Question

Free-energy change, ΔG∘, is related to cell potential, E∘, by the equationΔG∘=−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.1. 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.2. Calculate the standard cell potential at 25 ∘C for the reactionX(s)+2Y+(aq)→X2+(aq)+2Y(s)where ΔH∘ = -675 kJ and ΔS∘ = -357 J/K .Express your answer to three significant figures and include the appropriate units.

Answer 1

Answer:

a)$\Delta G=372490 J$

b)$\Delta G=-568614 J$

Explanation:

a) The reaction:

$Mg(s) +Fe^{2+}(aq) \longrightarrow Mg^{2+}(aq) + Fe(s)$

The free-energy expression:

$\Delta G=-n*F*E$

$E=E_{red}-E_{ox]$

The element wich is reduced is the Fe and the one that oxidates is the Mg:

$-0.44V=E_{red}-(-2.37V)=1.93V$

The electrons transfered (n) in this reaction are 2, so:

$\Delta G=-2mol*96500 C/mol * 1.93 V$

$\Delta G=-372490 J$

b) If you have values of enthalpy and enthropy you can calculate the free-energy by:

$\Delta G=\Delta H - T* \Delta S$

with T in Kelvin

$\Delta G=-675 kJ*\frac{1000J}{kJ} - 298K*-357 J/K$

$\Delta G=-568614 J$