Question

When magnesium metal is added to a beaker of \(\mathrm{HCl}(a q)\), a gas is produced. Knowing that magnesium is oxidized and that hydrogen is reduced, write the balanced equation for the reaction. How many electrons are transferred in the balanced equation? What quantity of useful work can be obtained when \(\mathrm{Mg}\) is added directly to the beaker of HCl? How can you harness this reaction to do useful work?

Short answer

The balanced equation for the reaction between magnesium and hydrochloric acid is \(Mg + 2HCl \rightarrow MgCl_{2} + H_{2}\). In this reaction, 2 electrons are transferred: \(Mg \rightarrow Mg^{2+} + 2e^{-}\) and \(2H^{+} + 2e^{-} \rightarrow H_{2}\). The reaction releases energy in the form of heat and gas (hydrogen gas is produced), which can be harnessed to do useful work. One way to harness this reaction is by using a magnesium-air fuel cell, where electric energy is produced and can be used as a portable power source.

Step-by-step solution

Write the half-reactions

Recall that in a redox reaction, oxidation and reduction occur simultaneously. For this reaction, we know that magnesium (Mg) is being oxidized, and hydrogen (H) is being reduced, with hydrochloric acid HCl as the reactant. The half-reactions are: Oxidation (Mg to Mg²⁺): \(Mg \rightarrow Mg^{2+} + 2e^{-}\) Reduction (H⁺ to H₂): \(2H^{+} + 2e^{-} \rightarrow H_{2}\)

Combine the half-reactions

Now, we need to combine the half-reactions to obtain the balanced equation for the overall reaction. Since the number of electrons involved in both half-reactions is the same (2), we can simply add the half-reactions without multiplying them by any factors: \(Mg + 2H^{+} \rightarrow Mg^{2+} + H_{2}\)

Include the aqueous chloride ions

In the balanced equation, we haven't yet considered the chloride ions (Cl⁻) that are present in the aqueous \(\mathrm{HCl}(a q)\). To include these, we simply add them to the reaction: \(Mg + 2HCl \rightarrow Mg^{2+} + 2Cl^{-} + H_{2}\)

Write the balanced net ionic equation

Since the magnesium and chloride ions will combine to form magnesium chloride (MgCl₂) in the products, we can rewrite the equation as: \(Mg + 2HCl \rightarrow MgCl_{2} + H_{2}\) This is the balanced equation for the reaction.

Determine the number of electrons transferred

The balanced equation shows that 2 electrons are transferred from magnesium to hydrogen: \(Mg \rightarrow Mg^{2+} + 2e^{-}\) \(2H^{+} + 2e^{-} \rightarrow H_{2}\)

Determine the useful work and how to harness the reaction

The reaction between magnesium and hydrochloric acid releases energy in the form of heat and gas (hydrogen gas is produced) that can be harnessed to do useful work. However, the amount of useful work to be calculated would require information about the Gibbs free energy change and the moles of reactants involved. To harness the energy produced by the reaction, you could use a magnesium-air fuel cell, where magnesium reacts with oxygen and produces electric energy, which can be used immediately or stored for later use. Such fuel cells can be used as portable power sources for various applications.

Key concepts

Oxidation and Reduction

Understanding how substances interact in redox reactions is crucial for comprehending many natural processes and technological applications such as batteries. Oxidation and reduction, often referred to together as redox reactions, are chemical processes involving electron transfer between reactants.

Oxidation involves the loss of electrons — when a substance loses electrons, we say it has been oxidized. In our exercise, magnesium (Mg) loses two electrons to form Mg²⁺. Conversely, reduction is the gain of electrons. Hydrogen ions (H⁺), in receiving electrons, are reduced to form hydrogen gas (H₂).

It's essential to remember that these two reactions always occur together; one substance cannot be oxidized unless another is reduced, making it a sort of chemical 'give and take'.

Balancing Chemical Equations

The importance of balancing chemical equations cannot be overstated, as it ensures the law of conservation of mass is respected, meaning matter is neither created nor destroyed during a chemical reaction. When balancing equations, we adjust coefficients (never subscripts) to have the same number of atoms of each element on both sides of the equation.

In the given example, we balanced the equation by ensuring the number of hydrogen atoms and magnesium atoms are the same on both sides. The chloride ions were included since they're part of the hydrochloric acid but remain unchanged during the reaction. We end up with a balanced net ionic equation showing reactants and products without spectator ions, simplifying our understanding of the chemical changes taking place.

Determining Electrons Transferred

The number of electrons transferred in a reaction tells us about the reaction's stoichiometry and helps to determine its potential to do work or its electrical characteristics when utilized in applications like batteries. In redox reactions, it's vital to ensure that the same number of electrons is lost by the oxidized substance as is gained by the reduced substance to maintain charge balance.

In our exercise, magnesium metal loses 2 electrons, which are then gained by hydrogen ions to form hydrogen gas. Remember, recognizing and counting these electrons correctly is the backbone of electrochemistry, which explores the relationships between chemical changes and electrical energy.

Magnesium-Air Fuel Cell

The magnesium-air fuel cell is a type of battery that harnesses the redox reaction between magnesium and oxygen from the air to generate electricity. This process is a clean energy source because the only by-products are magnesium oxide and potentially hydrogen, depending on the specific design of the cell. These fuel cells are known for their high energy density and are considered for emergency power supplies and portable power applications.

To harness the reaction from the exercise in a practical application, we could theoretically adapt it to the mechanics of a magnesium-air fuel cell. Instead of magnesium reacting with HCl, it would react with O₂ in the air, under controlled conditions, to provide a steady flow of electrical current — a process that is eco-friendly, with no greenhouse gas emissions.