Question

\(2 \mathrm{MnO}_{4}^{-}+\mathrm{aH}^{+}+\mathrm{bH}_{2} \mathrm{O}_{2} \longrightarrow 2 \mathrm{Mn}^{+2}+\mathrm{H}_{2} \mathrm{O}+\mathrm{dO}_{2}\) What are the values of \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) and \(\mathrm{d} ?\) (a) \(4,5,4,5\) (b) \(6,5,8,5\) (c) \(3,2,4,8\) (d) \(2,5,4,6\)

Short answer

The answer is: None of the given options are correct.

Step-by-step solution

Write the oxidation half-reaction

In the reaction, hydrogen peroxide \( H_2O_2 \) acts as a reducing agent, losing an oxygen atom. The half-reaction indicating this change is written as: \[ H_2O_2 \rightarrow O_2 + 2H^+ + 2e^- \]

Write the reduction half-reaction

Manganate ions \( MnO_4^- \) are reduced to \( Mn^{2+} \). The reduction half-reaction is: \[ MnO_4^- + 8H^+ + 5e^- \rightarrow Mn^{2+} + 4H_2O \]

Balance electrons in oxidation and reduction half-reactions

For balancing, equalize the number of electrons transferred in both half-reactions. Multiply oxidation half-reaction by 5 and reduction half-reaction by 2 to equate electrons: 1. \( 5(H_2O_2 \rightarrow O_2 + 2H^+ + 2e^-) \)2. \( 2(MnO_4^- + 8H^+ + 5e^- \rightarrow Mn^{2+} + 4H_2O) \)

Combine and simplify the balanced half-reactions

Add the two balanced half-reactions together: - From oxidation: \( 5H_2O_2 \rightarrow 5O_2 + 10H^+ + 10e^- \)- From reduction: \( 2MnO_4^- + 16H^+ + 10e^- \rightarrow 2Mn^{2+} + 8H_2O \)Combine: \( 2MnO_4^- + 16H^+ + 5H_2O_2 \rightarrow 2Mn^{2+} + 8H_2O + 5O_2 \)

Identify coefficients \(a, b, c, d\)

The combined equation shows the coefficients determining the number of each species. Comparing with the given equation structure, we find: \( a = 16 \), \( b = 5 \), \( c = 8 \), and \( d = 5 \).

Key concepts

Balancing Chemical Equations

Balancing chemical equations is an essential skill in chemistry that ensures the conservation of mass in a reaction. To balance an equation, we adjust the coefficients of the reactants and products until the number of each type of atom is equal on each side of the equation. This process reflects the principle that matter is neither created nor destroyed in chemical reactions. Here’s a simple approach to get started:

• Write the unbalanced equation.
• List all elements involved in the reaction.
• Count the number of atoms for each element on both sides of the reaction.
• Adjust coefficients, not subscripts, to balance the atoms. Begin with the most complex molecule.
• Re-check your work to ensure all elements are balanced.

In many redox reactions, balancing requires extra steps, like assigning oxidation states and using the half-reaction method, which ensures both mass and charge balance, as we’ll discuss in the next sections.

Oxidation-Reduction

Oxidation-reduction (redox) reactions are unique because they involve the transfer of electrons between substances. In these reactions, one substance loses electrons (oxidized) while another gains them (reduced). Understanding this electron transfer is crucial for balancing redox reactions. To identify what's being oxidized and reduced:

• Determine the oxidation state of each element before and after the reaction.
• The substance whose oxidation state increases is oxidized.
• The substance whose oxidation state decreases is reduced.

In our example, hydrogen peroxide acts as a reducing agent, losing electrons and oxygen, while manganate ions gain electrons thus reduced to Mn²⁺. Redox also involves supporting ions, such as hydrogen ions in acidic solutions, to facilitate the electron transfer. These reactions are often more complex, thus requiring systematic methods to ensure accurate balancing, such as the half-reaction method.

Half-Reaction Method

The half-reaction method is a systematic procedure used in balancing redox reactions. It breaks the process down into smaller, manageable parts by focusing on oxidation and reduction separately. Here’s how this method works:

• Separate the reactions: Identify and write the oxidation and reduction half-reactions.
• Balance atoms and charges: Balance all elements except oxygen and hydrogen first, then balance oxygen by adding water molecules, and hydrogen by adding hydrogen ions. Add electrons to balance the charge on each side.
• Equalize electron transfer: Multiply the half-reactions as necessary to ensure the number of electrons lost in oxidation equals the number gained in reduction.
• Combine half-reactions: Add the two half-reactions, canceling out electrons and other species present on both sides.
• Final adjustments: Check to ensure all elements and charges are balanced correctly in the final combined equation.

By the end of this procedure, you should have a fully balanced redox equation, like the combination of manganate ions and hydrogen peroxide in the given exercise. The half-reaction method is particularly helpful in cases involving complex reactions and ionic equations.