Question

Balance these redox reactions that occur in aqueous solution. Use whatever water-derived species is necessary; there may be more than one correct balanced equation. a) \(\mathrm{H}_{2} \mathrm{O}_{2}+\mathrm{NO} \rightarrow \mathrm{N}_{2} \mathrm{O}_{3}+\mathrm{H}_{2} \mathrm{O}\) b) \(\mathrm{VO}_{2}^{+}+\mathrm{NO} \rightarrow \mathrm{V}^{3+}+\mathrm{NO}_{2}\)

Short answer

a) Already balanced with given equation; b) Balanced with provided coefficients.

Step-by-step solution

Write the unbalanced equation for Reaction A

The unbalanced redox reaction given is:\[\mathrm{H}_{2}\mathrm{O}_{2} + \mathrm{NO} \rightarrow \mathrm{N}_{2}\mathrm{O}_{3} + \mathrm{H}_{2}\mathrm{O}\] We need to balance the atoms on both sides of the equation.

Balance the oxygen atoms by adding water

In the reaction \(\mathrm{H}_{2}\mathrm{O}_{2} + \mathrm{NO} \rightarrow \mathrm{N}_{2}\mathrm{O}_{3} + \mathrm{H}_{2}\mathrm{O}\), add \(\mathrm{H}_{2}\mathrm{O}\) to the side deficient in oxygen. You'll find that adding one additional water molecule to the right side helps:\[\mathrm{H}_{2}\mathrm{O}_{2} + \mathrm{NO} \rightarrow \mathrm{N}_{2}\mathrm{O}_{3} + 2\mathrm{H}_{2}\mathrm{O}\] This balances the oxygen atoms.

Balance the hydrogen atoms by adjusting coefficients

Let's balance the hydrogens. After Step 2, hydrogens from \(\mathrm{H}_{2}\mathrm{O}_{2}\) and added water must match. Since there are a total of 4 hydrogens on the left side (2 from \(\mathrm{H}_{2}\mathrm{O}_{2}\) and none from \(\mathrm{NO}\)), we already have 4 hydrogens in \(2\mathrm{H}_{2}\mathrm{O}\) on the right side.

Balance the nitrogen atoms by changing coefficients

Ensure nitrogen atoms are balanced. There are 1 nitrogen in \(\mathrm{NO}\) and 2 nitrogens in \(\mathrm{N}_{2}\mathrm{O}_{3}\). Accordingly, we have:\[2\mathrm{H}_{2}\mathrm{O}_{2} + \mathrm{2NO} \rightarrow \mathrm{N}_{2}\mathrm{O}_{3} + 2\mathrm{H}_{2}\mathrm{O}\]This ensures that nitrogen is also balanced.

Write the unbalanced equation for Reaction B

The unbalanced reaction given is:\[\mathrm{VO}_{2}^{+} + \mathrm{NO} \rightarrow \mathrm{V}^{3+} + \mathrm{NO}_{2}\]We will balance this equation following similar steps.

Balance the oxygen by adding water

Balance the oxygen atoms by adding water. From the equation:\[\mathrm{VO}_{2}^{+} + \mathrm{NO} \rightarrow \mathrm{V}^{3+} + \mathrm{NO}_{2}\]Balance the oxygen by ensuring both sides have equal numbers. This is accomplished by altering hydration or placing waters in products or reactants.

Balance the charges by adding electrons

Observe the charge balancing. \(\mathrm{VO}_{2}^{+}\) is initially +5, thus losing electrons is necessary. Adjust with appropriate integer multiples to balance final charges between reactants and products:\[2\mathrm{VO}_{2}^{+} + 2\mathrm{NO} + 2\mathrm{H}_{2}\rightarrow 2\mathrm{V}^{3+} + 2\mathrm{NO}_{2} + 2\mathrm{H}_{2}\mathrm{O}\]

Verify balance of atoms and charge

Check each atom's count and overall charges on both sides coinciding. If counts and charges are equal on both reactant and product sides, the reaction is balanced.

Key concepts

Aqueous Solution Reactions

Aqueous solution reactions take place in a water-based environment. The solvent, water, plays a crucial role in facilitating these reactions. When compounds dissolve in water, they dissociate into ions, making it easier for these ions to interact and react. This process is particularly important in redox reactions, where transferring electrons between substances occurs efficiently in an aqueous medium.

These reactions are common in biological and environmental processes. The redox reactions in the given problems occur within an aqueous solution, showing how reactants interact within this medium. Ensuring that water-derived species such as water (\(\mathrm{H}_2\mathrm{O}\)) or hydroxide ions (\(\mathrm{OH}^-\)) are appropriately used can help balance the reaction in terms of both mass and charge. Understanding how water influences chemical reactions can lead to better insights into the reaction mechanisms.

Balancing Chemical Equations

Balancing chemical equations is an essential skill in chemistry. It ensures that the law of conservation of mass and charge is maintained during a chemical reaction. This means that the number of atoms for each element must be the same on both sides of the equation.

In the provided solutions, balancing involves manipulating coefficients. This changes the number of molecules to ensure that atoms such as hydrogen, oxygen, and nitrogen are equal on both sides. For example, in the redox reaction involving \(\mathrm{H}_2\mathrm{O}_2 + \mathrm{NO}\rightarrow \mathrm{N}_2\mathrm{O}_3 + \mathrm{H}_2\mathrm{O}\), balancing required adding water to balance oxygen. Afterward, the hydrogen and nitrogen atoms were balanced by adjusting the coefficients.

It is good practice to start by balancing elements that appear in a single reactant and product first. Following this, adjust other elements, and finally, balance charge if the reaction involves ions.

Oxidation and Reduction

Oxidation and reduction are processes that occur simultaneously in redox reactions. Oxidation involves the loss of electrons, while reduction involves gaining electrons. A substance that gives away electrons becomes oxidized, and one that accepts electrons gets reduced.

In the given exercises, consider the movement of electrons. Reaction A, \(\mathrm{H}_2\mathrm{O}_2 + \mathrm{NO}\rightarrow \mathrm{N}_2\mathrm{O}_3 + \mathrm{H}_2\mathrm{O}\), includes these processes where \(\mathrm{NO}\) gets oxidized while \(\mathrm{H}_2\mathrm{O}_2\) is reduced to \(\mathrm{H}_2\mathrm{O}\). Reaction B further illustrates redox processes, where \(\mathrm{VO}_2^+\) is reduced to \(\mathrm{V}^{3+}\) and \(\mathrm{NO}\) is oxidized to \(\mathrm{NO}_2\).

Understanding how to identify oxidation and reduction can help predict the outcome of reactions and balance them correctly, ensuring that both atoms and electrons are accounted for.

Chemical Stoichiometry

Chemical stoichiometry involves calculating the relationships between reactants and products in a chemical reaction. This subject incorporates the use of balanced chemical equations to determine how much of each reactant is needed, and what quantity of products can be produced.

The balanced equations from the exercises demonstrate stoichiometry in action. When equations are balanced, they indicate the mole ratios of reactants to products. This is fundamental to solving quantitative problems in chemistry, such as determining masses or volumes in reactions.

Stoichiometry allows chemists to predict the amounts of substances consumed and produced in a reaction. Proper stoichiometric calculations are crucial in industrial settings, where they ensure that reactants are used efficiently to generate desired products without excess waste.