Chem 257
Experiment 4
Thermodynamic Parameters from the Variation of an Equilibrium Constant with
Temperature:
The Solubility of Salicylic Acid
This experiment will be done in pairs.
A fundamental equation of thermodynamics chemistry is the
Gibbs Equation
:
∆
G =
∆
G° + RT ln Q
(i)
aA + bB ↔ cC +dD
Q = [a
C
]
c
[a
D
]
d
/[a
A
]
a
[a
B
]
b
Q = [C]
c
[D]
d
/[A]
a
[B]
b
where the a refers to activity of a species and [C], [D] etc are the actual concentrations
(activities) at some point in the reaction.
The reaction quotient Q equals the activity of
products raised to the power of their stoichiometric coefficients divided by the activities of
the reactants raised to their stoichiometric coefficients,
In this experiment, the activities are
replaced by their concentrations since these solutions are dilute.
Activities of solids are
1.000.
A process is spontaneous , ie. goes toward more products, if the Gibbs Free Energy is
negative. The process is at equilibrium, if
∆
G is zero.
If
∆
G is positive, the reaction actually
proceeds toward reactants, ie. backwards.
At equilibrium, the reaction quotient, Q, has changed to the value of the equilibrium
constant, K, and
∆
G
is zero, resulting in equation (ii)
∆
G° = - RT ln K
(ii)
The change in Gibbs Free Energy in the standard state is related to temperature, enthalpy
and entropy by equation (iii)
∆
G° =
∆
H° - T
∆
S°
(iii)
Equations (ii) and (iii) can be combined to give (iv):
ln K = -
∆
H°/RT +
∆
S°/R
(iv)
Equation (iv) describes the variation of the equilibrium constant as a function of
temperature.
Given a number of measurements of K at different temperatures, and
assuming
∆
H° and
∆
S° are independent of temperature, the thermodynamic parameter
∆
H°/R can be obtained from the slope respectively of a plot of ln K vs
. T
-1
and
∆
S° from the
intercept.
T is Kelvin and T=273.15 + t(
0
C).
Note that this is the natural logarithm, not log
base 10.
In this way
∆
H° for a chemical reaction can be determined without calorimetric
measurements.
The assumption that
∆
H° and
∆
S° are temperature invariant is true if
∆
C
p
=
0, i.e. there is no change in heat capacity, C
p
, between reactants and products or if the
temperature range is somewhat limited.
Although it is seldom exactly zero,
∆
C
p
is often
small.
Experimentally one would expect to see non-linear plots of ln K vs
. T
-1
if
∆
C
p
0.
In this experiment we will measure the equilibrium constant of a solubility
equilibrium, that of salicylic acid (I) in water, as a function of temperature and fit the results
to equation (iv) in order to determine
∆
H° and
∆
S° for the dissolution process.
At a temperature, T,
I
(s) dissolves until it reaches its equilibrium concentration.