Question

$$ \mathrm{Hg}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \rightarrow \mathrm{Hg}(\mathrm{l}) \text { and } \mathrm{Cr}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \rightarrow \mathrm{Cr}(\mathrm{s}) $$

Short answer

In the given half-reactions, both mercury and chromium ions undergo reduction processes by gaining electrons. Mercury ions (\(\mathrm{Hg}^{2+}\)) gain two electrons to form liquid mercury (\(\mathrm{Hg}\)), while chromium ions (\(\mathrm{Cr}^{2+}\)) gain two electrons to form solid chromium (\(\mathrm{Cr}\)). In both cases, the oxidation state decreases from +2 to 0, indicating a transition from ionic to elemental form.

Step-by-step solution

Identify the half-reactions

Each half-reaction represents a reduction or oxidation process involving an exchange of electrons. In both cases, there are two electrons being added and taken away by the metal ions: 1. Mercury (Hg) half-reaction: $$\mathrm{Hg}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \rightarrow \mathrm{Hg}(\mathrm{l}) $$ 2. Chromium (Cr) half-reaction: $$\mathrm{Cr}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \rightarrow \mathrm{Cr}(\mathrm{s})$$

Understand the Mercury half-reaction

The mercury half-reaction represents the reduction of mercury ions to liquid mercury. The reaction shows that a mercury ion (Hg^2+, in aqueous solution) gains two electrons to form liquid mercury (Hg). This process is a reduction since the mercury ions gain electrons.

Understand the Chromium half-reaction

The chromium half-reaction represents the reduction of chromium ions to solid chromium. The reaction indicates that a chromium ion (Cr^2+, in aqueous solution) gains two electrons to form solid chromium (Cr). This process is also a reduction since the chromium ions gain electrons.

Observations on Oxidation States

In both half-reactions, the metal ions undergo a change in their oxidation states: 1. Mercury (Hg) half-reaction: The oxidation state of mercury drops from +2 (Hg^2+) to 0 (Hg). 2. Chromium (Cr) half-reaction: The oxidation state of chromium drops from +2 (Cr^2+) to 0 (Cr). In both cases, the oxidation state decreases, indicating that both reactions involve a change from an ion to its elemental form, i.e., a reduction process.

Recap

In summary, the provided half-reactions involve the reduction of mercury and chromium ions by gaining electrons. Both metal ions change from their ionic forms to their elemental forms, with their oxidation states dropping from +2 to 0.

Key concepts

Oxidation and Reduction

In the world of chemistry, oxidation and reduction are two halves of the same whole called redox reactions. They describe how atoms or molecules either lose or gain electrons, respectively. During oxidation, an element's oxidation state increases as it loses electrons, becoming more positive. Meanwhile, reduction describes the process where an element gains electrons, leading to a decrease in its oxidation state, becoming more negative or neutral. It's easy to remember this through the mnemonic 'LEO says GER' which stands for 'Loss of Electrons is Oxidation; Gain of Electrons is Reduction'.

For example, in the case of the mercury and chromium half-reactions, the mercury ions (Hg²⁺) and chromium ions (Cr²⁺) gain two electrons and are reduced to their elemental forms, hence experiencing a decrease in their oxidation states from +2 to 0.

Electrochemistry

At the heart of electrochemistry lies the study of redox reactions that occur with a transfer of electrons and the generation of electrical current. It explores the flow of electrons from one species to another. This field plays a critical role in everything from batteries to electrolysis. In electrochemical cells, oxidation occurs at the anode (positive electrode) and reduction occurs at the cathode (negative electrode), separating the two half-reactions spatially. The two half-reactions described for mercury and chromium are reductions that would occur at the cathode in an electrochemical cell, where electrons are supplied to the metallic ions to reduce them to their elemental forms.

Redox Reactions

Redox reactions combine the concepts of oxidation and reduction into one unified process. In any redox reaction, there is always both oxidation and reduction taking place simultaneously, which is why these reactions are often referred to as 'redox' (reduction-oxidation) reactions. In a typical redox reaction, one species will donate electrons (gets oxidized) while another will accept electrons (gets reduced). An essential part of understanding these reactions is balancing the total number of electrons lost and gained to ensure mass and charge are conserved. Considering the half-reactions given, one could pair each with a corresponding oxidation half-reaction to form a complete redox process.

Oxidation States

The concept of oxidation states allows chemists to keep track of electron transfer during redox reactions. These states are assigned as integers to elements in chemical species, reflecting the potential charge an atom might carry as if all molecules were ionic rather than covalent. Changes in oxidation state during a reaction indicate whether oxidation or reduction has occurred. Elements in their elemental form, like Hg(l) and Cr(s) after reduction, have an oxidation state of 0. In contrast, the positive values of Hg²⁺ and Cr²⁺ indicate that these atoms originally lost electrons, thus were oxidized, before undergoing the reduction presented in the half-reactions shown.