Problem 98 - Chemistry: An Atoms-Focused Approach

Question

Permanganate ion \(\left(\mathrm{MnO}_{4}^{-}\right)\) is used in water purification to remove oxidizable substances. Complete and balance the following reactions for the removal of sulfide, cyanide, and sulfite. Assume that reaction conditions are basic: a. \(\mathrm{MnO}_{4}^{-}(a q)+\mathrm{S}^{2-}(a q) \rightarrow \mathrm{MnS}(s)+\mathrm{S}_{8}(s)\) b. \(\mathrm{MnO}_{4}^{-}(a q)+\mathrm{CN}^{-}(a q) \rightarrow \mathrm{MnO}_{2}(s)+\mathrm{CNO}^{-}(a q)\) c. \(\operatorname{Mn} \mathrm{O}_{4}^{-}(a q)+\mathrm{SO}_{3}^{2-}(a q) \rightarrow \mathrm{MnO}_{2}(s)+\mathrm{SO}_{4}^{2-}(a q)\)

Step-by-Step Solution

Answer

Question: Identify the balanced chemical equations for the following reactions: a. S^2- (aq) + MnO4^- (aq) → MnS (s) + S8 (s) b. MnO4^- (aq) + CN- (aq) → MnO2 (s) + CNO- (aq) c. MnO4^- (aq) + SO3^2- (aq) → MnO2 (s) + SO4^2- (aq) Answer: a. \(9\,\mathrm{S}^{2-}(a q)+\mathrm{MnO}_{4}^{-}(a q)\rightarrow \mathrm{MnS}(s)+\mathrm{S}_{8}(s)+8\,\mathrm{OH}^{-}(a q)\) b. \(\mathrm{MnO}_{4}^{-}(a q)+\mathrm{CN}^{-}(a q) \rightarrow \mathrm{MnO}_{2}(s)+\mathrm{CNO}^{-}(a q)+2\,\mathrm{OH}^{-}(a q)\) c. \(\operatorname{Mn} \mathrm{O}_{4}^{-}(a q)+\mathrm{SO}_{3}^{2-}(a q) \rightarrow \mathrm{MnO}_{2}(s)+\mathrm{SO}_{4}^{2-}(a q)+3\,\mathrm{OH}^{-}(a q)\)

Step 1: Balancing Mn

There is already 1 Mn atom on each side of the equation, so it doesn't need any further balancing.

Step 2: Balancing S

There is 1 S on the left-hand side and 9 on the right side (1 for MnS and 8 for S_8). To balance sulfur, we need to multiply the left-hand side's S molecule by 9. Now we have: \(9 \mathrm{S}^{2-}(a q) + \mathrm{MnO}_{4}^{-}(a q) \rightarrow  \mathrm{MnS}(s) + \mathrm{S}_{8}(s)\)

Step 3: Balancing charges

The left side has a total charge of -8 and the right side has no charge. To balance the charges, add 8 OH^- ions to the right. The balanced equation becomes: \(9\,\mathrm{S}^{2-}(a q)+\mathrm{MnO}_{4}^{-}(a q)\rightarrow \mathrm{MnS}(s)+\mathrm{S}_{8}(s)+8\,\mathrm{OH}^{-}(a q)\) b. Balancing the second reaction

Step 1: Balancing Mn

Again, there is already 1 Mn atom on each side of the equation. No need to balance further.

Step 2: Balancing C and N

There is 1 C and 1 N atom on each side. No need to balance further.

Step 3: Balancing charges

The left side has a total charge of -2. To balance the charges, add 2 OH^- ions to the right side. The balanced equation becomes: \(\mathrm{MnO}_{4}^{-}(a q)+\mathrm{CN}^{-}(a q) \rightarrow \mathrm{MnO}_{2}(s)+\mathrm{CNO}^{-}(a q)+2\,\mathrm{OH}^{-}(a q)\) c. Balancing the third reaction

Step 1: Balancing Mn

There is 1 Mn atom on each side. No need to balance further.

Step 2: Balancing S and O

There is 1 S atom and 4 O atoms on each side. No need to balance further.

Step 3: Balancing charges

The left side has a total charge of -3. To balance the charges, add 3 OH^- ions to the right side. The balanced equation becomes: \(\operatorname{Mn} \mathrm{O}_{4}^{-}(a q)+\mathrm{SO}_{3}^{2-}(a q) \rightarrow \mathrm{MnO}_{2}(s)+\mathrm{SO}_{4}^{2-}(a q)+3\,\mathrm{OH}^{-}(a q)\)

Key Concepts

Permanganate Ion in Oxidation Reactions

The permanganate ion, represented as \( \mathrm{MnO}_{4}^{-} \), is a potent oxidizing agent. It plays a crucial role in many redox (oxidation-reduction) reactions due to its ability to accept electrons. When permanganate ions are used in reactions under basic conditions, they commonly reduce to manganese dioxide \( \mathrm{MnO}_{2} \), a stable solid form. In chemical equations, it's essential to balance the number of atoms and charges. This ensures that the law of conservation of mass and charge is upheld. In redox reactions, especially, permanganate ions help remove unwanted oxidizable substances by turning them into less harmful compounds. It does this by delivering its powerful oxidizing potential to the substances needing purification. So, whenever you see \( \mathrm{MnO}_{4}^{-} \) in a reaction, it's quite likely playing the role of a 'clean-up' molecule, tackling various pollutants effectively.

Water Purification Through Chemistry

Water purification is a critical process that ensures safe drinking water by removing contaminants. Permanganate ions are often utilized for this because they are very effective at oxidizing harmful substances present in water. For example, sulfides, cyanides, and sulfites are compounds that can be dangerous if present in drinking water. By reacting these with permanganate ions, they can be converted to non-toxic forms. For instance:

• Sulfides react to form solid manganese sulfide and elemental sulfur.
• Cyanides convert to manganese dioxide, with cyanate ions as by-products.
• Sulfites turn into sulfate, a safer compound.

Utilizing permanganate ions in purification processes helps protect public health by ensuring the water is safe and clean. Water treatment facilities can rely on these chemical reactions to improve water quality efficiently.

Understanding Redox Balancing

Redox balancing is a critical skill in chemistry, especially when working with reactions involving oxidizing agents like permanganate ions. The aim is to ensure that both sides of a chemical equation have equal numbers of atoms for each element and equal total charges. The process involves several steps:

• Balance the main elements involved, such as Mn in permanganate reactions.
• Adjust the number of atoms that appear on each side. For instance, balance sulfur atoms by determining their appearance in various compounds.
• Finally, adjust the charges using ions, like \( \mathrm{OH}^{-} \), to ensure both sides of the equation have the same net charge.

This systematic approach is particularly important in basic conditions where hydroxide ions play a role in balancing charges. Understanding these steps is essential for anyone aiming to master redox reactions in chemistry.

Reactions Under Basic Conditions

Basic conditions in a chemical reaction mean that the solution has an abundance of \( \mathrm{OH}^{-} \) ions, or hydroxide ions. These conditions can influence the outcome of chemical reactions, particularly oxidation-reduction processes.In the reactions involving permanganate ions, basic conditions require special attention to charge balance. When completing and balancing reactions in basic conditions, you'd typically add \( \mathrm{OH}^{-} \) ions to balance the overall charge. This differs from reactions in acidic conditions where hydrogen ions (\( \mathrm{H}^{+} \)) are used. By maintaining basic conditions, you ensure that the calculations and balances result in environmentally benign and stable compounds. Thus, considering the reaction conditions is crucial to correctly implementing reactions involving permanganate ions, making full use of their oxidizing capacity.