Design of the Experiment and Relevant Background
For a series of boraxcontaining samples taken at various temperatures, the concentration of borate
ion will be determined.
The borate ion reacts with monoprotic acid (such as HCl) in a 1:2 fashion:
B
4
O
5
(OH)
4
2

(
aq
)
+
2HCl(
aq
)
+
3H
2
O(
l
) >
4 B(OH)
3
(
aq
)
+
2 Cl

(
aq
)
The amount of HCl consumed (in L) multiplied by the molarity of the acid gives moles HCl.
It is a trivial
exercise to determine moles borate ion from there, and dividing by the volume of borate ioncontaining
sample in liters gives concentration of borate ion.
This general procedure is repeated for borate ion
containing samples of constant volume obtained at various temperatures.
Calculation of these temperaturedependent values for
K
sp
of borate ion is but the first step in a
greater sequence of obtaining complete thermodynamic parameters for the dissolution of borax in water.
There are several other important thermodynamic parameters that can be found: free energy change,
enthalpy, and entropy, upon further treatment of the equilibrium constant/temperature base data set.
The
next goal will be to estimate the free energy change for this solubility equilibrium.
The following equation
immediately shows the relationship between free energy change (
∆
G
) and equilibrium constant (
K
):
∆
G =

RT ln
K
sp
(A)
A value for the equilibrium constant at a given temperature gives (after a sense) the value for free energy
change directly.
The free energy change at a given temperature is itself related to both the change in
enthalpy, and the change in entropy, by the following equation:
∆
G =
∆
H

T
∆
S
(B)
Combining the two equations relates
K
,
∆
H, and
∆
S in a single statement:

RT ln K
sp
=
=
∆
H

T
∆
S
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The preceding equation can be rearranged into a form that is
linear
.
When rearranged into a linear form,
1/T and ln K
sp
can be used as (x,y) points on a graph.
The slope of such a graph is related to the change in
enthalpy and the change in entropy is related to the yintercept:
A summary of the postdata collection activities reveals the true beauty of this experiment.
Once the
solubility product constants have been determined for 5 different temperatures,
•
A table of free energy values (
∆
G) with the temperatures those values correspond to should be compiled.
This is most conveniently done using equation
(A)
, with values for K
sp
and the temperatures for which they
are valid.
•
A graph of ln K
sp
vs. 1/T should be made, the slope of which is related to change in enthalpy.
•
The same graph has a relationship between change in entropy and its yintercept
The experiment requires that the solubility of borax be found at various temperature values.
Samples of
saturated borax solution are collected at no less than 5 different temperatures, four above room temperature,
and one close to or at room temperature.
These samples are then warmed (if necessary) to redissolve any
precipitated borax, and titrated to the yellow bromocresol green endpoint with standardized aqueous
hydrochloric acid.
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 Fall '12
 professoridon'tknow
 Thermodynamics, Borax, free energy change, borax solution

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