Exp.3 Determination of the Thermodynamic functions
for the Borax Solution
Theory:
The relationship between Gibb’s energy (ΔG), Enthalpy (ΔH), Entropy
(ΔS) and the equilibrium constant (K) for a chemical reaction at a specific
temperature (T), is shown in equation (1) below.
The Gas Constant, R, is equal to 8.314 J/mol·K.
ΔG° = – R T ln K = ΔH° – TΔS° .... (1)
ΔG° (Std. Gibb’s Energy Change), ΔHo (Std. Enthalpy Change) and ΔSo (Std.
Entropy Change) , ΔHo is a measure of the degree of change in the
intermolecular forces and the bond energy for the molecules involved
(Exothermic and Endothermic reactions). ΔS° is a measure of the change in
randomness in the system . ΔGo is negative for any reaction for which ΔHo is
negative and ΔSo is positive , therefore conclude that any reaction for which
ΔGo is negative should be favorable, or spontaneous.
ΔGo < 0
Conversely, ΔGo is positive for any reaction for which ΔHo is positive and
ΔSo is negative. Any reaction for which ΔGo is positive is therefore
unfavorable.
ΔGo > 0
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A process at constant temperature and pressure will be spontaneous in the
direction in which Gibbs energy decreases (–ΔG°). When equation (1) is
rearranged to eliminate ΔG°.
log K = −ΔH° / 2.303RT + ΔS° / 2.303R ......(2)
The solubility of a salt is dependent on the temperature of the solution. When
equilibrium is established in a saturated solution at a specific temperature, the
rate of formation of ions in solution is equal to the rate of deposition of solid.
The equilibrium constant for the dissolution of a solid in a solvent is called
the "solubility product constant" (Ksp). It is equal to the product of the
concentration of ions in solution. Since the concentration of ions can change
with temperature, Ksp is temperature dependent.
Sodium tetraborate decahydrate ("borax") dissociates in water to form sodium
and borate ions and water molecules:
Na2B4O7.10 H2O(s)
2Na+ (aq) + B4O5(OH) 42- (aq) + 8H2O(l)....(3)
And the solubility product (equilibrium) constant, Ksp, is:
Ksp = [Na+]2 [B4O5(OH)42-] ....(4)
Note that two sodium ions are produced for each borate ion (B4O5(OH)42-) in
the reaction.
[Na+] = 2 [B4O5(OH)42-] .....(5)
The equilibrium constant can now be expressed in terms of borate ion
concentration alone by substituting the equality from (5) into equation (4),
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and can be calculated when the borate ion concentration at equilibrium is
determined. Ksp = 4 [B4O5(OH)42-]3 ....(6)
The borate ion is a base, its concentration can be determined by a simple
acid-base titration. The endpoint is signaled by the color change of
bromocresol green or Methyl orange indicator.
B4O5(OH)42- + 2H+ + 3H2O
4B(OH)3 ......(7)
Also If the Equilibrium Constant (Ksp) determined by two different
temperatures, T1 and T2, apply van't Hoff's formulation for the determine the
ΔH°for this reaction :
ln (Ksp2 / Ksp1) = - (ΔH° / R) x (1/T2 - 1/T1) ......(8)
Chemicals and tools:
1. Hydrochloric acid (HCl).
2. Distill water.
3. Sodium tetraborate decahydrate "borax" Na2B4O7.10 H2O
4. Bromocresol green or Methyl orange indicator.
5. Conical flask.
6. Water bath.
7. Burette.
8. Pipette.
9. Thermometer.
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10.Stirrer.
11.Volumetric flask.
Procedure:
1- Prepare 0.5 N in volume 250 ml from HCl solutions in Volumetric
flask and add.to burette .
2- In a 250 mL beaker, dissolve 25g of borax in 50mL of DI water. Heat
with stirring to 60 °C.
3- If all solid dissolves, add a tittle more borax to the solution until a tiny
amount of excess solid is present and the solution is COMPLETELY
SATURATED.
4- Transfer 10 ml of borax solution to conical flask be very careful not
to transfer any of the solid borax from the beaker to the conical flask
and record the exact temperature of the solution.
5- Add 2-3 d of bromocresol green indicator to the conical flask .
6- Add the standard HCl from burette till the end point .
7- Repeat the steps above cooling the solution to 50 and 40 Co .
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Calculations:
Titration
Temperature
40Co
50Co
60Co
Final burette reading
Initial burette reading
Volume of acid used
1- Calculate [B4O5(OH)42-] unknown at different temperatures.
N1 * V1 HCl = N2 * V2 [B4O5(OH)42-]
2- Calculate the Ksp at different temperatures.
3- Draw the equation to calculate ΔH°:
log ksp = −ΔH° / 2.303RT + constant
Temp(K)
Log Ksp
1/T(K-1)
[B4O5(OH)42-]
Log
Ksp
ΔHo
Kj mol-1
ΔGo
ΔSo
KJ mol1-
J mol-1k-1
Slope = –ΔH°/2.303R
Intercept ΔS° / 2.303R
1/T
If the System Exothermic (Spontaneous Reactions)
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