Question

Which of the following reactions would you expect to proceed at a faster rate at room temperature? Why? (Hint: Think about which reaction would have the lower activation energy.) $\begin{array}{rl}2{\mathrm{Ce}}^{4+}(aq)+{\mathrm{Hg}}_2^{2+}(aq)& ⟶2{\mathrm{Ce}}^{3+}(aq)+2{\mathrm{Hg}}^{2+}(aq)\\ {\mathrm{H}}_3{\mathrm{O}}^{+}(aq)+{\mathrm{OH}}^{-}(aq)& ⟶2{\mathrm{H}}_2\mathrm{O}(l)\end{array}$

Short answer

At room temperature, the acid-base reaction, $H_3{O}^{+}(aq)+O{H}^{-}(aq)⟶2H_{2}O(l)$, is expected to proceed at a faster rate than the redox reaction, $2C{e}^{4+}(aq)+H{g}_2^{2+}(aq)⟶2C{e}^{3+}(aq)+2H{g}^{2+}(aq)$. This is because acid-base reactions generally have lower activation energies compared to redox reactions, as the transfer of protons requires less energy than the transfer of electrons.

Step-by-step solution

Identify reaction types

In order to compare the activation energies of the reactions, it will be helpful to first identify the reaction types. Reaction 1 involves the transfer of electrons between ions (a redox reaction). Specifically, the Ce^4+ ions are reduced to Ce^3+ ions, while the Hg_2^2+ ion is oxidized to two Hg^2+ ions. Reaction 2 involves the transfer of a proton (a Bronsted-Lowry acid-base reaction). The H_3O^+ ion (hydronium ion, a strong Bronsted-Lowry acid) donates a proton to the OH^- ion (hydroxide ion, a strong Bronsted-Lowry base), resulting in the formation of two water molecules.

Compare activation energies

In general, acid-base reactions (such as Reaction 2) have lower activation energies compared to redox reactions (such as Reaction 1). This is because acid-base reactions typically involve the transfer of protons which are generally faster and require lesser energy than the transfer of electrons in redox reactions.

Determine the faster reaction

Based on the comparison of activation energies, we can expect Reaction 2, the acid-base reaction, to have a lower activation energy and thus proceed at a faster rate at room temperature: $H_3{O}^{+}(aq)+O{H}^{-}(aq)⟶2H_{2}O(l)$ This reaction should proceed faster compared to Reaction 1: $2C{e}^{4+}(aq)+H{g}_2^{2+}(aq)⟶2C{e}^{3+}(aq)+2H{g}^{2+}(aq)$

Key concepts

Activation Energy

Activation energy is a crucial concept in reaction kinetics, dictating how quickly a chemical reaction will occur. It refers to the minimum energy that molecules must possess in order to collide effectively and trigger a reaction.

In simpler terms, think of activation energy as a hurdle that reactants need to clear to transform into products. If this hurdle is too high, the reaction proceeds slowly, as fewer molecules possess the necessary energy.

This is why reactions with lower activation energies generally proceed quicker than those with higher ones. The energy barrier is easier to overcome, allowing more reactant molecules to participate in forming products.

In the exercise example, the acid-base reaction (Reaction 2) likely has a lower activation energy compared to the redox reaction (Reaction 1), indicating that the first reaction will occur more rapidly at room temperature.

Acid-Base Reactions

Acid-base reactions involve the transfer of protons between substances, which is a relatively simple process requiring less energy.

• A Bronsted-Lowry acid, like the hydronium ion $H_3{O}^{+}$, donates a proton.
• A Bronsted-Lowry base, like the hydroxide ion $O{H}^{-}$, accepts a proton.

When these ions meet, a water molecule $H_{2}O$ is formed.

The simplicity and speed of this proton transfer explain why acid-base reactions generally have low activation energies.

These reactions are prevalent because they require minimal energy investment to achieve the desired product, thus making them occur at a brisk pace under normal conditions. In our exercise, the transformation of $H_3{O}^{+}$ and $O{H}^{-}$ into water is predicted to occur quickly.

This emphasizes the frequent applicability of acid-base reactions in both laboratory settings and natural biological processes, where organisms rely on the quick conversion of reactants.

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, involve the transfer of electrons between substances, fundamentally altering their oxidation states.

• Reduction occurs when a molecule gains electrons.
• Oxidation involves the loss of electrons.

These processes occur concurrently, where one species is reduced and another is oxidized.

In our example, $C{e}^{4+}$ is reduced to $C{e}^{3+}$ while $H{g}_2^{2+}$ is oxidized to $H{g}^{2+}$.

Redox reactions have higher activation energies in comparison to acid-base reactions.

This is due to the more significant energy barrier needed to facilitate electron transfers between atoms or ions. As a result, redox reactions typically proceed at a slower pace under standard conditions, requiring either increased temperatures or the presence of a catalyst to accelerate the process.

Understanding these principles is vital for applications involving energy storage, corrosion prevention, and various industrial processes.