EMF of a disproportionation reaction

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SUMMARY

The discussion focuses on calculating the standard electromotive force (emf) for the disproportionation reaction of permanganate ions in an acidic medium. The sequence of reactions involves the transformations of \(MnO_4^-\) to \(MnO_4^{2-}\), \(MnO_2\), \(Mn^{3+}\), and \(Mn^{2+}\), with standard emf values provided for each step. The user attempts to derive the emf for the reaction \(3MnO_4^{2-}+4H^+ \rightarrow MnO_2(s)+2MnO_4^-+2H_2O\) but arrives at an incorrect value of \(E=1.696 V\). The correct approach involves careful manipulation of the Gibbs free energy equations associated with the half-reactions.

PREREQUISITES
  • Understanding of standard electromotive force (emf) calculations
  • Familiarity with Gibbs free energy and its relation to electrochemical reactions
  • Knowledge of half-reaction methods in redox chemistry
  • Basic principles of acid-base chemistry in aqueous solutions
NEXT STEPS
  • Review the Nernst equation for calculating emf under non-standard conditions
  • Study the derivation of Gibbs free energy changes for electrochemical reactions
  • Explore the concept of disproportionation reactions in redox chemistry
  • Learn about the role of acid concentration in influencing emf values
USEFUL FOR

Chemistry students, electrochemists, and anyone studying redox reactions and their thermodynamic properties will benefit from this discussion.

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Homework Statement


Consider the following sequence of reactions occurring in the acid medium. All emf (standard) are measured at ##25^{\circ} C## and expressed in volt unit:
$$MnO_4^-\stackrel{0.564}{\rightarrow}MnO_4^{2-}\stackrel{2.26}{\rightarrow}MnO_2\stackrel{0.95}{\rightarrow}Mn^{3+} \stackrel{1.51}{\rightarrow}Mn^{2+}\stackrel{-1.18}{\rightarrow}Mn$$
Determine the standard emf of the following reaction:
$$3MnO_4^{2-}+4H^+ \rightarrow MnO_2(s)+2MnO_4^-+2H_2O$$

Homework Equations


The Attempt at a Solution


$$MnO_4^{2-}+4H^++2e^- \rightarrow MnO_2+2H_2O \,\,\,\, \Delta G^{\circ}=-4.52F$$
$$MnO_4^{2-}\rightarrow MnO_4^{-}+e^- \,\,\,\, \Delta G^{\circ}=+0.564F$$
Multiplying the second equation by two and adding with the first, I get the equation presented in the problem and ##\Delta G^{\circ}=-3.392F##. Let E be the emf of the resulting reaction, then ##\Delta G^{\circ}## is also equal to ##-2FE##. Equating and solving for E, I get ##E=1.696 V## which is incorrect.

Any help is appreciated. Thanks!
 
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