What is the correct representation of reaction occurring when \(\mathrm{HCl}\) is heated with \(\mathrm{MnO}_{2} ?\) (a) \(\mathrm{MnO}_{4}^{-}+5 \mathrm{Cl}^{-}+8 \mathrm{H}^{+} \rightarrow \mathrm{Mn}^{2+}+5 \mathrm{Cl}^{-}+5 \mathrm{H}_{2} \mathrm{O}\) (b) \(\mathrm{MnO}_{2}+2 \mathrm{Cl}^{-}+4 \mathrm{H}^{+} \rightarrow \mathrm{Mn}^{2+}+\mathrm{Cl}_{2}+2 \mathrm{H}_{2} \mathrm{O}\) (c) \(2 \mathrm{MnO}_{2}+4 \mathrm{Cl}^{-}+8 \mathrm{H}^{+} \rightarrow 2 \mathrm{Mn}^{2+}+2 \mathrm{Cl}_{2}+4 \mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{MnO}_{2}+4 \mathrm{HCl} \rightarrow \mathrm{MnCl}_{4}+\mathrm{Cl}_{2}+\mathrm{H}_{2} \mathrm{O}\)

When balancing chemical equations, it is crucial to ensure that the number of atoms of each element is the same on both sides of the equation. We operate under the fundamental law of conservation of mass, which states that mass can neither be created nor destroyed in a chemical reaction. Consequently, the same amount of each element must be present before and after the reaction.

For instance, if we compare option (a) and option (b) from the exercises, we count the atoms of each element. Considering chlorine (Cl), there is an issue with option (a) — the reactants show 5 chloride ions, while the products also have 5 chloride ions and additionally free Cl₂ on the right side; the chlorine atoms are not balanced. However, in option (b), the number of chloride ions and the chlorine atoms in the products match correctly, hinting that this is the properly balanced equation.

To proficiently balance the equations, start by balancing the atoms of elements that appear only once on each side of the equation and then proceed to balance the rest, usually leaving hydrogen and oxygen for last. It’s often helpful to use coefficients, whole numbers placed in front of compounds, to equalize the number of atoms on both sides. This is an essential skill in chemistry, which supports further understanding of reaction stoichiometry.

Reaction stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction. It is the part of chemistry that tells us the relative amounts of substances involved in a reaction, using mole ratios derived from the balanced equation.

In the given examples, stoichiometry will indicate the specific ratio of HCl and MnO₂ needed to produce the products. For a correct reaction representation, the coefficients in the balanced equation provide the necessary molar ratios. These ratios are pivotal for calculating how much of each reactant is needed and what amount of product will be yielded.

In option (b), the reaction stoichiometry indicates that one mole of MnO₂ reacts with four moles of hydrogen ions (H⁺) and two moles of chloride ions (Cl⁻) to produce one mole of Mn²⁺, one mole of chlorine gas (Cl₂), and two moles of water (H₂O). This ratio is critical for understanding the scale of the reaction and for performing tasks such as scaling up reactions for industrial purposes or predicting the outcome of laboratory experiments.

Hydrochloric acid (HCl) and manganese dioxide (MnO₂) are two distinct chemicals with unique properties that govern their behavior in reactions.

Properties of HCl:

• It is a strong, corrosive acid commonly used in laboratory and industrial settings.
• In aqueous solution, HCl completely dissociates into hydrogen ions (H⁺) and chloride ions (Cl⁻).
• As a strong acid, it reacts readily with bases and is often used for acid-base neutralizations.

Properties of MnO₂:

• Manganese dioxide is a black or brown solid compound used frequently as a catalyst or in batteries.
• It is stable at room temperature but becomes reactive under heating, leading to the release of oxygen.
• It often acts as an oxidizing agent in chemical reactions.

Understanding the properties of HCl and MnO₂ is essential when predicting and explaining the products of their reaction. When heated with MnO₂, HCl acts as a reducing agent, causing MnO₂ to reduce and form MnCl₂ (manganese chloride), and in the process, Cl₂ (chlorine gas) and H₂O (water) are also produced. The equations in the given exercise should reflect this chemical behavior to be correct.