Estimate ℰ^∘ for the half-reaction 2 H2 O+2 e^- ⟶H2+2 OH^- given the following values of ΔGf^∘ :

Estimate ℰ^∘ for the half-reaction 2 H2 O+2 e^- ⟶H2+2 OH^-...

Estimate $\mathscr{E}^{\circ}$ for the half-reaction $$2 \mathrm{H}_{2} \mathrm{O}+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_{2}+2 \mathrm{OH}^{-}$$ given the following values of $\Delta G_{\mathrm{f}}^{\circ} :$ $$\quad\quad\quad \mathrm{H}_{2} \mathrm{O}(l)=-237 \mathrm{kJ} / \mathrm{mol}$$ $$\mathrm{H}_{2}(g)=0.0$$ $$\quad\quad\quad \mathrm{OH}^{-}(a q)=-157 \mathrm{kJ} / \mathrm{mol}$$ $$\quad \mathrm{e}^{-}=0.0$$ Compare this value of $\mathscr{E}^{\circ}$ with the value of $\mathscr{E}^{\circ}$ given in Table 18.1

Estimate $\mathscr{E}^{\circ}$ for the half-reaction
$$2 \mathrm{H}_{2} \mathrm{O}+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_{2}+2 \mathrm{OH}^{-}$$
given the following values of $\Delta G_{\mathrm{f}}^{\circ} :$
$$\quad\quad\quad \mathrm{H}_{2} \mathrm{O}(l)=-237 \mathrm{kJ} / \mathrm{mol}$$
$$\mathrm{H}_{2}(g)=0.0$$
$$\quad\quad\quad \mathrm{OH}^{-}(a q)=-157 \mathrm{kJ} / \mathrm{mol}$$
$$\quad \mathrm{e}^{-}=0.0$$
Compare this value of $\mathscr{E}^{\circ}$ with the value of $\mathscr{E}^{\circ}$ given in Table 18.1

Key Concepts

Relationship Between ?G° and E°

This key relationship, expressed as ?G° = -nFE°, connects the thermodynamic properties of a reaction with its electrochemical behavior. Here, ?G° is the standard Gibbs free energy change, n is the number of electrons transferred in the half-reaction, F is the Faraday constant, and E° is the standard electrode potential. This relation is fundamental in converting energetic information into electrical work that can be harnessed in a cell.

Electrochemical Half-Reaction

An electrochemical half-reaction represents either the oxidation or reduction part of a full redox reaction. It isolates one of the two simultaneous processes in an electrochemical cell, allowing the individual study of electron transfer processes and the computation of associated potentials, which can later be combined to obtain the overall cell reaction potential.

Gibbs Free Energy of Formation

This concept refers to the change in free energy when one mole of a compound is formed from its constituent elements in their standard states. It provides the baseline energy levels for compounds and plays a key role in calculating the overall Gibbs free energy change of a reaction, which in turn is used to determine the spontaneity and the electrochemical potential via thermodynamic relations.

Standard Electrode Potential

The standard electrode potential is a measure of the intrinsic tendency of a chemical species to gain or lose electrons under standard conditions. It is directly linked to the Gibbs free energy change of an electrochemical reaction through the equation ?G° = -nFE°, which allows us to estimate the cell potential from known free energy changes.

Transcript

00:01 In this problem, we are given information about this following half -reaction.

00:05 We are told what the values are for the change in gibbs -free energy at standard conditions of formation of each one of these chemical species, and we want to use this information in order to calculate the cell potential and compare it to the literature value from the table, which comes out to negative 0 .83 volts.

00:27 So this is the equation that we use to find delta g of the overall reaction, the change in gibbs free energy, we start with the product side and we multiply the number of moles of each species by its value of the given standard gives free energy change of formation.

00:44 We add that together for all the products and then subtract the same for the reactants.

00:51 So starting with the products, the changing gibbs free energy of formation at standard conditions of h2 is zero, so we do not include it.

00:59 And the other product is two moles.

01:01 Moles of oh minus.

01:03 So we multiply those two moles of oh minus by the given value of the change in gives free energy of formation at standard conditions for oh minus and kilojoules per mole.

01:14 So when we cancel off units of moles, we are left with total energy units of kilojoules.

01:19 That comes out to the total change in gibbs free energy of the products.

01:23 Then we subtract the same for the reactants.

01:27 The two electrons on the reactants side have a change and gibbs free energy of formation at standard conditions value of zero as well, just like h2.

01:37 And so we only focus on the two moles of water as a reactant...

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