Question

± Cell Potential and Free Energy Free-energy change, ΔG∘, is related to cell potential, E∘, by the equation ΔG∘=−nFE∘ where n is the number of moles of electrons transferred and F=96,500C/(mol e−) is the Faraday constant. When E∘ is measured in volts, ΔG∘ must be in joules since 1 J=1 C⋅V.

Part A Calculate the standard free-energy change at 25 ∘C for the following reaction:

Mg(s)+Fe2+(aq)→Mg2+(aq)+Fe(s)

Express your answer to three significant figures and include the appropriate units.

Part B Calculate the standard cell potential at 25 ∘C for the reaction

X(s)+2Y+(aq)→X2+(aq)+2Y(s) where ΔH∘ = -751 kJ and ΔS∘ = -247 J/K .

Express your answer to three significant figures and include the appropriate units.

Answer #1

PART A:

Mg(s) + Fe^{2+}
Mg^{2+} + Fe(s)

Mg(s)
Mg^{2+} + 2e- ; E^{0} = +2.38 V

Fe^{2+} + 2e- Fe(s) ;
E^{0} = -0.41 V

----------------------
---------------------------------------------------------------------------------------------

Mg(s) + Fe^{2+}
Mg^{2+} + Fe(s) E^{0} = +2.38 V + (
-0.41 V ) = +1.97 V

It's the same two electrons being "lost" and "gained".

So, n = 2

From the half reactions you can see that two electrons are
transferred.

Hence,

G^{0} = -
n F E^{0}

= - (2 mol e^{-}) (96500 C /∙mol e^{-}) ∙ (1.97
V)

= - 380210 CV

= - 380210 J

= - 380.21 kJ

PART B:

X(s) + 2Y^{+}(aq)
X^{2+}(aq) + 2Y(s)

Here 2 electrons are exchanged, that is two electrons being "lost" and "gained."

T = 25 ^{o}C = (273 + 25) K = 298 K

G^{0} =
H^{0} - T
S^{0}

= (- 751 kJ) - (298 K) (-247 J/K)

= - 751000 J + 73606 J

= - 677394 J

Again

G^{0} = -
n F E^{0}

E^{0} = G^{0} /
(-n F)

= (- 677394 J ) / [ - (2 mole e^{-}) (96,500 C / mole
e^{-}) ]

= 3.51 V

What is the cell potential for the reaction
Mg(s)+Fe2+(aq)→Mg2+(aq)+Fe(s)
at 75 ∘C when [Fe2+]= 3.10 M and [Mg2+]= 0.110
M .
Express your answer to three significant figures and include the
appropriate units.

Consider the reaction
Mg(s)+Fe2+(aq)→Mg2+(aq)+Fe(s)
at 79 ∘C , where [Fe2+]= 3.30 M and [Mg2+]= 0.310
M .
Part A
What is the value for the reaction quotient, Q, for the
cell?
Part B
What is the value for the temperature, T, in
kelvins?
Express your answer to three significant figures and include the
appropriate units.
Part C
What is the value for n?
Express your answer as an integer and include the appropriate
units (i.e. enter mol for moles).
Part...

Consider the reaction Mg(s)+Fe2+(aq)→Mg2+(aq)+Fe(s) at 69 ∘C ,
where [Fe2+]= 3.20 M and [Mg2+]= 0.110 M .
Part A:What is the value for the reaction quotient, Q,
for the cell?
Express your answer numerically.
Part B:What is the value for the temperature, T, in
kelvins?
Express your answer to three significant figures and
include the appropriate units.
Part C:What is the value for n?
Express your answer as an integer and include the
appropriate units (i.e. enter mol for moles)....

4a. Use the Nernst equation to calculate the cell voltage (E)
for the following redox reaction:
i. Fe3+(aq)+Cu(s)→Cu2+(aq)+Fe2+(aq), given that [Fe3+]=0.05 and
[[Cu2+]=0.125M at 25°C, and
Fe3++e→Fe2+ E0=0.77
V
Cu2+2e→Cu E0=0.34
V
4b. Use the information provided in question 4a to calculate the
change in free energy (ΔG) and change in entropy (ΔS) for the redox
reaction:
i. Fe3+(aq)+Cu(s)→Cu2+(aq)+Fe2+(aq)
What do the ΔG and ΔS values indicate about the spontaneity of
the redox reaction?

he thermodynamic properties for a reaction are related by the
equation that defines the standard free energy, ΔG∘, in
kJ/mol:
ΔG∘=ΔH∘−TΔS∘
where ΔH∘ is the standard enthalpy change in kJ/mol and
ΔS∘ is the standard entropy change in J/(mol⋅K). A good
approximation of the free energy change at other temperatures,
ΔGT, can also be obtained by utilizing this
equation and assuming enthalpy (ΔH∘) and entropy
(ΔS∘) change little with temperature.
Part A
For the reaction of oxygen and nitrogen to...

± Gibbs Free Energy: Temperature Dependence Gibbs free energy
(G) is a measure of the spontaneity of a chemical reaction. It is
the chemical potential for a reaction, and is minimized at
equilibrium. It is defined as G=H−TS where H is enthalpy, T is
temperature, and S is entropy.
The chemical reaction that causes aluminum to corrode in air is
given by
4Al+3O2→2Al2O3
in which at 298 K
ΔH∘rxn
= −3352 kJ
ΔS∘rxn
= −625.1 J/K
Part A
What is...

1) Calculate the standard cell potential (E∘) for the
reaction
X(s)+Y+(aq)→X+(aq)+Y(s)
if K = 1.12×10−3.
2)Calculate the standard cell potential at 25 ∘C for the
reaction
X(s)+2Y+(aq)→X2+(aq)+2Y(s)
where ΔH∘ = -573 kJ and ΔS∘ = -415 J/K .

Determine the free energy(ΔG) from the standard cell
potential (Ecell0 ) for the
reaction:
2ClO2-(aq)+Cl2(g)→2ClO2(g)+
2Cl-(aq)
where:
ClO2+e-→ClO2-Ered0
=+0.954 V.
Cl2+2e-→2Cl-Ered0
=+1.36 V.
ΔG=+79 kJ
ΔG=-790 kJ
ΔG=-79 kJ
ΔG=-0.79 kJ

What is the cell potential for the reaction
Mg(s)+Fe2+(aq)→Mg2+(aq)+Fe(s) at 47 ∘C when [Fe2+]= 3.10 M and
[Mg2+]= 0.110 MM . Express the potential numerically in volts.

ΔG° and E° can be said to measure the same
thing, and are convertible by the equation
ΔG° = −nFE⁰cell
where n is the total number of moles of electrons being
transferred, and F is the Faraday constant
9.64853415 ✕ 104 C/mol. The free energy (ΔG°)
of a spontaneous reaction is always negative.
For each of the electrochemical cells below, calculate the free
energy of the system and state whether the reaction is spontaneous
or non-spontaneous as written based on...

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