Consider the following unbalanced oxidation-reduction reactions in aqueous solution: $$ \begin{aligned} \mathrm{Ag}^{+}(a q)+\mathrm{Li}(s) & \longrightarrow \mathrm{Ag}(s)+\mathrm{Li}^{+}(a q) \\ \mathrm{Fe}(s)+\mathrm{Na}^{+}(a q) \longrightarrow \mathrm{Fe}^{2+}(a q)+\mathrm{Na}(s) \\ \mathrm{K}(s)+\mathrm{H}_{2} \mathrm{O}(l) & \longrightarrow \mathrm{KOH}(a q)+\mathrm{H}_{2}(g) \end{aligned} $$ (a) Balance each of the reactions. (b) By using data in Appen\(\operatorname{dix} C,\) calculate \(\Delta H^{\circ}\) for each of the reactions. (c) Based on the values you obtain for \(\Delta H^{\circ}\), which of the reactions would you expect to be thermodynamically favored? (d) Use the activity series to predict which of these reactions should occur. (Section 4.4) Are these results in accord with your conclusion in part (c) of this problem?

Step by step solution

01

The first reaction

The half-reactions for the first reaction are: \[\mathrm{Ag}^+ \rightarrow \mathrm{Ag}\] \[\mathrm{Li} \rightarrow \mathrm{Li}^+\] Balanced reaction: \(\mathrm{Ag}^+(aq) + \mathrm{Li}(s) \rightarrow \mathrm{Ag}(s) + \mathrm{Li}^+(aq)\)

02

The second reaction

The half-reactions for the second reaction are: \[\mathrm{Fe} \rightarrow \mathrm{Fe}^{2+}\] \[\mathrm{Na}^+ \rightarrow \mathrm{Na}\] Balanced reaction: \(\mathrm{Fe}(s) + 2\mathrm{Na}^+(aq) \rightarrow \mathrm{Fe}^{2+}(aq) + 2\mathrm{Na}(s)\)

03

The third reaction

The half-reactions for the third reaction are: \[\mathrm{K} \rightarrow \mathrm{K}^+\] \[\mathrm{H_2O} \rightarrow \mathrm{OH}^- + \frac{1}{2}\mathrm{H_2}\] Balanced reaction: \(\mathrm{K}(s) + \mathrm{H_2O}(l) \rightarrow \mathrm{KOH}(aq) + \frac{1}{2}\mathrm{H_2}(g)\) Now, we move on to part (b) to calculate ΔH° for each of the reactions using data from Appendix C. (b) By using data in Appendix C, calculate ΔH° for each of the reactions.

04

Enthalpy Change Formula

We need the following formula for calculating the enthalpy change, ΔH°: \[\Delta H^{\circ} = \sum \Delta H^{\circ}_\text{products} - \sum \Delta H^{\circ}_\text{reactants}\]

05

Calculating ΔH° for the first reaction

Let's assume the given data provides the standard enthalpy of formation for each species. Then, for the first reaction: \[\Delta H^{\circ}_1 = [(\Delta H^{\circ}_\text{Ag,s})+( \Delta H^{\circ}_\text{Li^+,aq})] - [(\Delta H^{\circ}_\text{Ag^+, aq}) + (\Delta H^{\circ}_\text{Li,s})]\]

06

Calculating ΔH° for the second reaction

For the second reaction: \[\Delta H^{\circ}_2 = [( \Delta H^{\circ}_\text{Fe^{2+}, aq})+(2\Delta H^{\circ}_\text{Na,s})] - [(\Delta H^{\circ}_\text{Fe,s}) + (2\Delta H^{\circ}_\text{Na^+, aq})]\]

07

Calculating ΔH° for the third reaction

For the third reaction: \[\Delta H^{\circ}_3 = [(\Delta H^{\circ}_\text{KOH,aq})+(\frac{1}{2} \Delta H^{\circ}_\text{H_2,g})] - [(\Delta H^{\circ}_\text{K,s}) + (\Delta H^{\circ}_\text{H_2O,l})]\] (c) Based on these values for ΔH°, we can determine which reaction is the most thermodynamically favored.

08

Thermodynamically favored reaction

Lower (more negative) values of ΔH° indicate a stronger tendency to release heat and favor the forward reaction. Therefore, among the calculated values, the reaction with the lowest ΔH° will be the most thermodynamically favored. (d) Use the activity series to predict which of these reactions should occur. Compare these results with the conclusion from part (c) of this problem.

09

Consulting the activity series

According to the activity series, we can predict whether a redox reaction will occur or not. In our case, we need to check the relative positions of the corresponding elements to determine which reaction will proceed spontaneously. Compare the predictions from the activity series with the ΔH° values obtained in part (c) to see if they are in agreement.

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