Question

Balance each of the following half-reactions, which take place in acidic solution. a. ${\mathrm{O}}_2(g)\to {\mathrm{H}}_2\mathrm{O}(l)$ $\mathrm{b}.{\mathrm{SO}}_4^{2-}(aq)\to {\mathrm{H}}_2{\mathrm{SO}}_3(aq)$ c. ${\mathrm{H}}_2{\mathrm{O}}_2(aq)\to {\mathrm{H}}_2\mathrm{O}(l)$ d. ${\mathrm{NO}}_2^{-}(aq)\to {\mathrm{NO}}_3^{-}(aq)$

Short answer

a. ${\mathrm{O}}_2(g)+2{\mathrm{H}}^{+}(aq)\to {\mathrm{H}}_2\mathrm{O}(l)$ b. ${\mathrm{SO}}_4^{2-}(aq)+2{\mathrm{H}}^{+}(aq)\to {\mathrm{H}}_2{\mathrm{SO}}_3(aq)+{\mathrm{H}}_2\mathrm{O}(l)$ c. ${\mathrm{H}}_2{\mathrm{O}}_2(aq)\to {\mathrm{H}}_2\mathrm{O}(l)$ d. ${\mathrm{NO}}_2^{-}(aq)+{\mathrm{H}}_2\mathrm{O}(l)\to {\mathrm{NO}}_3^{-}(aq)+2{\mathrm{H}}^{+}(aq)+2{\mathrm{e}}^{-}$

Step-by-step solution

1. Balance atoms other than H and O

There are no other atoms to balance, so we can move on to the next step.

2. Balance O atoms by adding water molecules

There are 2 oxygen atoms on each side of the equation, so we don't need to add any water molecules to balance the O atoms.

3. Balance H atoms by adding protons (H+ ions)

Currently, there are no H atoms on the left side of the equation and 2 on the right side. To balance, add 2 H+ ions to the left side: $${\mathrm{O}}_2(g)+2{\mathrm{H}}^{+}(aq)\to {\mathrm{H}}_2\mathrm{O}(l).$$

4. Balance charges by adding electrons (e-)

Both sides are neutral right now, so there is no need to add any electrons.

5. Verify mass and charge balance in the half-reaction

The balanced half-reaction is: $${\mathrm{O}}_2(g)+2{\mathrm{H}}^{+}(aq)\to {\mathrm{H}}_2\mathrm{O}(l).$$ Mass and charge are balanced. b. ${\mathrm{SO}}_4^{2-}(aq)\to {\mathrm{H}}_2{\mathrm{SO}}_3(aq)$

1. Balance atoms other than H and O

First, balance the S atoms: $${\mathrm{SO}}_4^{2-}(aq)\to {\mathrm{H}}_2{\mathrm{SO}}_3(aq).$$

2. Balance O atoms by adding water molecules

As we have 4 O atoms on the left side and 3 on the right, add a water molecule to the right side: $${\mathrm{SO}}_4^{2-}(aq)\to {\mathrm{H}}_2{\mathrm{SO}}_3(aq)+{\mathrm{H}}_2\mathrm{O}(l).$$

3. Balance H atoms by adding protons (H+ ions)

We have 4 H atoms on the right side, so to balance, add 2 H+ ions to the left side: $${\mathrm{SO}}_4^{2-}(aq)+2{\mathrm{H}}^{+}(aq)\to {\mathrm{H}}_2{\mathrm{SO}}_3(aq)+{\mathrm{H}}_2\mathrm{O}(l).$$

4. Balance charges by adding electrons (e-)

The left side has a net charge of +2-2 = 0, and the right side also has a net charge of 0. Thus, no electrons are needed to balance the charges.

5. Verify mass and charge balance in the half-reaction

The balanced half-reaction is: $${\mathrm{SO}}_4^{2-}(aq)+2{\mathrm{H}}^{+}(aq)\to {\mathrm{H}}_2{\mathrm{SO}}_3(aq)+{\mathrm{H}}_2\mathrm{O}(l).$$ Mass and charge are balanced. c. ${\mathrm{H}}_2{\mathrm{O}}_2(aq)\to {\mathrm{H}}_2\mathrm{O}(l)$

1. Balance atoms other than H and O

There are no other atoms to balance, so we can move on to the next step.

2. Balance O atoms by adding water molecules

As we have 2 O atoms on each side of the equation, no need to add water molecules to balance the O atoms.

3. Balance H atoms by adding protons (H+ ions)

There are 2 H atoms on each side of the equation, so there is no need to add protons to balance the H atoms.

4. Balance charges by adding electrons (e-)

The left side has a net charge of 0, and the right side also has a net charge of 0. Thus, no electrons are needed to balance the charges.

5. Verify mass and charge balance in the half-reaction

The balanced half-reaction is: $${\mathrm{H}}_2{\mathrm{O}}_2(aq)\to {\mathrm{H}}_2\mathrm{O}(l).$$ Mass and charge are balanced. d. ${\mathrm{NO}}_2^{-}(aq)\to {\mathrm{NO}}_3^{-}(aq)$

1. Balance atoms other than H and O

First, balance the N atoms: $${\mathrm{NO}}_2^{-}(aq)\to {\mathrm{NO}}_3^{-}(aq).$$

2. Balance O atoms by adding water molecules

As we have 2 O atoms on the left side and 3 on the right, add a water molecule to the left side: $${\mathrm{NO}}_2^{-}(aq)+{\mathrm{H}}_2\mathrm{O}(l)\to {\mathrm{NO}}_3^{-}(aq).$$

3. Balance H atoms by adding protons (H+ ions)

We have 2 H atoms on the left side and none on the right side, so to balance, add 2 H+ ions to the right side: $${\mathrm{NO}}_2^{-}(aq)+{\mathrm{H}}_2\mathrm{O}(l)\to {\mathrm{NO}}_3^{-}(aq)+2{\mathrm{H}}^{+}(aq).$$

4. Balance charges by adding electrons (e-)

The left side has a net charge of -1, while the right side has a net charge of -1+2 = +1. To balance the charges, we need to add 2 electrons (2e-) to the right side: $${\mathrm{NO}}_2^{-}(aq)+{\mathrm{H}}_2\mathrm{O}(l)\to {\mathrm{NO}}_3^{-}(aq)+2{\mathrm{H}}^{+}(aq)+2{\mathrm{e}}^{-}.$$

5. Verify mass and charge balance in the half-reaction

The balanced half-reaction is: $${\mathrm{NO}}_2^{-}(aq)+{\mathrm{H}}_2\mathrm{O}(l)\to {\mathrm{NO}}_3^{-}(aq)+2{\mathrm{H}}^{+}(aq)+2{\mathrm{e}}^{-}.$$ Mass and charge are balanced.

Key concepts

balancing chemical equations

Balancing chemical equations is essential to maintaining the law of conservation of mass. This law states that matter cannot be created or destroyed in a closed system. Thus, the number of each type of atom must be equal on both the reactant and product sides of a chemical equation. When you balance equations, you are ensuring that an equal number of atoms exist on both sides. This involves adjusting the coefficients (numbers in front of molecules) to get the same number of atoms of each element in the reactants and the products. For instance, in a redox reaction, you must balance not just atoms but also the charges. Here are some key points to remember while balancing chemical equations:

• Start by balancing the atoms of elements that appear only once in both reactants and products.
• Next, balance the atoms of elements that appear multiple times.
• Change only the coefficients, never the subscripts in chemical formulas, to preserve the identity of the compounds involved.

In our exercise, each half-reaction follows these rules to achieve balance in acidic solutions by adjusting the number of $ext{H}^{+}$ ions and electrons.

acidic solutions

An acidic solution refers to a solution with an excess of hydrogen ions, $ext{H}^{+}$. These conditions are often used in redox reactions to facilitate the balancing of the reaction. In an acidic environment, you can add $ext{H}_{2}extO$ to balance oxygen atoms and $ext{H}^{+}$ ions to balance hydrogen atoms.
Redox reactions in acidic solutions often require the following steps:

• Balance all atoms except for hydrogen and oxygen first.
• Add waters to balance oxygen atoms.
• Add $ext{H}^{+}$ ions to balance hydrogen atoms.
• Ensure that charge balance is achieved by adjusting the number of electrons transferred in the reaction.

The acidic environment, therefore, provides a medium in which hydrogens and oxygens can be added with ease, assisting in the balancing of otherwise complex equations. This is crucial in the step-by-step balancing shown as each half-reaction is treated independently in an acidic medium.

half-reactions

Half-reactions are a way to break down redox reactions, which consist of oxidation and reduction processes. Each half-reaction represents either the oxidation or reduction part of a redox reaction, and consists of a change in oxidation states accompanied by a gain or loss of electrons. The goal in balancing redox reactions is to ensure that both mass and charge are conserved.
Here's how half-reactions are balanced in an acidic solution:

• Identify and write out each half-reaction separately based on the species undergoing change.
• Balance all elements except $extH$ and $extO$.
• Balance oxygen by adding $ext{H}_{2}extO$ molecules.
• Balance hydrogen by adding $ext{H}^{+}$ ions.
• Finish by balancing the charge through the addition or subtraction of electrons ($e^{-}$).

After balancing the half-reactions, they can be recombined, ensuring that electrons gained and lost are equal. It is crucial to check that both the mass and charge are balanced in the final equation. In our examples, we see each half-reaction specifically tailored to balance atoms and charges while maintaining consistency in an acidic environment.