EXPERIMENT 1 : CHANGE OF STANDARD GIBBS FREE ENERGY FOR THE DECOMPOSITION OF SODIUM HYDROGEN CARBONATE

OBJECTIVETo determine the change of standard Gibbs free energy for the decomposition of sodium hydrogen carbonate from the change of standard enthalpy and the change of standard entropy.

INTRODUCTIONGibbs free energy combines enthalpy and entropy into a single value. The change of free energy is equal to the sum of its enthalpy plus the product of the temperature and entropy of the system. ΔG can also predict the direction of the chemical reaction. If ΔG is positive then the reaction is non-spontaneous. If it is negative, then it is spontaneous.In 1875, Josiah Gibbs introduced a thermodynamic quantity combining enthalpy and entropy into a single value called Gibbs free energy. This quantity can be defined as:

G=H−TSG=U+PV−TS

where U = internal energy (SI unit: joule) P = pressure (SI unit: pascal) V = volume (SI unit: m3) T = temperature (SI unit: kelvin) S = entropy (SI unit: joule/kelvin) H = enthalpy (SI unit: joule)

Gibbs Free Energy (G) - The energy associated with a chemical reaction that can be used to do work.  The free energy of a system is the sum of its enthalpy (H) plus the product of the temperature (Kelvin) and the entropy (S) of the system:

G=H−TSFree energy of reaction (ΔG)In chemical reactions involving the changes in thermodynamic quantities we often use another variation of this equation:

[1]

 The sign of delta G can allow us to predict the direction of a chemical reaction:

 

Terminology:

If ΔH  < 0 and  ΔS  > 0  then the reaction will be SPONTANEOUS (ΔG  < 0 ) at any temperature. If ΔH  > 0  and entropy ΔS  < 0  then the reaction will be NON SPONTANEOUS (ΔG  > 0 ) at any

temperature.

Standard-state free energy of reaction ( G )

The free energy of reaction at standard state conditions:

By determining the quantity of ∆ H ° experimentally according to Hess’s Law and extraction of

∆ S° from the standard data, ∆G° of the reaction can be estimated easily.

In our experiment, a double vacuum stainless steel calorimeter is used to measure the heat released or absorbed by decomposition of NaHCO3 . the thermo chemical equation for the decomposition of NaHCO3 (s) is

2NaHCO3 ( s )→Na2CO3 (s )+H 2O( l)+CO2(g)However in the laboratory, the quantity of∆ H ° of NaHCO3 (s) cannot be determined directly.

Instead, two separate experiments in determining the quantities for ∆ H ° for the reaction of

NaHCO3 (s) and Na2CO3 (s ), respectively with H 2SO4 (aq) are carried out. Hess’s law is applied in

estimation of ∆ H ° of NaHCO3 (s) .

The reaction are as follow :

2NaHCO3 ( s )+H 2SO4 (aq )→Na2CO4 (aq )+2CO2 (g )+2H 2O (l )∆H 1θ : y KJ mol−1

Na2CO3 (s )+H 2SO4 (aq )→Na2CO4 (aq )+CO2 (g )+H 2O (l )∆H 2θ: z KJ mol−1

A simple double-wall vacuum steel calorimeter is used for determining the quantity of ∆ H θ. It may

serve as the constant-pressure calorimeter (at atmospheric pressure under the experimental conditions).The enthalpy (H) is defined as

H = U + PV

A simple double-wall vacuum steel calorimeter is used for determining the quantity of ∆ H θ. It may

serve as the constant-pressure calorimeter (at atmospheric pressure under the experimental

conditions).

The enthalpy (H) is defined as

H = U + PV

A change in enthalpy is equal to the heat supplied at constant pressure to a system in the case

where the system does no additional work.

dH = dq

For measurable change,

∆ H=q p

A known amount of NaHCO3 (s) or Na2CO3 (s) is added to an excess of H2SO4 (aq) and the change in temperature (∆T ) is measured. The heat released or absorbed by each reaction (q p) is calculated

by using the formula :

q p=mCp∆T

Where m denotes mass of the solution (in unit g) in the calorimeter by assuming no change in the volume of the solution and the density of the solution is 1 g mL -1 and C p (specific heat capacity of

the solution at constant pressure) = 4.18 J g -1 ℃-1. Express quantity q p in unit kJ. The quantity C p for the double-wall vacuum stainless steel calorimeter is small and any heat absorbed is negligible. Quantity ∆ H θ is negative for exothermic reaction (increase in temperature during the experiment) and is positive for endothermic reaction (decrease in temperature during experiment).

CHEMICALS

Sodium hydrogencarbonate, NaHCO3

Sodium carbonate, Na2CO3

1 M sulphuric acid, H2SO4

APPARATUS50 mL clear glass volumetric pipette250 mL double-wall vacuum stainless steel calorimeter with double-wall cover

General purpose and mercury filled thermometer 0 – 100 ℃, gradually every 1℃100 mL beakerStopwatch

PROCEDURE

1. 4.0 to 4.5 g of NaHCO3 was measured exactly.2. 50 mL of 1 M H2SO4 was transferred into the double-wall vacuum stainless steel calorimeter

using a volumetric pipette. The cover of the double wall and the thermometer were replaced.

3. The temperature of H2SO4 was recorded for every one minute for 4 minutes. At the 5th, the NaHCO3 was quickly transferred into the H2SO4 .

4. The cover was replaced and the content in the calorimeter was being stirred carefully using thermometer.

5. The temperature was recorded for the next 4 minutes every 10 seconds.6. Step 1 to 5 was repeated with 3.0 to 3.5 g of Na2CO3

RESULT

Mass of NaHCO3 : 4.4309 gMass of Na2CO3 : 3.2432 g

Room temperature : 28.5 ℃

NaHCO3 with H2SO4 Na2CO3 with H2SO4

Time (s) T(℃) Time (s) T(℃)60 30 60 29

120 30 120 29180 30 180 29240 30 240 29310 25 310 30320 25 320 30330 25 330 30340 25 340 30350 25 350 30360 25 360 30370 25 370 30380 25 380 30390 24 390 30400 24 400 30410 24 410 30420 24 420 30430 24 430 30440 24 440 30450 24 450 31460 24 460 31470 24 470 31480 24 480 31490 24 490 31500 24 500 31510 24 510 31520 24 520 31530 24 530 31540 24 540 31

CALCULATION

Heat change of NaHCO3 with H2SO4

q p=mCp∆T

q p=4.4309g×4.18J g−1℃−1× (−6℃ )

q p=−111.13 JNa2CO3 with H2SO4

q p=mCp∆T

q p=3.2432g×4.18 J g−1℃−1× (2℃ )

q p=27.11 J

2NaHCO3 ( s )+H 2SO4 (aq )→Na2CO4 (aq )+2CO2 (g )+2H 2O (l )∆H 1θ : y KJ mol−1

Na2CO3 (s )+H 2SO4 (aq )→Na2CO4 (aq )+CO2 (g )+H 2O (l )∆H 2θ: z KJ mol−1

∆ H 1θ : y KJ mol−1

∆ H 1θ :−111.13 J ( 1kJ1000 J )÷83.99mol

∆ H 1θ :−1.323k J mol−1

∆ H 2θ : z KJ mol−1

∆ H 2θ :27.11 J ( 1kJ

1000J )÷105.99mol∆ H 2

θ :0.256k J mol−1

2NaHCO3 ( s )+H 2SO4 (aq )→Na2CO4 (aq )+2CO2 (g )+2H 2O (l )∆H 1θ :−1.323kJmol−1

Na2CO4 (aq )+CO2 (g )+H 2O (l )→Na2CO3 (s )+H 2SO4 (aq )∆H 2θ:−0.256KJ mol−1

2NaHCO3 ( s )→Na2CO3 (s )+H 2O( l)+CO2(g)

∴∆ H θ=−1.323+−0.256

∴∆ H θ=−1.579kJ /mol

∆ H reaction=∑ ∆ Hproduct

−∑ ∆ Hreactant

2NaHCO3 ( s )→Na2CO3 (s )+H 2O( l)+CO2(g)

∆ H reaction°=(−393.5−285.8−1131)−(2×948)

∆ H reaction=85.7kJ ÷2

∆ H reaction=42.85kJ /mol

Heat required for decomposition of one moles NaHCO3 or 42.85kJ/mole NaHCO3 and the process is endothermic.

∆ Sreaction=∑ ∆ Sproduct

−∑ ∆ Sreactant

2NaHCO3 ( s )→Na2CO3 (s )+H 2O( l)+CO2(g)

∆ Sreaction=(135.0+213.6+188.7 )−(2×102)

∆ Sreaction=333.3J /mol K

∆ Sreaction=0.3333kJ /mol K

∆Gtheory=∑ ∆Gproduct

−∑ ∆Greactant

∆Gtheory=(−376.56−394.38+228.59 )−(2×−851.86)

∆Gtheory=1161.37kJ /mol

∆Gexp=−1.579−298 (0.3333)

∆Gexp=−100.90kJ /mol

DISCUSSION

Recalling the condition for spontaneous change

ΔG = ΔH – TΔS < 0

It is apparent that the temperature dependence of ΔG depends almost entirely on the entropy

change associated with the process. We say "almost" because the values of ΔH and ΔS are

themselves slightly temperature dependent; both gradually increase with temperature. In the

equation above, the sign of the entropy change determines whether the reaction becomes more or

less spontaneous as the temperature is raised.For any given reaction, the sign of ΔH can also be positive or negative. ∆Gtheory Presented a

positive value while the ∆Gexp gives out a negative value. Apparently in our experiment, the ΔH is

less than 0 while ΔS is greater than 0. Under these conditions, both the ΔH and TΔS terms will

be negative, so ΔG will be negative regardless of the temperature. An exothermic reaction whose

entropy increases will be spontaneous at all temperatures.

In order to make use of Gibbs energies to predict chemical changes, we need to know the free

energies of the individual components of the reaction. For this purpose we had combine the

standard enthalpy of formation and the standard entropy of a substance to get its standard free

energy of formation

We then determine the standard Gibbs energy of the reaction according to

∆Gtheory=∑ ∆Gproduct

−∑ ∆Greactant

As for the sources of error in this experiment, we believe that the major reason was heat lost as we

added sodium hydrogen carbonate into the H2SO4 in the double-wall vacuum steel calorimeter. The heat lost here relatively alter the value of ∆q. Besides, we also struggle to literally stir the content

of the calorimeter while having to take the reading of the thermometer each 10 seconds which

might cause small faults in the temperature reading.

CONCLUSION

The change of standard Gibbs free energy for the decomposition of sodium hydrogen carbonate from the change of standard enthalpy and the change of standard entropy is obtained. The value is

−100.90kJ /mol meanwhile the theoretical value is found to be 1161.37 kJ /mol

The experiment would be lot more accurate and successful if the major error occurring is avoided.