Question

Determine whether each of the following equations is balanced or not balanced: a. \(\mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{3}(g)\) b. \(2 \mathrm{Al}(s)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AlCl}_{3}(s)\) c. \(\mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g)\) d. \(\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)\)

Short answer

a. Not balancedb. Balancedc. Not balancedd. Balanced

Step-by-step solution

Analyze Equation a

Check if the number of each type of atom is the same on both sides of the equation: For \(\text{S} \text{on the left} = 1, \text{S on the right} = 1\) For \(\text{O}_2 \text{on the left} = 2, \text{O in } SO_3 = 3\)The equation is not balanced since there are different numbers of oxygen atoms on each side.

Analyze Equation b

Check if the number of each type of atom is the same on both sides of the equation: For \(\text{Al} \text{on the left} = 2, \text{Al in } 2AlCl_3 = 2\) For \(\text{Cl}_2 \text{on the left} = 3 \times 2 = 6, \text{Cl in } 2AlCl_3 = 6\)The equation is balanced since the number of aluminum and chlorine atoms is the same on both sides.

Analyze Equation c

Check if the number of each type of atom is the same on both sides of the equation: For \(\text{H}_2 \text{on the left} = 2, \text{H in } H_2O = 2\) For \(\text{O}_2 \text{on the left} = 2, \text{O in } H_2O = 1\)The equation is not balanced since there are different numbers of oxygen atoms on each side.

Analyze Equation d

Check if the number of each type of atom is the same on both sides of the equation: For \(\text{C}_3H_8 \text{on the left} = 3 \text{ C and 8 H}\, \text{and on right, } 3CO_2 = 3 \text{ C and } 4H_2O = 8 H\) For \(\text{O}_2 \text{on the left} = 5 \times 2 = 10, \text{ O in } 3CO_2 = 6 \text{ and } 4H_2O = 4\)The equation is balanced since the number of carbon, hydrogen, and oxygen atoms is the same on both sides.

Key concepts

Chemical Equations

When discussing chemical equations, we describe a process where reactants transform into products. A chemical equation uses symbols and formulas to convey this transformation. For example, in the equation \(\text{S}(s)+\text{O}_2(g) \rightarrow \text{SO}_3(g)\), sulfur (S) and oxygen gas (O\textsubscript{2}) are reactants, and sulfur trioxide (SO\textsubscript{3}) is the product. Each equation must adhere to certain rules:

• Reactants on the left side.
• Products on the right side.
• Arrow meaning 'yields' or 'produces.'

Remember, chemical equations must be balanced to reflect the Law of Conservation of Mass, ensuring the same number of atoms for each element are present on both sides of the equation.

Stoichiometry

Stoichiometry is the quantitative study of reactants and products in a chemical reaction. It allows us to determine the ratio of molecules or moles involved. For instance, in the balanced equation \(2 \text{Al}(s) + 3 \text{Cl}_2(g) \rightarrow 2 \text{AlCl}_3(s)\), stoichiometry tells us that two aluminum atoms react with three chlorine molecules to produce two units of aluminum chloride. Using stoichiometry, you can:

• Predict the amounts of reactants needed.
• Calculate the amounts of products formed.
• Convert between moles and grams.

Understanding stoichiometry is crucial for tasks ranging from laboratory experiments to industrial production.

Atoms Conservation

Atoms Conservation, or the Law of Conservation of Mass, is a fundamental concept in chemistry stating that atoms are neither created nor destroyed in a chemical reaction. They merely rearrange to form new compounds. To see this in practice, consider the equation \( \text{C}_3 \text{H}_8(g) + 5 \text{O}_2(g) \rightarrow 3 \text{CO}_2(g) + 4 \text{H}_2 \text{O}(g) \). Here we ensure:

• 3 carbon (C) atoms on both sides.
• 8 hydrogen (H) atoms on both sides.
• 10 oxygen (O) atoms on both sides (6 in CO\textsubscript{2} and 4 in H\textsubscript{2}O).

If an equation isn't balanced, it means the atoms don't match up, violating the law. This conservation principle is foundational to ensuring accuracy in chemical equations.

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and forming of chemical bonds. They can be represented by balanced chemical equations, which help us visualize and quantify the changes taking place. For example, the reaction \(2 \text{Al}(s) + 3 \text{Cl}_2(g) \rightarrow 2 \text{AlCl}_3(s)\) tells us that solid aluminum reacts with chlorine gas to yield aluminum chloride. Chemical reactions can be classified into different types:

• Combination reactions (e.g., \( \text{S}(s) + \text{O}_2(g) \rightarrow \text{SO}_3(g) \)).
• Decomposition reactions.
• Single displacement reactions.
• Double displacement reactions.

Each type has unique characteristics, but all follow the principle of atom conservation. Understanding these concepts ensures a solid foundation in chemistry.