other ions can’t attack because it’s guarded. and K+ has less water, so other ions can attack more readily, activity goes down quicker.

explain this

charge has a bigger different than size, so lines cluster in the charges (pos/neg doesn’t matter it’s squared)

strongest effect on polyvalent ions (in different clusters)

how does DH compare to measured values?

good job on any temperature up to 3 molal solutions, and predicts act coeffs up to IS=1

does not predict 6 molal below 150°C

works better in concentrated solutions at high temp

what are the activity coefficients of dissolved gases like?

they increase as ionic strength increases, starting at >1

none of them have act coeff of 1 at high IS

all neutral species behave this way

what is “salting out”

gamma(CO2(aq)) increases with increasing IS

KH = gammaCO2(aq) * m CO2(aq) / fCO2

KH and fCO2 are still fixed, so mCO2(aq) must be decreasing

as we add salt, CO2 goes out of solution

how to calculate saturation index

sat ind: Q/K

Q: (gammaCa2+ * mCa2+) * (gammaCO32- * mCO32-) / calcite

K: {Ca2+}*{CO32-} / calcite

ionically bound minerals such as ___, and sulphate minerals such as ____, have simple solubility relationships which are (almost) ____

halite

gypsum

independent of pH

solubility of halite is basically the same whether pH is 2 or 10

solubility in simple terms

the concentration of the species in solution

the amount of a mineral that can be dissolved in water

the sum of all relevant species

halite solubility simplified

Ksp = {Na+}*{Cl-} / {NaCl(s)} = {Na+}*{Cl-} = {Na+}² = {Cl-}²

simplify first because {NaCl(s)} = 1 and then {Na+} = {Cl-} when we dissolve halite in pure water

explain solubility product constant Ksp

when multiplied together, activities of Na+ and Cl- give a constant value solubility product constant, Ksp

one of the ions can be really high an dhte other very low, all we know is that the product gives the Ksp value, for halite Ksp=36
log Ksp = log{Na+} + log{Cl-} = 1.55

what is importance of Rimstidt data

14 year experiments to determine quartz solubility

databases are systematically offset now

we know ∆G because we know K (∆G = -RTlnk)

explain the solubility of quartz as it relates to pH

not pH dependent below pH=9

after pH=9, solubility increases quickly

reaction H2O + SiO2 <-> HSiO3 + H+ pka =9.8

most natural water’s don’t have pH above 9.8, so doesn’t matter, but if pH is that higher, then solubility also depends on other ions (HSiO3- and H2SiO42-)

explain solubility of SiO2 (quartz) 1st dissociation

SiO2 is an acid, dissociates at high pH first into HSiO3 then to H2SiO42-

reaction: K = H+ * HSiO3- / SiO2(aq) *H2O
increasing pH, H+ does down, SiO2(aq) is constant, so HSiO3- must increase (linearly bc H+ decreases linearly), slope=1

T/F: The solubility of SiO2(aq) is constant with increasing pH

true

explain solubility of SiO2 (quartz) 2nd dissociation

H4SiO4 is an acid, dissociates at high pH first into H3SiO4- then H2SiO42-

reaction: K = H2SiO42- * H+ / HSiO3- * H2O

increasing pH, H going down, HSiO3- is still going up (now in denominator), H2SiO4 must go up 2x, slope=2

what is saturation state?

what is saturation index?

equilibrium of mineral in water
compares ion concentrations with the solubility product

index is log of saturation state

is calcite more or less soluble with increasing pH?

less

explain the states of saturation state

more than 1: supersaturation, system driven towards precipitation

less than 1: undersaturation, system driven towards dissolution

omega: cannot be negative

explain the states of saturation index

more than 0: supersaturation, system driven towards precipitation

less than 0: undersaturation, system driven towards dissolution

details on undersaturated solutions

Q/K = ({Ca2+}*{SiO42-} / K) <1

we need to dissolve more CaSO4 to have enough Ca2+ and SO42- to be in eqlm
need to raise Q to get to eqlm

details on supersaturated solutions

Q/K = ({Ca2+}*{SiO42-} / K) >1

we would need to remove CaSO4 in solution to have less Ca2+ and SO42- from solution to be in eqlm. We have too much Ca2+ and SO42-

T/F: saturation states indicate thermodynamic drive and how quickly it proceeds

false, does indicate thermodynamic drive, but not when the reaction will proceed. that’s kinetics

mystery of dolomite

logQ/K = 3.025, so 10³

it’s very super saturated, but it’s not precipitating in natural environments

rate of reaction is ridiculously low, about 800 years to see 10% growth in dolomite

explain how complexes change solubility

complexation lowers the activity of free ions, and increases the solubility of minerals

CaSO4 is a SOLUTE, not solid

K = CaSO4 / Ca2+ * So42- = 10^(2.5)

perrier water example

3.5 L of CO2 per L H2O
3.5 ×0.043molCO2/LCO2 = 0.1505 mol/L CO2

ambient is 0.8 L CO2 per L H2O
0.8×0.043molCO2/LCO2 = 0.0344 mol/L CO2

3.5/0.8= 4.3. 4 times too much CO2 in perrier than ambient CO2