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Chapter 15: Problem 24

Use the half-reaction method to balance each of the following in acidic solution: a. \(\mathrm{Mn}(s)+\mathrm{NO}_{3}^{-}(a q) \longrightarrow \mathrm{Mn}^{2+}(a q)+\mathrm{NO}_{2}(g)\) b. \(\mathrm{C}_{2} \mathrm{O}_{4}{ }^{2-}(a q)+\mathrm{MnO}_{4}^{-}(a q) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{Mn}^{2+}(a q)\) c. \(\mathrm{ClO}_{3}^{-}(a q)+\mathrm{SO}_{3}^{2-}(a q) \longrightarrow \mathrm{Cl}^{-}(a q)+\mathrm{SO}_{4}^{2-}(a q)\)

Short Answer

Expert verified
(a) Mn(s) + 2NO鈧冣伝(aq) + 4H鈦(aq) 鈫 Mn虏鈦(aq) + 2NO鈧(g) + 2H鈧侽(l)(b) 5C鈧侽鈧劼测伝(aq) + 2MnO鈧勨伝(aq) + 16H鈦(aq) 鈫 10CO鈧(g) + 2Mn虏鈦(aq) + 8H鈧侽(l)(c) ClO鈧冣伝(aq) + 3SO鈧兟测伝(aq) + 6H鈦(aq) 鈫 Cl鈦(aq) + 3SO鈧劼测伝(aq) + 3H鈧侽(l)

Step by step solution

01

Separate into Half-Reactions (a)

First, identify and separate the oxidation and reduction half-reactions for the given equation. For part (a), the half-reactions are:Mn(s) 鈫 Mn虏鈦(aq) (oxidation) NO鈧冣伝(aq) 鈫 NO鈧(g) (reduction)
02

Balance Atoms (Excluding O and H) (a)

Balance all atoms except for oxygen and hydrogen in each half-reaction. For part (a): The atoms already balance.Mn(s) 鈫 Mn虏鈦(aq) NO鈧冣伝(aq) 鈫 NO鈧(g)
03

Balance Oxygen Atoms with H鈧侽 (a)

Add H鈧侽 molecules to balance the oxygen atoms: NO鈧冣伝(aq) 鈫 NO鈧(g) + H鈧侽(l)
04

Balance Hydrogen Atoms with H鈦 (a)

Add H鈦 ions to balance the hydrogen atoms: NO鈧冣伝(aq) + 2H鈦(aq) 鈫 NO鈧(g) + H鈧侽(l)
05

Balance Charge with Electrons (a)

Add electrons to balance the charge in each half-reaction: For oxidation: Mn(s) 鈫 Mn虏鈦(aq) + 2e鈦籉or reduction: NO鈧冣伝(aq) + 2H鈦(aq) + e鈦 鈫 NO鈧(g) + H鈧侽(l)
06

Equalize Electron Transfer (a)

Multiply the half-reactions to equalize the number of electrons transferred: 2(NO鈧冣伝(aq) + 2H鈦(aq) + e鈦 鈫 NO鈧(g) + H鈧侽(l)) Mn(s) 鈫 Mn虏鈦(aq) + 2e鈦
07

Combine and Simplify (a)

Add the two half-reactions together and eliminate any common species:Mn(s) + 2NO鈧冣伝(aq) + 4H鈦(aq) 鈫 Mn虏鈦(aq) + 2NO鈧(g) + 2H鈧侽(l)
08

Repeat Steps 1-7 for (b)

Follow the same steps for part (b). Separate into half-reactions:C鈧侽鈧劼测伝(aq) 鈫 CO鈧(g) MnO鈧勨伝(aq) 鈫 Mn虏鈦(aq)Balanced form:Oxidation: C鈧侽鈧劼测伝(aq) 鈫 2CO鈧(g) + 2e鈦 Reduction: MnO鈧勨伝(aq) + 8H鈦(aq) + 5e鈦 鈫 Mn虏鈦(aq) + 4H鈧侽(l)Multipli: 5(C鈧侽鈧劼测伝(aq) 鈫 2CO鈧(g) + 2e鈦) 2(MnO鈧勨伝(aq) + 8H鈦(aq) + 5e鈦 鈫 Mn虏鈦(aq) + 4H鈧侽(l))Combined: 5C鈧侽鈧劼测伝(aq) + 2MnO鈧勨伝(aq) + 16H鈦(aq) 鈫 10CO鈧(g) + 2Mn虏鈦(aq) + 8H鈧侽(l)
09

Repeat Steps 1-7 for (c)

Follow the same steps for part (c). Separate into half-reactions:ClO鈧冣伝(aq) 鈫 Cl鈦(aq) SO鈧兟测伝(aq) 鈫 SO鈧劼测伝(aq)Balanced form:Oxidation: SO鈧兟测伝(aq) + H鈧侽(l) 鈫 SO鈧劼测伝(aq) + 2H鈦(aq) + 2e鈦 Reduction: ClO鈧冣伝(aq) + 6H鈦(aq) + 6e鈦 鈫 Cl鈦(aq) + 3H鈧侽(l)Multipli: 3(SO鈧兟测伝(aq) + H鈧侽(l) 鈫 SO鈧劼测伝(aq) + 2H鈦(aq) + 2e鈦)Combined: ClO鈧冣伝(aq) + 3SO鈧兟测伝(aq) + 6H鈦(aq) 鈫 Cl鈦(aq) + 3SO鈧劼测伝(aq) + 3H鈧侽(l)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Half-Reaction Method
Understanding the half-reaction method is essential when dealing with redox reactions. This method splits a redox reaction into two parts: oxidation and reduction half-reactions. By doing this, it becomes easier to balance the overall chemical equation.

  • Oxidation half-reaction: This part involves the loss of electrons.
  • Reduction half-reaction: This part involves the gain of electrons.

The steps to balance these half-reactions include:
  • Identify and separate the oxidation and reduction reactions.
  • Balance all atoms except for hydrogen and oxygen.
  • Add H2O to balance oxygen atoms.
  • Add H+ to balance hydrogen atoms.
  • Add electrons to balance the charges.
  • Combine the half-reactions making sure the number of electrons is the same in both.
Oxidation-Reduction Reactions
Oxidation-reduction (redox) reactions involve the transfer of electrons between chemical species. These reactions are fundamental in chemistry as they describe changes in oxidation states.

  • Oxidation: Involves the loss of electrons and an increase in oxidation state.
  • Reduction: Involves the gain of electrons and a decrease in oxidation state.

To identify redox reactions:
  • Determine the oxidation states of the reactants and products.
  • Identify which species is oxidized and which is reduced.
  • Use the half-reaction method to balance the overall equation.
Acidic Solutions
When balancing redox reactions in acidic solutions, certain additional steps are necessary. Acidic conditions provide H+ ions, which are used to balance hydrogen atoms in the half-reactions.

The general steps for balancing redox reactions in acidic solutions are:
  • Separate into oxidation and reduction half-reactions.
  • Balance all atoms except hydrogen and oxygen.
  • Add H2O to balance the oxygen atoms.
  • Add H+ to balance the hydrogen atoms.
  • Balance the charges by adding electrons.

This method ensures the reaction is correctly balanced in the acidic medium.
Electron Transfer
Electron transfer is at the core of redox reactions. Understanding the flow of electrons allows us to balance these reactions accurately. In every redox reaction:

  • One species loses electrons (oxidation).
  • Another species gains electrons (reduction).

To effectively balance the electron transfer:
  • Determine the number of electrons lost in the oxidation half-reaction.
  • Determine the number of electrons gained in the reduction half-reaction.
  • Ensure the electrons lost equal the electrons gained when combining the half-reactions.

This equalization of electrons is crucial for maintaining the law of conservation of charge.
Chemical Equation Balancing
Balancing chemical equations ensures that the law of conservation of mass is upheld. Each element must have the same number of atoms on both sides of the equation.

Steps to balance a chemical equation include:
  • Write the unbalanced equation.
  • Identify and write down the oxidation and reduction half-reactions.
  • Balance the atoms in each half-reaction.
  • Balance the oxygen atoms by adding H2O.
  • Balance the hydrogen atoms by adding H+.
  • Balance the charges by adding electrons.
  • Combine the half-reactions and simplify.

Following these steps ensures a properly balanced chemical equation that adheres to fundamental chemical principles.

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Most popular questions from this chapter

Assign oxidation numbers to the elements in each of the following: (15.1) a. \(\mathrm{H}_{2} \mathrm{O}_{2}\) b. \(\mathrm{Cl}_{2} \mathrm{O}_{7}\) c. \(\mathrm{SO}_{3}^{2-}\) d. \(\mathrm{N}_{2} \mathrm{H}_{4}\)

For each of the following reactions, identify the substance that is oxidized, the substance that is reduced, the oxidizing agent, and the reducing agent: a. \(2 \mathrm{HgO}(s) \longrightarrow 2 \mathrm{Hg}(l)+\mathrm{O}_{2}(g)\) b. \(\mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g)\) c. \(2 \mathrm{Na}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{Na}^{+}(a q)+2 \mathrm{OH}^{-}(a q)+\mathrm{H}_{2}(g)\) d. \(14 \mathrm{H}^{+}(a q)+6 \mathrm{Fe}^{2+}(a q)+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q) \longrightarrow\) $$ 6 \mathrm{Fe}^{3+}(a q)+2 \mathrm{Cr}^{3+}(a q)+7 \mathrm{H}_{2} \mathrm{O}(l) $$

Identify each of the following as an oxidation or a reduction reaction: a. \(\mathrm{Ni}^{2+}(a q) \longrightarrow \mathrm{Ni}^{3+}(a q)+e^{-}\) b. \(\mathrm{K}^{+}(a q)+e^{-} \longrightarrow \mathrm{K}(s)\) c. \(\mathrm{Br}_{2}(l)+2 e^{-} \longrightarrow 2 \mathrm{Br}^{-}(a q)\)

Assign oxidation numbers to all the elements in each of the following: a. \(\mathrm{N}_{2} \mathrm{O}\) b. \(\mathrm{LiOH}\) c. \(\mathrm{SbO}_{2}^{=}\) d. \(\mathrm{IO}_{4}^{-}\)

Write the balanced half-reactions and a balanced redox equation for each of the following reactions in acidic solution: \((15.2)\) a. \(\mathrm{Sn}^{2+}(a q)+\mathrm{IO}_{4}^{-}(a q) \longrightarrow \mathrm{Sn}^{4+}(a q)+\mathrm{I}^{-}(a q)\) b. \(\mathrm{S}_{2} \mathrm{O}_{3}{ }^{2-}(a q)+\mathrm{I}_{2}(s) \longrightarrow \mathrm{S}_{4} \mathrm{O}_{6}^{2-}(a q)+\mathrm{I}^{-}(a q)\) c. \(\mathrm{Mg}(s)+\mathrm{VO}_{4}{ }^{3-}(a q) \longrightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{V}^{2+}(a q)\) d. \(\mathrm{Al}(s)+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q) \longrightarrow \mathrm{Al}^{3+}(a q)+\mathrm{Cr}^{3+}(a q)\)
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