Problem 114 - Chemistry: The Central Science

Question

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 Appendix \(C\), 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? (That is, which would you expect to be spontaneous?) (d) Use the activity series to predict which of these reactions should occur. ono (Section 4.4) Are these results in accord with your conclusion in part (c) of this problem?

Step-by-Step Solution

Answer

The balanced reactions are: 1. \(\mathrm{Ag}^{+}(a q)+\mathrm{Li}(s) \longrightarrow \mathrm{Ag}(s)+\mathrm{Li}^{+}(a q)\) 2. \(\mathrm{Fe}(s)+\mathrm{Na}^{+}(a q) \longrightarrow \mathrm{Fe}^{2+}(a q)+\mathrm{Na}(s)\) 3. \(2\mathrm{K}(s)+\mathrm{H}_{2}\mathrm{O}(l) \longrightarrow 2\mathrm{KOH}(a q)+\mathrm{H}_{2}(g)\) Standard enthalpy changes are: 1. \(\Delta H^{\circ}_{1} = -201.4 \, kJ/mol\) 2. \(\Delta H^{\circ}_{2} = -341.4 \, kJ/mol\) 3. \(\Delta H^{\circ}_{3} = -849.4 \, kJ/mol\) All three reactions are determined to be spontaneous based on their enthalpy changes, and this is consistent with the activity series.

Step 1: Balance the first reaction

The reaction is given by: \[ \mathrm{Ag}^{+}(a q)+\mathrm{Li}(s) \longrightarrow \mathrm{Ag}(s)+\mathrm{Li}^{+}(a q) \] The reaction is already balanced with a stoichiometry of 1:1 for all species.

Step 2: Balance the second reaction

The reaction is given by: \[ \mathrm{Fe}(s)+\mathrm{Na}^{+}(a q) \longrightarrow \mathrm{Fe}^{2+}(a q)+\mathrm{Na}(s) \] Since Fe and Na each have a stoichiometry of 1, the reaction is balanced.

Step 3: Balance the third reaction

The reaction is given by: \[ \mathrm{K}(s)+\mathrm{H}_{2}\mathrm{O}(l) \longrightarrow \mathrm{KOH}(a q)+\mathrm{H}_{2}(g) \] To balance this reaction, we must have the same number of H and O atoms on each side. For that, we need 2 K on the reactant side and 2 KOH on the product side. The balanced reaction is: \[ 2\mathrm{K}(s)+\mathrm{H}_{2}\mathrm{O}(l) \longrightarrow 2\mathrm{KOH}(a q)+\mathrm{H}_{2}(g) \] (b) Calculate the standard enthalpy change for each reaction

Step 4: First reaction enthalpy

Using the data provided in Appendix C: \[\pi H^{\circ}(\mathrm{Li}^{+}(a q)) = -278.5 \, kJ/mol \] \[\pi H^{\circ}(\mathrm{Ag}^{+}(a q)) = 77.1 \, kJ/mol \] Substituting these values into the equation \(\Delta H^{\circ} = \sum{n \Delta H_{\mathrm{products}}} - \sum{n \Delta H_{\mathrm{reactants}}}\): \[\Delta H^{\circ}_{1} = \Delta H^{\circ}(\mathrm{Ag}(s)) - \Delta H^{\circ}(\mathrm{Li}(s))+ \Delta H^{\circ}(\mathrm{Li}^{+}(a q)) - \Delta H^{\circ}(\mathrm{Ag}^{+}(a q)) = -278.5 \, kJ/mol + 77.1 \, kJ/mol = -201.4 \, kJ/mol\]

Step 5: Second reaction enthalpy

Using the data provided in Appendix C: \[\Delta H^{\circ}(\mathrm{Fe}^{2+}(a q)) = -341.4 \, kJ/mol\] \[\Delta H^{\circ}_{2} = \Delta H^{\circ}(\mathrm{Fe}^{2+}(a q)) - \Delta H^{\circ}(\mathrm{Na}^{+}(a q))+ \Delta H^{\circ}(\mathrm{Fe}(s)) - \Delta H^{\circ}(\mathrm{Na}(s)) = -341.4 \, kJ/mol = -341.4 \, kJ/mol\]

Step 6: Third reaction enthalpy

Using the data provided in Appendix C: \[\Delta H^{\circ}(\mathrm{KOH}(a q)) = -424.7 \, kJ/mol\] \[\Delta H^{\circ}_{3} = 2\Delta H^{\circ}(\mathrm{KOH}(a q)) - \Delta H^{\circ}(\mathrm{H}_{2}\mathrm{O}(l))-2\Delta H^{\circ}(\mathrm{K}(s))+ \Delta H^{\circ}(\mathrm{H}_{2}(g)) = -2(424.7 \, kJ/mol) = -849.4 \, kJ/mol\] (c) Determine which reactions are spontaneous

Step 7: Identify spontaneous reactions

Spontaneous reactions typically have a negative value for their enthalpy change. Thus, all three reactions should be spontaneous based on their respective values of \(\Delta H^{\circ}\) (d) Use the activity series to determine which reactions should occur

Step 8: Activity series

According to the activity series, the relative reactivities of the metals are: \[ \mathrm{Li} > \mathrm{K} > \mathrm{Na} > \mathrm{Fe} > \mathrm{Ag} \] In each reaction: 1. Li (more reactive) displaces Ag (less reactive) - it should occur 2. Na (more reactive) displaces Fe (less reactive) - it should occur 3. K (more reactive) displaces H (less reactive) - it should occur

Step 9: Compare enthalpy and activity series results

The enthalpy results indicate that all three reactions should be spontaneous, and the activity series also shows that all three reactions should occur. Thus, the results are in accord with each other.

Key Concepts

Balancing Chemical Equations

Balancing chemical equations is crucial in understanding the stoichiometry of a reaction. It ensures that the same number of each type of atom is present on both sides of the equation. Let's explore this with the reactions presented. For instance, in the third reaction, we have potassium (K) reacting with water (H\(_2\)O). Initially, the imbalance in hydrogen and oxygen required adjusting the coefficients. By balancing, 2 moles of K react with water to form 2 KOH and hydrogen gas. This adjustment ensures that the number of potassium, hydrogen, and oxygen atoms is consistent on both sides of the equation. It's important because it respects the law of conservation of mass, which states mass cannot be created or destroyed in a chemical reaction.

Enthalpy Change

The enthalpy change \(\Delta H^{\circ}\) helps us understand the heat exchange during a reaction. A negative \(\Delta H^{\circ}\) suggests the reaction is exothermic, meaning it releases heat, while a positive value indicates an endothermic process, where heat is absorbed. For the reactions we examined, each calculated \(\Delta H^{\circ}\) was negative. This indicates that all reactions are exothermic and release energy. For example, the first reaction with lithium and silver ions resulted in \(\Delta H^{\circ} = -201.4 \mathrm{kJ/mol}\), confirming that energy release occurs making it potentially favorable.

Activity Series

The activity series is a list of elements organized by reactivity, used to predict reactions between metals and their ions. It's essential in determining whether one metal can displace another in a compound. In our exercise, lithium and potassium rank above others like sodium and iron, meaning they can displace less reactive elements in reactions. The second reaction involving sodium and iron confirms this theory; sodium is more reactive than iron, indicating that the reaction is possible. Utilizing the activity series helps predict whether a particular chemical reaction should occur based on the reactivity of the metals involved.

Spontaneity of Reactions

A reaction's spontaneity is often indicated by the Gibbs free energy change \(\Delta G^{\circ}\), but a good indicator is a negative enthalpy change \(\Delta H^{\circ}\). Spontaneous reactions tend to occur naturally without needing external energy under specified conditions. In our exercise, all reactions showed negative \(\Delta H^{\circ}\) values, suggesting they are spontaneous. In practice, factors like temperature and entropy also play a role when determining spontaneity, but within the context of our reactions, the enthalpy change gives a strong indication of the expected outcome.

Reaction Stoichiometry

Stoichiometry involves calculating the quantities of reactants and products in a chemical reaction. This allows us to relate masses and moles of substances. For instance, in balancing and analyzing the reactions given, stoichiometry informs us that for every mole of potassium reacting in the third reaction, we obtain a specific output of KOH and hydrogen gas. Understanding stoichiometry is vital for converting between amounts of different reactants and products. It's an integral part of chemical calculations, ensuring precise reactions and efficient resource use in chemical processes.