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Chapter 19: Problem 10

Discuss the spontaneity of an electrochemical reaction in terms of its standard \(\operatorname{emf}\left(E_{\text {cell }}^{\circ}\right)\).

Short Answer

Expert verified
The standard emf (\(E_{\text {cell }}^{\circ}\)) of an electrochemical reaction is used to determine if the reaction is spontaneous. If \(E_{\text {cell }}^{\circ}\) is positive, the reaction is spontaneous; if it is negative, the reaction is non-spontaneous.

Step by step solution

01

Define Electrochemical Reaction

An electrochemical reaction is one where chemical change is brought about by the passage of electrical current. It involves the conversion of chemical energy into electrical energy or vice versa.
02

Define Spontaneity

Spontaneity in this context refers to the ability of a reaction to occur without the application of external energy. If a reaction can proceed on its own without any outside force or energy being applied, it is said to be spontaneous.
03

Define Standard Emf (\(E_{\text {cell }}^{\circ}\))

\(\(E_{\text {cell }}^{\circ}\)\) generally refers to the potential difference between the two half-cells of an electrochemical cell when all reactants and products are in their standard states (usually 1 M concentration for soluble species and 1 atm pressure for gases) at 25° C.
04

Relation between Spontaneity and \(E_{\text {cell }}^{\circ}\)

The spontaneity of electrochemical reactions can be determined by the sign of \(E_{\text {cell }}^{\circ}\). If \(E_{\text {cell }}^{\circ}\) is positive, the reaction is spontaneous; if it is negative, the reaction is not spontaneous. This is based on the formula for the Gibbs free energy change (\(ΔG = -nFE_{\text {cell }}^{\circ}\)), where \(ΔG\) is the Gibbs free energy change, \(n\) is the number of electrons transferred, \(F\) is the Faraday constant and \(E_{\text {cell }}^{\circ}\) is the standard emf. A negative \(ΔG\) means the reaction is spontaneous, and since \(E_{\text {cell }}^{\circ}\) is in the formula with a minus sign, a positive \(E_{\text {cell }}^{\circ}\) will give a negative \(ΔG\).

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Most popular questions from this chapter

Gold will not dissolve in either concentrated nitric acid or concentrated hydrochloric acid. However, the metal does dissolve in a mixture of the acids (one part \(\mathrm{HNO}_{3}\) and three parts \(\mathrm{HCl}\) by volume ), called aqua regia. (a) Write a balanced equation for this reaction. (Hint: Among the products are \(\mathrm{HAuCl}_{4}\) and \(\mathrm{NO}_{2} .\) ) (b) What is the function of \(\mathrm{HCl} ?\)

Given the following standard reduction potentials, calculate the ion-product, \(K_{\mathrm{w}},\) for water at \(25^{\circ} \mathrm{C}\) : \(2 \mathrm{H}^{+}(a q)+2 e^{-} \longrightarrow \mathrm{H}_{2}(g) \quad E^{\circ}=0.00 \mathrm{~V}\) \(2 \mathrm{H}_{2} \mathrm{O}(l)+2 e^{-} \longrightarrow \mathrm{H}_{2}(g)+2 \mathrm{OH}^{-}(a q)\) $$ E^{\circ}=-0.83 \mathrm{~V} $$

One of the half-reactions for the electrolysis of water is $$ 2 \mathrm{H}^{+}(a q)+2 e^{-} \longrightarrow \mathrm{H}_{2}(g) $$ If \(0.845 \mathrm{~L}\) of \(\mathrm{H}_{2}\) is collected at \(25^{\circ} \mathrm{C}\) and \(782 \mathrm{mmHg}\), how many faradays of electricity had to pass through the solution?

Write the Nernst equation for the following processes at some temperature \(T\) : (a) \(\mathrm{Mg}(s)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Mg}^{2+}(a q)+\operatorname{Sn}(s)\) (b) \(2 \mathrm{Cr}(s)+3 \mathrm{~Pb}^{2+}(a q) \longrightarrow 2 \mathrm{Cr}^{3+}(a q)+3 \mathrm{~Pb}(s)\)

From the following information, calculate the solubility product of AgBr: $$ \begin{array}{ll} \mathrm{Ag}^{+}(a q)+e^{-} \longrightarrow \mathrm{Ag}(s) & E^{\circ}=0.80 \mathrm{~V} \\ \operatorname{AgBr}(s)+e^{-} \longrightarrow \mathrm{Ag}(s)+\mathrm{Br}^{-}(a q) & E^{\circ}=0.07 \mathrm{~V} \end{array} $$
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