Question

Balance this redox reaction by inspection. $$ \mathrm{S}_{8}+\mathrm{O}_{2} \rightarrow \mathrm{SO}_{2} $$

Short answer

The balanced equation is \(\mathrm{S}_{8} + 8\ \mathrm{O}_{2} \rightarrow 8\ \mathrm{SO}_{2}\).

Step-by-step solution

Write the unbalanced equation

Start with the given chemical reaction. The unbalanced formula is:\[ \mathrm{S}_{8} + \mathrm{O}_{2} \rightarrow \mathrm{SO}_{2} \]

Balance sulfur atoms

Ensure that the number of sulfur atoms is equal on both sides. Since there are 8 sulfur atoms in \(\mathrm{S}_8\), we need 8 molecules of \(\mathrm{SO}_2\):\[ \mathrm{S}_{8} + \mathrm{O}_{2} \rightarrow 8\ \mathrm{SO}_{2} \]

Balance oxygen atoms

Count the oxygen atoms. There are 16 oxygen atoms on the right side (8 molecules of \(\mathrm{SO}_2\) each with 2 oxygen atoms). Balance by placing 8 in front of \(\mathrm{O}_2\):\[ \mathrm{S}_{8} + 8\ \mathrm{O}_{2} \rightarrow 8\ \mathrm{SO}_{2} \]

Verify the balance

Check that both reactants and products have the same number of each element:- Sulfur: 8 on both sides- Oxygen: 16 on both sides (from 8 molecules of \(\mathrm{O}_2\) on the left and 8 molecules of \(\mathrm{SO}_2\) on the right)The equation is now balanced.

Key concepts

Stoichiometry

Stoichiometry is the study of the quantitative relationships between the amounts of reactants and products in a chemical reaction. This branch of chemistry uses balanced chemical equations to determine these relationships and allows us to predict how much of each substance is needed or produced. In our example reaction, sulfur and oxygen react to form sulfur dioxide. To understand stoichiometry, consider the following key points:

• Conservation of Mass: In a balanced chemical equation, the mass of the reactants equals the mass of the products, reflecting the law of conservation of mass.
• Coefficients: Numbers placed before molecules in chemical equations denote the mole ratio of the substances involved.
• Mole Ratios: These ratios are derived from the balanced equation and can be used to calculate the amounts of reactants or products involved in the reaction.

Understanding these points allows chemists to "scale-up" reactions, predicting how much product will be formed from given reactants, or determining how much reactant is needed to produce a desired amount of product.

Chemical Equations

Chemical equations represent chemical reactions using symbols and formulas. They include the reactants on the left side and the products on the right, separated by an arrow which indicates the direction of the reaction. The chemical equation for our exercise is:\[ \mathrm{S}_{8} + \mathrm{O}_{2} \rightarrow 8\ \mathrm{SO}_{2} \]Chemical equations convey important information about the reaction, such as:

• Reactants and Products: In this equation, \( \mathrm{S}_{8} \) and \( \mathrm{O}_{2} \) are the reactants, and \( \mathrm{SO}_{2} \) is the product.
• States of Matter: While not shown in this example, equations often include the states of matter, like solid (s), liquid (l), gas (g), or aqueous (aq).
• Chemical Change: The equation represents the transformation of reactants into products through chemical change, involving the making and breaking of chemical bonds.

Balancing chemical equations ensures the conservation of atoms, reflecting the chemical law that atoms cannot be created or destroyed in a chemical reaction.

Inspection Method

The inspection method is a straightforward technique for balancing chemical equations. It involves adjusting the coefficients in front of the chemical formulas until the number of atoms of each element is equal on both sides of the equation. In our exercise, the inspection method involves these steps:

• List Elements: Identify and list all the elements in the equation to ensure none are missed in balancing.
• Balance One Element at a Time: Start by balancing the atoms of one element. Typically, more complex molecules or elements in single form are balanced first.
• Adjust Coefficients: Change the coefficients of the molecules as needed. For example, we adjust for the 8 sulfur atoms in \( \mathrm{S}_8 \) by placing an '8' in front of \( \mathrm{SO}_2 \).
• Verify Balance: After adjusting, ensure the number of atoms on each side is equal and double-check the entire equation for accuracy.

The inspection method requires practice to understand the nuances of balancing, but it becomes intuitive with repeated use. It's ideal for simple reactions, like our sulfur and oxygen equation, where careful counting ensures a balanced result.