SHS
GENERAL CHEMISTRY 2
Science Activity Sheet
Quarter 4
2 – MELC 2
Week 2
1B
Gibbs Free Energy
General Chemistry 2 Activity Sheet No. 2
Gibbs Free Energy
First Edition, 2020
Published in the Philippines
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Region 6 – Western Visayas
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Grade& Section______________________________Date: ___________________
GENERAL CHEMISTRY 2 ACTIVITY SHEET NO. 2
Gibbs Free Energy
I. Learning Competency with Code
Use Gibbs’ free energy to determine the direction of a reaction
(STEM_GC11CT-IVa-b-143)
II. Background Information for Learners
The thermodynamic entity that takes into account both enthalpy and
entropy changes and is useful for determining whether a process is spontaneous
or not is called Gibbs free energy. The Gibbs free energy change (∆G) for reaction
carried out at constant temperature in Kelvin and pressure is given by
∆G = ∆H -T∆S
where both ∆H and ∆S refer to the system.
The Gibbs free energy change is equal to the maximum possible work (w)
that can be obtained from a process. Any process that occurs spontaneously can
be utilized to perform useful work. The Gibbs free energy of the system will
decrease (∆G<0) in a spontaneous process, and will increase (∆G >0) in a
nonspontaneous process. For example, the movement of water in waterfall is
spontaneous. Useful work, for example, in turning the wheels of a turbine, can
be derived from the process. On the other hand, a positive ∆G indicates that work
has to be done on the system for the process to take place. Such process is
nonspontaneous. The maintenance of life is nonspontaneous process; it requires
the sustained input of work or energy as maybe obtained from food. The free
energy criteria (at constant temperature and pressure) are summarized as follows:
If ∆G < 0, the forward reaction is spontaneous.
If ∆G = 0, the reaction is at equilibrium.
If ∆G < 0, the forward reaction is nonspontaneous. The reverse reaction
will have a negative ∆G and will be spontaneous.
The standard free-energy change of reaction (∆Gºrxn) is the free –energy
change for a reaction when it occurs under standard state conditions, when
reactants in their standard states are converted to products in their standard
states.
Calculation of ∆Gºrxn.
The free energy change for a reaction can be calculated in two ways. When
both ∆H and ∆S are known, then ∆G = ∆H -T∆S will give the free energy change
at the temperature T. ∆Gºrxn can also be calculated from standard free energies of
formation in a manner analogous to the calculation of ∆Hº by using enthalpies of
formation of the reactants and products. The standard free energies of formation
(∆Gºf) of selected compounds are tabulated below (Table 2.1). Just as for the
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standard enthalpies of formation, the free energies of formation of elements in
their standard states are equal to zero.
For a general reaction
aA + bB
cC + dD
The standard free energy change is given by
∆Gºrxn = [c∆Gºf (C) + d∆Gºf (D)] - [a∆Gºf (A) + b∆Gºf (B)]
In general:
∆Gºrxn = ∑n∆Gºf(products) - ∑m∆Gºf(reactants)
Where n and m are stoichiometric coeficients.
Table 2.1 Standard Gibbs free energy of formation of selected substances.
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Sample Problem 1:
Calculate ∆Gºrxn at 25ºC for the following reaction given that:
∆Gºf (Fe2O3) = -741.0 kJ/mol
∆Gºf (Al2O3) = -1576.4 kJ/mol
2
2Al(s) + Fe2O3(s)
Method of Solution
Al2O3(s) + 2Fe(s)
∆Gºrxn = [∆Gºf (Al2O3) + 2∆Gºf (Fe)] - [2∆Gºf (Al) + ∆Gºf (Fe2O3)]
= [ 1mol (-1576.41 kJ/mol) + 0 ]-[ 0+ 1mol (741.0 kJ/mol))
∆Gºrxn = -1576.41 kJ + 741.0 kJ
= - 835.4 kJ
Temperature and the Free Energy Change
From the equation ∆G = ∆H - T∆S we can see that temperature too will
influence the spontaneity of reaction. If both ∆H and ∆S are positive then at low
temperature, as long as ∆H > T∆S, ∆G is positive and the process will be
nonspontaneous. However, as temperature increases, the T∆S term increases and
eventually ∆H = T∆S. At this point ∆G is zero. With further T increase, T∆S > ∆H,
making ∆G < 0, and the reaction becomes spontaneous. Table 2.1 summarizes
the four possible situtions affecting the ∆G of a reaction.
Table 2.2. Enthalpy and Entropy Factors that the signs of ∆Gºrxn
∆H
+
∆S
+
∆G
∆G is positive at low
temperatures and negative at
high temperature
Characteristic of Reaction
Nonspontaneous at lower
temperature
Spontaneous at higher
temperature
+
_
∆G is positive at all
tempratures
Nonspontaneous at any
temperature
-
+
∆G
is
negative
temperatures
-
-
∆G
is
negative
at
low Nonspontaneous at higher
temperatures and positive at temperature
high temperature
Spontaneous at lower
temperature
at
all Spontaneous at all
temperature
Brown, Le May and Bursten. Chemistry: The Central Science, 9th ed. 2004
Sample Problem 2:
The old camera flash bulb used Mg metal sealed in a bulb with oxygen. The
reaction is:
S° J/K mol:
ΔH°f kJ/mol:
Mg
32.7
0
+
½ O2
—>
205.0
0
3
MgO
26.9
-601.2
Calculating the ΔS°
ΔS° = ΣnS° (products) − ΣmS° (reactants)
= [(1) S° MgO] – [(1) S° Mg + (½) S° O2]
= [(1) (26.9)] – [(1)(32.7) + (½) (205.0)]
ΔS° = -108.3 J/K mol
Calculating the ΔH°
ΔH° = Σ nΔHf° (products) – Σ mΔHf° (reactants)
= [(1) ΔHf ° MgO] – [(1) ΔHf°Mg + (½) ΔHf°O2]
= [(1) (-601.2)] – [(1) (0) + (½) (0)]
ΔH° = -601.2k
Calculating the ΔG
ΔG = ΔH - TΔS
= 601.2kJ - (298K) (-108.3J/K) (1kJ/1000J)
= -601.2 + 32.3kJ
ΔG = -568.9kJ
Since ΔG is negative the reaction will form MgO amd it is spontaneous.
III. Activity Proper
Activity 1. Gibbs Free Energy
For the reaction to be spontaneous, the sign of ∆G (Gibbs free energy) must be
negative. The mathematical formula for this value is:
∆G = ∆H -T∆S
Where:
∆H – change in enthalpy
T- temperature in Kelvin
∆S – change in entropy
Complete the table for the sign of
∆G: -, + or undetermined. When
conditions
allow
for
an
undetermined
sign
of
∆G,
temperature
will
decide
spontaneously.
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∆H
+
∆S
-
+
+
-
+
_
_
∆G
Answer the following below:
1. The conditions in which ∆G is always negative is when ∆H is ____________
and ∆S is ____________.
2. The conditions in ∆G is always positive is when ∆H is ____________ and ∆S
is __________.
3. Under what conditions will a reaction with a decreasing entropy be
spontaneous or thermodynamically favorable?
4. Under what conditions will an endothermic reaction be spontaneous or
thermodynamically favorable?
5. An exothermic reaction is nonspontaneous or thermodynamically
unfavorable under what conditions of temperature and entropy change?
6. When the situation is indeterminate, a low temperature favors the
(entropy /enthalpy) factor, and a high temperature favors the (entropy/
enthalpy) factor.
7. Use complete sentences to explain how changes in enthalpy, temperature,
and entropy would create each type of reaction.
a. A reaction that is always favorable
b. A reaction that is always unfavorable
c. A reaction that is sometime favorable
Activity 2. Is It Favorable or Not?
Much like enthalpy and entropy, Gibbs free energy is a state function
because they describe quantitatively an equilibrium state of a thermodynamic
system, irrespective of how the system arrived in that state. Additionally, like
enthalpy and entropy, Gibbs free energy can be calculated independently using
the equation below.
∆Grxn˚ = ∑Gf˚ products - ∑Gf˚ reactants
1. What is the standard free energy change, ∆G˚, in kJ, for the following
reaction at 298K? Is the reaction spontaneous?
C2H5OH(l) + 3O2(g) —> 2CO2(g) + 3H2O(g)
Compound
C2H5OH(l)
O2(g)
CO2(g)
H2O(g)
∆Gf˚ kJ/mol
- 175
0
-394
-229
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2. Calculate the ∆Gº for the reaction of graphite and predict whether the
reaction is spontaneous or not:
2C(graphite) + H2(g) —> C2H2(g)
3. Copper (I) sulfide reacts with sulfur to produce copper (II) sulfide at
25°C. The process is exothermic (ΔH˚ = -26.7 kJ/mol) with a decrease in
disorder (ΔS˚ = -19.7 J/(mol•K)).
Determine the thermodynamic favorablity of the reaction by calculating
ΔG˚.
Cu2S(s) + S(s) → 2 CuS(s)
4. Is the reaction spontaneous at 298K and 1atm?
CO(NH2)2 aq +
H2O(l)
—> CO2 (g) + 2NH3 (g)
∆Hº = 119kJ
∆Sº = 354.8 J/K
T
= 25ºC = 298K
IV. Reflection
Complete the statements below.
I understand _________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
I don’t understand ___________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
I need more information about _______________________________________________
______________________________________________________________________________
______________________________________________________________________________
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V. Answer Key
VI. References
Barrameda, M.C.B., Jusayan, S.R., Macale, A.M, Sabularse, V.S. (2016).
Teaching Guide for Senior High School in General Chemistry 2.Commision on
Higher Education. pp. 413-440.
Brown, Le May and Bursten. Chemistry: The Central Science, 9th ed. 2004
Chang, R. (2007) Chemistry, 9th Ed. McGraw-Hill, Inc., USA.
Whitten, K.W., et al (2007) Chemistry, 8th Ed. Thomson-Brooks/Cole, USA.
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ddl.org%2Farticles%2Fs%2Ft%2Fa%2FFile~Standard_Free_Energies_of_Formati
on.jpg_c314.html&psig=AOvVaw06AWRbEU4gWDgDtqBzRyc2&ust=161167685
1721000&source=images&cd=v
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