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Exp 10 - Free Energy
‣ Free Energy ‣ Gibbs Free Energy (G)
‣ Relating to Equilibrium (K)
‣ This Weeks Experiment ‣ Preparing Solutions
‣ Standardization
‣ Determining K
‣ Next Meeting ‣ Electrochemistry
1
E10
orxnΔ = × ln −G RT K
o orxn rxnΔ Δ1
ln = +− ⎛ ⎞
⎜ ⎟⎝ ⎠H S
KR T R
Free Energy
‣ Free energy is the energy available in a change to do work.
‣ There is always some minimum energy lost in a change, all other energy is free energy.
‣ There are different models to identify how much of that energy is useable.
‣ Because Free Energy is always less than the total energy of change, all processes have a cost.
‣ It is not possible to create process that is entirely self sustaining.
‣ The most common ways to derive free energy are: ‣ Helmholtz Free Energy — A (work content)
‣ at constant temperature and volume
‣ Landau Free Energy — Ω ‣ in an open system
‣ Gibbs Free Energy — G ‣ at constant temperature and pressure
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Leonardo da Vinci’sPerpetual Motion Machine
∆G° = ∆H° – T∆S°
Free Energy
‣ Energy change values are often determined directly by measuring temperature changes when the reaction occurred.
‣ However, in many cases, this technique is not possible.
‣ The reaction may not go to completion, or it may give off such a small amount of heat that the temperature change is too small to measure.
‣ Also, there is no direct method for measuring ∆S° for a reaction.
‣ It is therefore useful to be able to determine ∆H°, ∆G° and ∆S° indirectly, by using their relationship to the equilibrium constant of a reaction.
∆G° = –RT ln K
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∆G° = ∆H° – T∆S°
8.314 J/mol-K
Relating K to ∆H° and ∆S°
‣ Combining these two equations gives the general relationship between K, ∆H°, and ∆S°:
–RT ln K = ∆H° – T∆S°
‣ Dividing both sides by –RT gives a particularly useful form of this relationship:
‣ This equation is in the form y = mx + b.
‣ The graph of ln(K) versus inverse T is a straight line with slope and y-intercept
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Relating K to ∆H° and ∆S°
‣ If we can determine K for a reaction at different temperatures, we can know ∆H° and ∆S°
‣ From ∆H°and ∆S° we can know the change in free energy of that reaction.
5
∆G° = ∆H° – T∆S°
Exp 10 - Free Energy
‣ Free Energy ‣ Gibbs Free Energy (G)
‣ Relating to Equilibrium (K)
‣ This Weeks Experiment ‣ Preparing Solutions
‣ Standardization
‣ Determining K
‣ Next Meeting ‣ Electrochemistry
6
E10
orxnΔ = × ln −G RT K
o orxn rxnΔ Δ1
ln = +− ⎛ ⎞
⎜ ⎟⎝ ⎠H S
KR T R
Exp 10: Borax Dissolution
Your job is to …
Determine the ΔG˚ for borax dissolving in water by first determining the ΔH˚ and ΔS˚ of the process.
#1 - determine the concentration of your HCl standard solutions using solid Na2CO3
#2 - prepare a solution of borax at three different temperatures, titrate each solution to determine it’s equilibrium concentrations (and therefore K) at different temperatures.
#3 - plot ln K (y-axis) vs 1/T (x-axis) to determine the slope and y-intercept. Multiple each value by R to get ΔS˚ from the intercept and ΔH˚ from the slope.
#4 - use ΔG˚ = -RT ln K to determine the change in free energy for the reaction.
Na2B4O5(OH)4•8H2O (s) ⇄ 2 Na+ (aq) + B4O5(OH)42– (aq) + 8 H2O (l)
Indicator Choice
‣ Q: Why is Bromocresol green used as the indicator for titration of hydrochloric acid with sodium tetraborate?
‣ A:
‣ Using strong acids the equivalence points between the product often has a lower pH than pure water.
‣ Bromocresol green exhibits two color changes within the pH range of 3.8 to 5.4. ‣ Within its approximate "neutral" pH range of 3.8 to 5.4, it
exhibits its namesake green color.
‣ Anything below the 3.8 pH mark causes bromocresol green to take on its acidic form and turn a yellow color.
‣ Anything above the 5.4 pH mark causes it to take on its base form and turn a blue color.
‣ The broad range of pH detection in the acid range, below the 7 pH mark, makes bromocresol green useful for testing the equivalence point solutions that have an acidic substance.
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‣ Use Na2CO3 as your primary standard. Weigh out about 0.15 grams each in two difference clean dry erlenmeyer flasks. Determine the weight and moles to 4 sig figs.
‣ By graduated cylinder, add 50.0 mL of deionized water to each and swirl to fully dissolve the solid.
‣ Add 4 drops bromocresol green indicator to each (solution will be blue).
‣ Setup a buret with stock 0.10 M HCl.
‣ Record the initial volume.
‣ Titrate to point where the solution turns green.
‣ Continue to titrate until the green tint is completely gone and the solution is fully yellow.
‣ Repeat. Calculate the molarity of your HCl. The numbers should agree within 5%. Repeat if necessary.
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Exp 10: Free Energy
#1 — Determine Concentration of HCl Standard
HCl (aq) + Na2CO3 (aq) ⇄ H2CO3 (aq) + NaCl (aq)
‣ Prepare a beaker and warm about 100 mL of deionized water to between 60-70˚C.
‣ There are three borax solutions maintained at different temperatures. For each, carefully buret off 10.00 mL of borax solution and add it to a clean dry Erlenmeyer flask. ‣ Use great care not to disturb the solid borax at the bottom
of the flask—if you do you will get poor results.
‣ Record the exact temperature of the borax solution when you remove your sample.
‣ Using a graduated cylinder, add 20.0 mL of the warm water to each of your flasks.
‣ Add four drops of bromocresol green to each flask.
‣ Titrate with the standardized HCl solution to a yellow endpoint (no green tint).
‣ Repeat the above procedure with the two remaining saturated borax solutions.
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Exp 10: Free Energy
#2 — Prepare & Titrate Borax Solution
‣ Determine the concentration of each dissociation component of borax in your 10.00 mL sample from the HCl titration.
‣ Determine K for each temperature from the concentrations of Na+ (aq) and B4O5(OH)4
2– (aq) found.
11
Exp 10: Free Energy
#3 — Stoichiometry & Equilibrium Calculations
B4O5(OH)42– (aq) + 2 H3O+
(aq) + H2O (l) → 4 H3BO3 (aq)
Na2B4O5(OH)4•8H2O (s) ⇄ 2 Na+ (aq) + B4O5(OH)42– (aq) + 8 H2O (l)
K = [Na+]2 [ B4O5(OH)42 –]
‣ Plot ln K (y-axis) vs 1/T (x-axis) to determine the slope and y-intercept.
‣ Multiple each value by R to get ΔS˚ from the intercept and ΔH˚ from the slope.
‣ Determine ∆G° for each sample at each temperature.
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Exp 10: Free Energy
#4 — Thermochemistry Calculations
y = mx + b
∆G° = –RT ln K
Exp 10 - Free Energy
‣ Free Energy ‣ Gibbs Free Energy (G)
‣ Relating to Equilibrium (K)
‣ This Weeks Experiment ‣ Preparing Solutions
‣ Standardization
‣ Determining K
‣ Next Meeting ‣ Electrochemistry
13
E10
orxnΔ = × ln −G RT K
o orxn rxnΔ Δ1
ln = +− ⎛ ⎞
⎜ ⎟⎝ ⎠H S
KR T R
Next Week
‣ Before next Meeting: ‣ Bring to class:
‣ Notebook ‣ You will not be turning in notebooks, but this
permanent record of your preparations, observations and notes will be essential to your success in this class.
‣ Textbook, calculator, pencils (yes, you can use pen)
‣ Safety Glasses (you cannot participate in the next class without them)
‣ Read and bring a copy of the next experiment Electrochemistry
‣ Produce and bring to class:
‣ Your pre-lab for exp 11
‣ Your procedure summary for exp 11
‣ Review from your lecture text:
‣ Half Cells & Electric Potential
14
We will start with a quiz about
the experiment and reading.
Questions?
