Problem 25 - Chemistry for Allied Health

Question

Balance the following equations. a. \(\mathrm{Fe}(\mathrm{s})+\mathrm{Cl}_{2}(g) \rightarrow \mathrm{FeCl}_{3}(g)\) b. \(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}+\mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\) C. \(\mathrm{As}+\mathrm{NaOH} \rightarrow \mathrm{Na}_{3} \mathrm{AsO}_{3}+\mathrm{H}_{2}\) d. \(\mathrm{SiO}_{2}+\mathrm{HF} \rightarrow \mathrm{SiF}_{4}+\mathrm{H}_{2} \mathrm{O}\) e. \(\mathrm{N}_{2}+\mathrm{O}_{2}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{HNO}_{3}\)

Step-by-Step Solution

Answer

The balanced equations are: a. 2Fe + 3Cl₂ → 2FeCl₃; b. C₄H₁₀O + 6O₂ → 4CO₂ + 5H₂O; c. 2As + 6NaOH → 2Na₃AsO₃ + 3H₂; d. SiO₂ + 4HF → SiF₄ + 2H₂O; e. N₂ + 3O₂ + H₂O → 2HNO₃.

Step 1: Analyze Equation A Components

Identify the reactants and products: Reactants: Fe, Cl₂ Product: FeCl₃. Notice that Fe and Cl atoms must be balanced. Fe occurs once on both sides, but Cl is in pairs on the left (Cl₂) and in groups of three on the right (FeCl₃). Rebalance these.

Step 2: Balance Chlorine in Equation A

To balance chlorine, adjust the Cl₂: multiplying Cl₂ by 3 gives 6 chlorine atoms on the left, matching the 2FeCl₃. Thus, the balanced equation is: 2Fe + 3Cl₂ → 2FeCl₃.

Step 3: Analyze Equation B Components

Reactants: C₄H₁₀O, O₂. Products: CO₂, H₂O. Count atoms: Carbon (C): 4 in reactant, aim for 4 CO₂ (4C) Hydrogen (H): 10 in reactant, aim for 5 H₂O (10H) Oxygen (O): Adjust O₂ accordingly.

Step 4: Balance Equation B

Assign coefficients matching C₄H₁₀O combustion principles: C₄H₁₀O + 6O₂ → 4CO₂ + 5H₂O. Oxygen sides: Add reactant O₂s to balance products (total of 13 O in products; 6 O₂ provides these).

Step 5: Analyze Equation C Components

Reactants: As, NaOH Products: Na₃AsO₃, H₂. Count atoms: Arsenic (As): present Sodium (Na), Hydrogen (H), and Oxygen (O) must match product numbers.

Step 6: Balance Equation C

Fix sodium and hydrogen by assigning coefficients: 2 As + 6 NaOH → 2 Na₃AsO₃ + 3 H₂. Balances all elements, particularly Na from NaOH associations.

Step 7: Analyze Equation D Components

Reactants: SiO₂, HF Products: SiF₄, H₂O. Focus on silicon (Si), oxygen (O), hydrogen (H), and fluorine (F) atoms.

Step 8: Balance Equation D

Because SiO₂ needs 4 F in SiF₄, adjust HF: SiO₂ + 4HF → SiF₄ + 2H₂O. Ensure F and H balance correctly, using 2 water molecules at end.

Step 9: Analyze Equation E Components

Reactants: N₂, O₂, H₂O Product: HNO₃. Identify initial elements: N, O, H, balance upon understanding compound multiplicity.

Step 10: Balance Equation E

Assign coefficients to align reactants to product breakdown: N₂ + 3O₂ + H₂O → 2HNO₃. Here, each side's N, O, and H amount should equalize.

Key Concepts

Chemical Reaction Components

Chemical reactions consist of reactants and products, both of which contain different substances combined or broken down. For Equation A, the reactants are elemental iron (Fe) and chlorine gas (Cl₂), forming the product iron(III) chloride (FeCl₃).

In Equation B, you begin with butanol (\(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}\)) and oxygen (\(\mathrm{O}_{2}\)) as reactants, which yield carbon dioxide (CO₂) and water (H₂O) as products.

Equation C links pure arsenic (\(\mathrm{As}\)) with sodium hydroxide (\(\mathrm{NaOH}\)) to produce sodium arsenite (\(\mathrm{Na}_{3} \mathrm{AsO}_{3}\)) and hydrogen gas (H₂).

In Equation D, silicon dioxide (\(\mathrm{SiO}_{2}\)) and hydrofluoric acid (HF) react to create silicon tetrafluoride (\(\mathrm{SiF}_{4}\)) and water.

Lastly, Equation E involves nitrogen (\(\mathrm{N}_{2}\)), oxygen, and water as reactants, producing nitric acid (\(\mathrm{HNO}_{3}\)).

Understanding these components is crucial since balancing involves having the same number of each type of atom on both sides of the equation.

Stoichiometry

Stoichiometry is the study of the quantitative relationships in a chemical reaction. It involves using the mole concept and coefficients in balanced chemical equations to predict the amounts of reactants and products.

For example, in Equation A, stoichiometry allows us to understand that for every two moles of iron (\(\mathrm{Fe}\)), three moles of chlorine gas (\(\mathrm{Cl}_2\)) are needed to form two moles of iron(III) chloride (\(\mathrm{FeCl}_3\)).

In Equation B, stoichiometry not only tells us the proportion of the reactants and products but also how much oxygen is needed alongside butanol to fully combust it into carbon dioxide and water.

Sufficient knowledge of stoichiometry is essential in solving chemical equations as it helps predict the amount of reactants required and products formed, ensuring that all elements are consumed in a balanced, proportional manner.

Molecule Coefficients

When balancing chemical equations, the coefficients of molecules indicate the multiple of each compound involved. They ensure the law of conservation of mass is obeyed by having the same number of atoms for each element in the reactants and products.

For instance, in Equation C, the coefficient '2' before arsenic and sodium arsenite implies that two molecules of each are involved before the equation can be considered balanced, based on stoichiometric calculations. This requires six sodium hydroxide (\(\mathrm{NaOH}\)) to yield the balanced equation.

The coefficients form an important part of any balanced equation, affecting calculations in stoichiometry significantly. They guide us towards the proper stoichiometric ratios necessary to keep reactions balanced and accurately simulate chemical processes.

Equation Balancing Steps

Balancing a chemical equation follows a systematic approach to maintain equal numbers of each type of atom on both sides.

Here are the general steps to balance:

• Identify and list all elements present in the reactants and products.
• Use coefficients to ensure the number of atoms for each element is the same on both sides by adjusting these accordingly, starting with substances that appear in only one reactant and product.
• Iterate through the coefficients, adjusting where needed, especially in more complex equations, to reach equilibrium.
• Confirm that the total number of each atom is the same on both sides to validate a balanced equation.

In Equation D, for example, balancing begins by ensuring that four molecules of HF contribute the necessary number of fluorine atoms to form SiF₄, while adjusting the water molecules to match hydrogen and oxygen counts.