Calorimetry
• Measurement of heat flow (through
temperature) associated with a reaction
• Because dH = q / dT, measuring
Temperature change at constant P yields
enthalpy
Problem
When 50.mL of 1.0M HCl and 50.mL of 1.0M NaOH are mixed in a calorimeter, the
temperature of the resultant solution increases from 21.0oC to 27.5oC. Calculate
the enthalpy change per mole of HCl for the reaction carried out at constant
pressure, assuming that the calorimeter absorbs only a negligible quantity of
heat, the total volume of the solution is 100. mL, the density of the solution is
1.0g/mL and its specific heat is 4.18 J/g-K.
qrxn = - (cs solution J/g-K) (mass of solution g) (DT K)
= - (4.18 J/g-K) [(1.0g/mL)(100 mL)] (6.5 K)
= - 2700 J or 2.7 kJ
DH = 2.7 kJ
Enthalpy change per mole of HCl = (-2.7 kJ)/(0.050 mol)
= - 54 kJ/mol
Hess’s Law
Known values of DH for reactions can be used to
determine DH’s for other reactions.
DH is a state function, and hence depends only on the
amount of matter undergoing a change and on the
initial state of the reactants and final state of the
products.
If a reaction can be carried out in a single step or
multiple steps, the DH of the reaction will be the same
regardless of the details of the process (single vs multistep).
CH4(g) + O2(g) --> CO2(g) + 2H2O(l)
DH = -890 kJ
If the same reaction was carried out in two steps:
CH4(g) + O2(g) --> CO2(g) + 2H2O(g)
DH = -802 kJ
2H2O(g) --> 2H2O(l)
DH = -88 kJ
CH4(g) + O2(g) --> CO2(g) + 2H2O(l)
DH = -890 kJ
Net equation
Hess’s law : if a reaction is carried out in a series of steps,
DH for the reaction will be equal to the sum of the enthalpy
change for the individual steps.
Determining Entropy
• As for H, dS=q/dT  can be measured as
heat energy (q)
• Another way to think of entropic energy –
for any reaction, energy is ‘dispersed’
to/from the surroundings –measured from
0K (actually just close to it), where S0=0 for
ANY substance (at 0 K, atoms do not
MOVE!)
• S0 for water = 69.9 J/mol
Entropy detemrination
• S0 for water = 69.9 J/mol
– 0 K to 298 K what happens to water?
– Heats up, changes phase (ice-ice  liquid)
– 69.9 joules/mol is a very small part of that
energy!
• How to evaluate that small heat change –
CAREFULLY determine Cp over this range
in incremental steps to subtract H
component
Theoretical estimations
• In natural systems, there are many species,
minerals, gases that are very difficult to
impossible to determine with any accuracy
by experiment
• Correlation methods based on isostructuralisovalent analogues, electrosatic models,
ligand field models exist, but are based on
empirical evidence and have little grounding
in theory – thus these often suffer from
innaccuracy (if that is even known!)
Theoretical determinations
• Ab initio (first principles) calculations
based on electron energy (complicated
rules for ESTIMATING this) can be used to
determine enthalpy, entropy, Gibbs energy
from a molecular basis
Determining K - Titrations
• Especially important in acid-base equilibrium
constants
[ A][ H  ]x
K
[ H x A]
[ MOH z 1 ][ H  ]
Ka 
Mz
 
12
11
10
9
pH
8
7
6
5
Carbonate titration
4
3
2
0
5
10
15
20
25
30
35
40
45
50
NaOH reacted (mmoles)
Greg Wed Oct 06 2004
Voltammetric titrations
• Can use voltammetry to meausure acid-base
reactions for electroactive species
– HS- + Hg = HgS + H+ + 2e– H2S + Hg = HgS + 2 H+ + 2e-
 
  



RT
HS
E  E0  
ln 

nF
H


– Where E is Ep from the analytical peak, E0 is the
formal potential, n is # e-’s, F is Faraday’s constant
– Plot of Ep vs. pH gives a slope proportional to H+
complexed to sulfide
Voltammetry for complexes
• DeHume and Ford formalism
– nM + L  [Mn(L)]
n 
M n L
M n L
• Stability constants can be fit from the relation:
– F0(X)=SBn[X]n=B0 + B1[X] + B2[X]2 + … + Bn[X]n
where F0(X) is a polynomial function representing
Bn=overall stability constant of the nth complex, [X]
is the added species (such as M)

 log( I p ) s  
nF 


F ( X )  anti log 0.434
[
D
E
]



p

RT
(
I
)



p c 



0
Where c is the complexed ion and s is the free ion, Ip
is the peak current, DEp=(Ep)s-(Ep)c, n=#e-s in rxn
Voltammetric titrations
• Can also titrate sulfide or metal into an
electrochemical cell and measure the
changes in free species associated with
complexation
• Competetive coomplexation approach –
where one species is displaced from a
weaker complex as a titrant is added
• Mole ratio approach -
Error in thermodynamic data
• There can be significant error in the
thermodynamic data used in different databases.
• For example, DG0 Fe2+ data was evaluated at 78.8 KJ/ml for a long time, recently re-evaluated
at -89.9 KJ/mol…
• One program, PHREEQC, has a function built in
to evaluate equilibrium values for minerals using
+/- 10% on the thermodynamic data used
(KNOBS…)
Calculating uncertainty
• Because so much of what we use in
thermodynamic databases is additive, the
general accumulation of error is estimated:
• σx=(a2σx2++ b2σx2++…)1/2
• BUT – that assumes none of the values are
directly related, which reduces the error (i.e. if 2
equations share the same data the error is not
additive for the same species…)
Thermodynamic Database
Consistency
1.
2.
3.
4.
5.
6.
Data consistent with thermodynamic relationships
(appropriate basic laws and consequences)
Common scales used for T, energy, mass, physical
constants
Conflicts between different reports for same data are
resolved
Same mathematical model used to fit data from
different sets
Same chemical model is used to fit data from different
sets
Appropriate standard states are used, and consistently
applied throughout
From Nordstrom and Munoz (1994; p. 370)
log Keq
• CaCO3(calcite) = Ca2+ + CO32-
-8.48
• CO2(g) + H2O = H2CO30
-1.47
• H2CO30 = H+ + HCO3-
-6.35
• H+ + CO32- = HCO3-
+10.33
CaCO3(calcite) + CO2(g) + H2O = Ca2+ + 2 HCO3-
-5.97
Another way to do this is to simply combine the Keq data algebraically:
K eq 
K calciteK CO2 K1
K2
Still another way is recompute the DG0R for the reaction
of interest and calculate Keq
What does a database look like?
2.0000 H2O + 1.0000 O2 + 1.0000 Mn++ = MnO4-- +4.0000 H+
-llnl_gamma
4.0
log_k
-32.4146
-delta_H
151.703
kJ/mol # Calculated enthalpy of
reaction
MnO4-2
# Enthalpy of formation:
-156 kcal/mol
-analytic -1.0407e+001 -4.6464e-002 -1.0515e+004 1.0943e+001
-1.6408e+002
#
-Range: 0-300