Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
An overview of the kinetics of mineral-solution reactions and rate laws in physical chemistry. It covers the forward and reverse reaction rates, reaction rate laws for elementary reactions, and the integration of rate laws. The document also discusses the concept of half-life and its application to mineral recrystallization, precipitation/dissolution, hydrolysis, gas dissolution, adsorption, and ion complexation.
Typology: Slides
1 / 9
This page cannot be seen from the preview
Don't miss anything!
Page ‹#›
Physical Chemistry of Minerals and Aqueous
Solutions
Consider a simple reaction:
The rate of the forward reaction is
f
r
The rate of the reverse reaction is
Page ‹#›
Rates of Chemical Reactions
At equilibrium, the rates are equal:
f
r
The equilibrium constant is
eq
f
r
Reaction Rate Laws In General
In general, for an elementary reaction
aA + bB → cC + dD
the rate of the reaction (neglecting back reaction) is
!
R = "
1
a
d [ A ]
dt
= "
1
b
d [ B ]
dt
=
1
c
d [ C ]
dt
=
1
d
d [ D ]
dt
= k f
[ A ]
a [ B ]
b
where n = a + b is the order of the reaction.
Page ‹#›
Integrating Rate laws (cont)..
!
ln
[ A ]
[ A ] 0
"
$
%
&
' = ( k f
t
!
d [ A ]
A [ A ] 0
A
" = # k f
dt
0
t
"
!
[ A ] = [ A ] 0
e
" k f t
Now we integrate both sides. We have our initial
condition that at t = 0, [ A ] = [ A ] 0
Half-Life
The half-life of A is the time it takes for half of A
to disappear (no reverse reaction):
If
!
A = A o
e
" k f t
Then when A = A 0
1/ 2
f
Page ‹#›
Half-Life
10
6 Mineral Recrystallization years
10
4 Precipitation/Dissolution years
Hydrolysis 1 hour-day
Gas dissolution <1 day
Adsorption <1 hour
Ion complexation <1 sec
Process Half-life
Transition State Theory: Temperature
Dependence of Reaction Rate
B
"# G
‡ / RT
Page ‹#›
Transition State Theory: Reaction Rate
and Disequilibrium
!
Rate forward
Rate reverse
=
e
"# G f
± / RT
e
"# G r
± / RT
= e
"# G / RT
!
Rate net
= Rate forward
(1" e
"# G / RT )
!
Rate net
= Rate forward
(1"
Q
K
)
Since Δ G = Δ G
‡ f
‡ r
Empirical Rate Laws..
For most reactions, the elementary steps are not known.
Empirical rate laws have been measured, however. For
example the dissolution of gypsum:
CaSO 4
2
O (gypsum) → Ca
2+
2-
has the rate law (Langmuir and Melchior, 1985):
w
With k = 3.1x
2 -s, A w
= wet surface area (m
2 )
exposed to a kg of water.
Page ‹#›
Implementation in PHREEQC
RATES
Gypsum
-start
1 A0 = parm(1)
2 V = parm(2)
10 rate = (A0/V)(m/m0)^0.67 * 3.110^-8 * (1-SR("Gypsum"))
20 save rate * time
-end
First, we need a “RATES” block to define the rate law for
the dissolution of gypsum:
Some of these are in the databases and don’t need to be
defined; however, you need to look at them to check which
parameters are needed in the KINETICS block...
Implementation in PHREEQC
KINETICS 1
Gypsum
-formula CaSO4 1.
-m0 0.43! Initial number of moles
-parms 0.5 1! Init. surface area (m2), V (L)
-tol 1e-
-steps 1.0E6 2.E6 3.0E6 4.0E6 !times in seconds
-runge_kutta 6
We call the RATES block with a KINETICS block which
specifies the initial parameters for that particular cell:
