Problem 56 - Chemistry: The Central Science in SI Units, Global Edition

Question

Write complete balanced half-reactions for (a) reduction of nitrate ion to NO in acidic solution, (b) oxidation of \(\mathrm{HNO}_{2}\) to \(\mathrm{NO}_{2}\) in acidic solution.

Step-by-Step Solution

Answer

(a) \(NO_3^- + 3e^- + 4H^+ -> NO + 2H_2O\) (b) \(HNO_2 + H^+ -> NO_2 + 2H_2O + 2e^-\)

Step 1: For the reduction reaction (a), the nitrate ion (NO3-) will be reduced to nitric oxide (NO), and for the oxidation reaction (b), nitrous acid (HNO2) will be oxidized to nitrogen dioxide (NO2). (a) NO3- -> NO (b) HNO2 -> NO2 #Step 2: Balance the elements other than oxygen and hydrogen#

In both cases, nitrogen is already balanced, as there is one nitrogen atom on each side of the reactions. (a) NO3- -> NO (b) HNO2 -> NO2 #Step 3: Balance oxygen atoms by adding water molecules#

Step 2: We will add water molecules to balance the oxygen atoms. (a) NO3- -> NO + 2H2O (b) HNO2 -> NO2 + H2O #Step 4: Balance hydrogen atoms by adding H+ ions#

Let's balance the hydrogen atoms by adding H+ ions to the reactions. (a) NO3- + 4H+ -> NO + 2H2O (b) HNO2 + H+ -> NO2 + 2H2O #Step 5: Balance the charges by adding electrons#

Step 3: Now, we will balance the charges by adding electrons to the appropriate side of the reactions. (a) NO3- + 3e- + 4H+ -> NO + 2H2O (b) HNO2 + H+ -> NO2 + 2H2O + 2e- #Step 6: Write the balanced half-reactions#

We can now write the balanced half-reactions for each case. (a) NO3- + 3e- + 4H+ -> NO + 2H2O (b) HNO2 + H+ -> NO2 + 2H2O + 2e- The balanced half-reactions for the reduction of nitrate ion to NO in acidic solution are given by (a) and for the oxidation of HNO2 to NO2 in acidic solution by (b) respectively.

Key Concepts

Half-Reactions

In redox chemistry, reactions are typically broken down into two separate parts known as half-reactions. One half-reaction represents oxidation, where electrons are lost, and the other indicates reduction, where electrons are gained. Understanding these half-reactions is crucial for balancing complex redox reactions.

• The reduction half-reaction involves the gaining of electrons, which decreases the oxidation state of a molecule.
• The oxidation half-reaction involves the loss of electrons, which increases the oxidation state of a molecule.

Breaking down the reactions into half-reactions allows for the easy balancing of chemical equations because you can adjust the electrons transferred in each part. This step is essential since it ensures that the number of electrons lost equals the number of electrons gained.

Acidic Solution

When dealing with redox reactions, the medium in which the reaction occurs can significantly influence the balancing process. Here, we are dealing with an acidic solution, which means the reaction takes place in an environment with excess hydrogen ions, \(H^+\). In such conditions, it's common practice to balance the hydrogen atoms by adding \(H^+\) ions.

• Acidic solutions provide protons (hydrogen ions), which are often involved in the half-reaction balancing.
• They also allow the addition of water molecules to balance the oxygen atoms.

By using acidic conditions for the balancing process, you take advantage of the ability to add \(H^+\) ions freely, which simplifies the balancing of hydrogen atoms.

Nitrate Ion Reduction

In the context of this exercise, we look at the reduction of the nitrate ion \(NO_3^-\) to nitric oxide (NO). Reduction is the process wherein a species gains electrons.

• The nitrate ion is reduced by gaining electrons.
• In the balanced half-reaction, 3 electrons () are added to the nitrate ion to balance the charge.

Here's the balanced reduction half-reaction with electron addition: \((NO_3^- + 3e^- + 4H^+ -> NO + 2H_2O)\). This equation shows the nitrate ion gaining electrons and protons to become reduced into NO, while water is formed as a byproduct to help balance oxygen.

Nitrous Acid Oxidation

Oxidation, in this exercise, refers to the conversion of nitrous acid \(HNO_2\) into nitrogen dioxide (NO_2).
The oxidation process involves the loss of electrons:

• Nitrous acid loses electrons, transferring them to support the oxidation process.
• The balanced half-reaction displays the release of electrons: 2 electrons () lost from \(HNO_2\) to form \( NO_2\).

The final balanced oxidation half-reaction shows the changes including the adjustment of water and \(H^+\) ions for stability: \(HNO_2 + H^+ -> NO_2 + 2H_2O + 2e^-\). This equation highlights the loss of electrons, forming nitrogen dioxide successfully, while also balancing out all other necessary atoms and charges.