The thermodynamics of the solubility of borax

```The thermodynamics of the
solubility of borax
Determination of ΔH&deg; and ΔS&deg;
• Borax has the formula Na2[B4O5(OH)4].8H2O
Borax
• [B4O5(OH)4]2- is the tetra-borate anion
• Borax is a weak base and reacts with acid
Na2B4O7&middot;10H2O + 2 HCl → 4 H3BO3 + 2 NaCl + 5 H2O
• H3BO3 is the conjugate acid (Boric acid) which as a pH around 4 or
so depending on the molarity
• It is a good water softener
Ca2+ (aq) + Na2B4O7 (aq) → CaB4O7 (s)↓ + 2 Na+ (aq)
Mg2+ (aq) + Na2B4O7 (aq) → MgB4O7 (s)↓ + 2 Na+ (aq)
Purpose
• To determine the thermodynamic quantities ΔH&deg; and ΔS&deg; ,for the solvation
reaction of borax in water
Na2[B4O5(OH)4].8H2O(s) ↔ 2 Na+ (aq) + [B4O5(OH)4]2- (aq) + 8 H2O (l)
• by measuring the solubility product constant, Ksp, over the temperature
range 50−15&deg;C
2&eacute;
K sp = &eacute;&euml; Na &ugrave;&ucirc; &euml; B4O5 (OH )4 &ugrave;&ucirc; = e
+ 2
DH o DS o
+
RT
R
• The temperature dependence of the equilibrium constant Ksp depends on
the enthalpy of solvation ΔH&deg; and the entropy of solvation ΔS&deg;
What is ΔS&deg; ?
Imagine the solvation is an elementary step reaction
• Na2[B4O5(OH)4].8H2O(s)
Eaf
RT
k1 A1e
A1
K sp =
=
= e
Eab
k-1
A2
RT
A2 e
-
2 Na+ (aq) + [B4O5(OH)4]2- (aq) + 8 H2O (l)
(Eaf -Eab )
RT
A1
= e
A2
-
DH o
RT
=e
-
DH o DS o
+
RT
R
f
Ea
A1
=e
A2
DS o
R
&aelig; A1 &ouml;
or DS = R &times; ln &ccedil; &divide;
&egrave; A2 &oslash;
o
b
Ea
What is ΔS&deg; ?
ΔS&deg; is called the entropy of solvation we can see it is somehow related
to the ratio of the collision factors for reaction in the forward and
backward direction
If A1 &gt; A2 ΔS&deg; &gt; 0
A1
=e
A2
DS o
R
&aelig; A1 &ouml;
or DS = R &times; ln &ccedil; &divide;
&egrave; A2 &oslash;
If ΔS&deg; &gt; 0 we say that process is spontaneous, it means that it is more
probable for the reactants to come together to react, than for the
products to come together and react to make reactants
What is ΔS&deg; ?
Consider what happens when the borax solid dissolves in water?
When the orange particles dissolve in water two things can happen
• can hang around near the crystal and potentially re-attach themselves
• they can move off further away from the crystal
It’s like reaching a crossroad where the road is going 4 ways. You
randomly choose a road – 3 take you further away and 1 takes you
back
What is ΔS&deg; ?
• You are 3 times more likely to leave than return home
• In the same way when borax dissolves there are more choices
which take it into solution than back to solid
• In this case A1 &gt; A2 ΔS&deg; &gt; 0
• Entropy is measuring the number of choices available to the system
Objective: knowing Ksp(T)
• If we know the quantities ΔH&deg; and ΔS&deg; then we now how the
equilibrium constant changes with T
DH o DS o
+
RT
R
2&eacute;
&eacute;
&ugrave;
K sp = &euml; Na &ucirc; &euml; B4O5 (OH )4 &ugrave;&ucirc; = e
• Make saturated solutions of borax in water at different
temperatures
• Measure the concentration of the tetraborate x=[B4O5(OH)4]2- in
the solution (by titration)
• Determine Ksp at that temperature T using Ksp = 4x3 (ICE table)
+ 2
Objective: knowing Ksp(T)
• Plot the ln(Ksp) vs 1/T (where T is in Kelvin)
• Should give a straight line graph
( )
ln K sp
y
• Where
DH o &aelig; 1 &ouml; DS o
=&ccedil;&egrave; &divide;&oslash; +
R T
R
= m i x + b
DH o
slope = R
DS o
intercept =
R
Preparing a Saturated Borax Solution
thermometer
20 g Borax in 80 mL of
deionized H2O
Stirrer and hotplate
• Heat to 52oC-55oC DO NOT LET IT GET ABOVE 55oC
• Leave it at 52oC-55oC for 30 mins
• While it is heating use a pipette to measure precisely 5.00 mL of water into each of
six small test tubes and mark the levels with a wax pencil
• Label the test tubes ~ 50&deg;, ~ 45&deg;, ~ 35&deg;, ~ 30&deg;, ~ 20&deg;, and ~15 &deg;C
• After 30 mins remove the beaker from hot plate
• As it cools decant 5 mL into test tubes at ~ 50&deg;, ~ 45&deg;, ~ 35&deg;, ~ 30&deg;, ~ 20&deg;, and ~15 &deg;C
• Record the actual temps to nearest 0.1oC
Standardized HCl Solution
• While 2 students are making the saturated solutions and
marking test tubes, the other student(s) will make a
standardized HCl solution for later titrations
• In a fume hood, add 8 mL of concentrated HCl to about 400mL
of distilled Water in a 500mL Erlenmeyer Flask. Stir well. This
gives a solution of approximately 0.2M HCl.
• To determine the exact concentration of the HCl in the
solution, we will titrate it against a base Na2CO3 whose mass
can be accurately measured and whose endpoint is pH=4
• Na2CO3(aq) + 2 HCl(aq)  2 NaCl(aq) + H2CO3(aq)
• Since the endpoint is at pH = 4 we use bromocresol green
Standardized HCl Solution
HCl to Standardize
endpoint
0.15 g anhydrous Na2CO3
50 mL deionized water
12 drops of bromocresol green indicator
Standardization
Na 2CO 3 (s) + 2HCl(aq) &reg; 2NaCl(aq) + H 2CO3 (aq)
moles HCl = g Na 2CO 3 &acute;
[HCl] =
1 mole Na 2CO 3
2 mole HCl
&acute;
105.9888 g Na 2CO 3 1 mole Na 2CO 3
moles HCl 1000mL
&acute;
V (mL)
1L
Calculation of Ksp
B4O5 (OH )4 2- + 3H 2O + 2HCl &reg; 4H 3 BO3 + 2Cl moles HCl = M HCl &times;V (mL)&times;
moles B4O5 (OH )4 2-
moles HCl
=
:
2
1L
1000mL
2moles
B
O
(OH
)
4 5
4
&eacute;&euml; B4O5 (OH )4 2- &ugrave;&ucirc; =
=x
-3
5.00 &acute; 10 L
K sp = 4x 3
Getting ΔH&deg; and ΔS&deg;
• Plot ln(Ksp) vs 1/T where T is in Kelvin
• ΔH&deg; = -slope x 8.314 J/mol/K
• ΔS&deg; = intercept x 8.314 J/mol/K
```