Question

Balance the following equations: $$ \begin{array}{l}{\text { (a) } \mathrm{Al}_{4} \mathrm{C}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Al}(\mathrm{OH})_{3}(s)+\mathrm{CH}_{4}(g)} \\ {\text { (b) } \mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}_{2}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { (c) } \mathrm{Fe}(\mathrm{OH})_{3}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)} \\ {\text { (d) } \mathrm{Mg}_{3} \mathrm{N}_{2}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{MgSO}_{4}(a q)+\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}(a q)}\end{array} $$

Short answer

(a) Al4C3(s) + 6H2O(l) → 4Al(OH)3(s) + 3CH4(g) (b) C5H10O2(l) + 7O2(g) → 5CO2(g) + 5H2O(g) (c) 2Fe(OH)3(s) + 3H2SO4(aq) → Fe2(SO4)3(aq) + 6H2O(l) (d) Mg3N2(s) + 6H2SO4(aq) → 3MgSO4(aq) + 3(NH4)2SO4(aq)

Step-by-step solution

(a) Balancing Al4C3(s) + H2O(l) → Al(OH)3(s) + CH4(g)

To balance this equation, follow these steps: 1. Count the number of atoms of each element on both sides of the equation. 2. Identify the imbalances and adjust the stoichiometric coefficients accordingly. 3. Verify that the updated equation has the same number of atoms of each element on both sides. Step 1: LHS: Al: 4, C: 3, H: 2, O: 1 RHS: Al: 1, C: 1, H: 7, O: 4 Step 2: Adjust coefficients: - For Al: multiply Al(OH)3 by 4 - For C: multiply CH4 by 3 - For H: multiply H2O by 6 Step 3: Updated equation: Al4C3(s) + 6H2O(l) → 4Al(OH)3(s) + 3CH4(g) LHS: Al: 4, C: 3, H: 12, O: 6 RHS: Al: 4, C: 3, H: 12, O: 6 The equation is now balanced.

(b) Balancing C5H10O2(l) + O2(g) → CO2(g) + H2O(g)

Follow similar steps to balance this equation: Step 1: LHS: C: 5, H: 10, O: 4 RHS: C: 1, H: 2, O: 3 Step 2: Adjust coefficients: - For C: multiply CO2 by 5 - For H: multiply H2O by 5 Step 3: Updated equation: C5H10O2(l) + 7O2(g) → 5CO2(g) + 5H2O(g) LHS: C: 5, H: 10, O: 14 RHS: C: 5, H: 10, O: 14 The equation is now balanced.

(c) Balancing Fe(OH)3(s) + H2SO4(aq) → Fe2(SO4)3(aq) + H2O(l)

Follow similar steps to balance this equation: Step 1: LHS: Fe: 1, O: 7, H: 8, S: 1 RHS: Fe: 2, O: 15, H: 2, S: 3 Step 2: Adjust coefficients: - For Fe: multiply Fe(OH)3 by 2 - For S: multiply H2SO4 by 3 - For H: multiply H2O by 6 Step 3: Updated equation: 2Fe(OH)3(s) + 3H2SO4(aq) → Fe2(SO4)3(aq) + 6H2O(l) LHS: Fe: 2, O: 15, H: 18, S: 3 RHS: Fe: 2, O: 15, H: 18, S: 3 The equation is now balanced.

(d) Balancing Mg3N2(s) + H2SO4(aq) → MgSO4(aq) + (NH4)2SO4(aq)

Follow similar steps to balance this equation: Step 1: LHS: Mg: 3, N: 2, H: 2, S: 1, O: 4 RHS: Mg: 1, N: 2, H: 8, S: 2, O: 8 Step 2: Adjust coefficients: - For Mg: multiply MgSO4 by 3 - For S: multiply H2SO4 by 2 - For H: multiply (NH4)2SO4 by 3 Step 3: Updated equation: Mg3N2(s) + 6H2SO4(aq) → 3MgSO4(aq) + 3(NH4)2SO4(aq) LHS: Mg: 3, N: 2, H: 12, S: 6, O: 24 RHS: Mg: 3, N: 2, H: 12, S: 6, O: 24 The equation is now balanced.

Key concepts

Stoichiometry

Stoichiometry is a section of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It's akin to a recipe in cooking where you need specific amounts of each ingredient to make the perfect meal. In the context of balancing chemical equations, stoichiometry is the method we use to ensure that the number of atoms for each element is conserved during the reaction.

For example, when you're looking at the reaction where aluminum carbide reacts with water to form aluminum hydroxide and methane, stoichiometry dictates how much of each reactant you'll need to ensure all the aluminum (Al) and carbon (C) atoms on the left side of the equation end up in the products on the right side without any loss or surplus. It's critical for predicting the amounts of reactants required and the amounts of products formed from a given chemical reaction. Accurate stoichiometric calculations are vital in fields ranging from laboratory chemistry to industrial production and environmental engineering.

Chemical Reactions

Chemical reactions are processes where reactants transform into products through the breaking and forming of chemical bonds. These transformations are represented by chemical equations that show the substances involved and their phase, such as solid (s), liquid (l), gas (g), or aqueous (aq). It's crucial to understand that chemical reactions abide by the law of conservation of mass, which states that matter is neither created nor destroyed in a closed system.

To align with this law, we balance chemical equations. For example, the reaction between magnesium nitride and sulfuric acid to form magnesium sulfate and ammonium sulfate must be balanced to reflect reality: you can't end up with more magnesium (Mg) atoms than you started with. Chemical reactions are the heart of chemistry, and mastery of balancing these reactions is a fundamental skill for any student of the science. Through balanced equations, we can deduce a tremendous amount of information about the properties and quantities of the materials involved.

Molecular Coefficients

Molecular coefficients, also known as stoichiometric coefficients, are the numbers placed before the compounds in a balanced chemical equation. They indicate the proportional amount of moles of each substance involved in a reaction. Adjusting these coefficients is how we balance chemical equations. Each coefficient multiplies the number of atoms in the respective molecule, leading to a balanced equation where the atoms on both sides are equal.

For example, in balancing the equation for the combustion of cyclopentanone, the molecular coefficient of oxygen is adjusted to seven, indicating that seven moles of oxygen react with one mole of cyclopentanone. These coefficients are essential for calculations in stoichiometry, allowing chemists to accurately predict how much product will form from given amounts of reactants, or vice versa. Understanding how to interpret and adjust molecular coefficients is key to solving stoichiometric problems and accurately describing chemical reactions.