Question

(a) \(6 \mathrm{HNO}_{3}+\mathrm{S} \longrightarrow 6 \mathrm{NO}_{2}+\mathrm{H}_{2} \mathrm{SO}_{4}+2 \mathrm{H}_{2} \mathrm{O}\) (b) \(2 \mathrm{CrCl}_{b}+3 \mathrm{MnO}_{2}+2 \mathrm{H}_{2} \mathrm{O} \rightarrow 3 \mathrm{MnCl}_{2}+2 \mathrm{H}_{2} \mathrm{CrO}_{4}\) (c) \(\begin{aligned} 2 \mathrm{KMnO}_{4}+6 \mathrm{HCl}+& 5 \mathrm{H}_{2} \mathrm{~S} \rightarrow \\ & 2 \mathrm{KCl}+2 \mathrm{MnCl}_{2}+5 \mathrm{~S}+8 \mathrm{H}_{2} \mathrm{O} \end{aligned}\)

Short answer

(a) Balanced. (b) After correcting a potential typo (CrClb to CrCl3) and adjusting water and hydrogen chloride molecules, the balanced equation is \(2 \mathrm{CrCl}_{3} + 3 \mathrm{MnO}_{2} + 8 \mathrm{H}_{2}O \rightarrow 3 \mathrm{MnCl}_{2} + 2 \mathrm{Cr}(\mathrm{OH})_{3} + 8 \mathrm{HCl}\). (c) Balanced.

Step-by-step solution

- Balancing Equation (a)

Whenever you are asked to balance a chemical equation, you should ensure that the number of atoms of each type is the same on both sides of the equation. For equation (a), no balancing is necessary as the equation is already balanced: on both sides there are 6 nitrogen atoms, 1 sulfur atom, 8 hydrogen atoms, and 18 oxygen atoms.

- Identifying the Error in Equation (b)

Inspect equation (b) carefully. Notice that the subscript 'b' next to CrCl seems to be a typo since typically this would be an integer representing the number of chloride ions. Confirm what the correct chemical formula should be, most likely it is a typo and should be CrCl3 instead of CrClb.

- Balancing Equation (b) after Correction

Assuming that the corrected formula is CrCl3, balance the revised equation: \(2 \mathrm{CrCl}_{3} + 3 \mathrm{MnO}_{2} + 8 \mathrm{H}_{2}O \rightarrow 3 \mathrm{MnCl}_{2} + 2 \mathrm{Cr}(\mathrm{OH})_{3} + 8 \mathrm{HCl}\). Each element type has the same count on each side: 2 chromium, 6 chlorine, 3 manganese, 14 hydrogen, and 10 oxygen atoms.

- Balancing Equation (c)

For equation (c), count the atoms of each type to make sure they are balanced on both sides. The equation is already balanced: 2 potassium, 2 manganese, 6 sulfur, 20 hydrogen, and 4+12=16 oxygen atoms.

Key concepts

Chemical Reaction

When substances interact to form new products, a chemical reaction occurs. This process involves breaking chemical bonds in reactants and forming new bonds in products. It's essential to understand that during a chemical reaction, atoms are neither created nor destroyed; instead, they are rearranged to become different substances. For instance, in exercise (a), sulfur (S) and nitric acid ((HNO3)) react to form nitrogen dioxide ((NO2)), sulfuric acid ((H2SO4)), and water ((H2O)). Here, sulfur and the nitrate from nitric acid change partners - sulfur pairs with oxygen and hydrogen to form sulfuric acid, while nitrogen pairs with oxygen to form nitrogen dioxide. Recognizing the substance interchange is key to comprehending chemical reactions.

Stoichiometry

The branch of chemistry called stoichiometry deals with the quantitative relationships of substances in a chemical reaction. It's like a recipe that tells you the exact amount of each ingredient you need. Stoichiometry is based on the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. Hence, you need the same number of each type of atom on both sides of a chemical equation. In exercise (a), for example, the stoichiometry indicates that one sulfur atom reacts with six molecules of nitric acid, yielding one sulfuric acid molecule, six molecules of nitrogen dioxide, and two molecules of water. Getting the stoichiometry right means ensuring the mass of reactants equals the mass of products.

Chemical Formula Correction

Sometimes, equations may contain typos or errors that need correction before balancing, which is termed chemical formula correction. An incorrect formula can lead to an incorrect stoichiometry, making it impossible to balance the equation properly. In step 2 of equation (b), the apparent typo 'CrClb' should be 'CrCl3', which represents chromium(III) chloride. Correcting chemical formulas is crucial because each element's subscript in the formula denotes the number of atoms in a molecule, influencing the outcome of a reaction. Accurate chemical formulas ensure that the stoichiometry reflects the true nature of the chemical reaction.

Reaction Balancing Steps

Reaction balancing steps are systematic procedures used to ensure that a chemical equation adheres to the law of conservation of mass. The balancing process involves adjusting the coefficients (whole numbers placed before reactants and products) to get the same number of atoms for each element on both sides of the equation. For instance, consider equation (b) after correcting the formula; to balance it, coefficients are adjusted so that the atoms of chromium, chlorine, manganese, hydrogen, and oxygen are equal on both sides. Practicing these balancing steps improves one's ability to visualize and solve chemical equation problems, which is a foundational skill for any chemistry student.