Question

Balance the following equations: $$ \begin{array}{l}{\text { (a) } \mathrm{Li}(s)+\mathrm{N}_{2}(g) \longrightarrow \mathrm{Li}_{3} \mathrm{N}(s)} \\ {\text { (b) } \mathrm{TiCl}_{4}(l)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{TiO}_{2}(s)+\mathrm{HCl}(a q)} \\ {\text { (c) } \mathrm{NH}_{4} \mathrm{NO}_{3}(s) \longrightarrow \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { (d) } \mathrm{AlCl}_{3}(s)+\mathrm{Ca}_{3} \mathrm{N}_{2}(s) \longrightarrow \mathrm{AlN}(s)+\mathrm{CaCl}_{2}(s)}\end{array} $$

Short answer

The balanced equations are: (a) \(6 \mathrm{Li}(s)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{Li}_{3} \mathrm{N}(s)\), (b) \(\mathrm{TiCl}_{4}(l)+2\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{TiO}_{2}(s)+4\mathrm{HCl}(a q)\), (c) \(\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \longrightarrow \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)+2\mathrm{H}_{2} \mathrm{O}(g)\), (d) \(2 \mathrm{AlCl}_{3}(s)+\mathrm{Ca}_{3} \mathrm{N}_{2}(s) \longrightarrow 2\mathrm{AlN}(s)+3\mathrm{CaCl}_{2}(s)\).

Step-by-step solution

(a) Balancing the Li + N₂ equation

To balance the equation Li(s) + N₂(g) → Li₃N(s), first identify the elements in the equation (Li and N). Now, compare the number of atoms of each element on both sides of the equation: - Li: 1 atom on the left and 3 atoms on the right - N: 2 atoms on the left and 1 atom on the right The equation is unbalanced. To balance the Li atoms, we need to multiply the Li(s) by a factor of 3. To balance the N atoms, we need to multiply the N₂(g) by a factor of 1/2. We can't use fractions as coefficients, so we will multiply the whole equation by 2 to get rid of the fraction: `2 * (3 Li(s) + 1/2 N₂(g) → Li₃N(s))` Now, the balanced equation is: \[6 \mathrm{Li}(s)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{Li}_{3} \mathrm{N}(s)\]

(b) Balancing the TiCl4 + H2O equation

To balance the equation TiCl₄(l) + H₂O(l) → TiO₂(s) + HCl(aq), identify the elements in the equation (Ti, Cl, H, and O). Compare the number of atoms of each element on both sides of the equation: - Ti: 1 atom on the left and 1 atom on the right - Cl: 4 atoms on the left and 1 atom on the right - H: 2 atoms on the left and 1 atom on the right - O: 1 atom on the left and 2 atoms on the right We can see that Cl, H, and O are unbalanced. To balance them, adjust the coefficients of HCl and H₂O: - Multiply HCl by 4 to balance the Cl atoms - Multiply H₂O by 2 to balance the H and O atoms Now, the balanced equation is: \[\mathrm{TiCl}_{4}(l)+2\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{TiO}_{2}(s)+4\mathrm{HCl}(a q)\]

(c) Balancing the NH4NO3 equation

To balance the equation NH₄NO₃(s) → N₂(g) + O₂(g) + H₂O(g), identify the elements in the equation (N, H, and O) and compare the number of atoms on both sides: - N: 2 atoms on the left and 2 atoms on the right - H: 4 atoms on the left and 2 atoms on the right - O: 3 atoms on the left and 3 atoms on the right The N and O atoms are balanced, but the H atoms are unbalanced. To balance the H atoms, multiply the H₂O by 2: Now, the balanced equation is: \[\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \longrightarrow \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)+2\mathrm{H}_{2} \mathrm{O}(g)\]

(d) Balancing the AlCl3 + Ca3N2 equation

To balance the equation AlCl₃(s) + Ca₃N₂(s) → AlN(s) + CaCl₂(s), identify the elements in the equation (Al, Cl, Ca, and N) and compare the number of atoms on both sides: - Al: 1 atom on the left and 1 atom on the right - Cl: 3 atoms on the left and 2 atoms on the right - Ca: 3 atoms on the left and 1 atom on the right - N: 2 atoms on the left and 1 atom on the right The equation is unbalanced for Cl, Ca, and N atoms. To balance them, adjust the coefficients of AlCl₃, CaCl₂, and AlN: - Multiply AlCl₃ by 2 to balance Cl atoms - Multiply CaCl₂ by 3 to balance Ca atoms - Multiply AlN by 2 to balance Al and N atoms Now, the balanced equation is: \[2 \mathrm{AlCl}_{3}(s)+\mathrm{Ca}_{3} \mathrm{N}_{2}(s) \longrightarrow 2\mathrm{AlN}(s)+3\mathrm{CaCl}_{2}(s)\]

Key concepts

Stoichiometry

Stoichiometry is the mathematical relationship between the quantities of reactants and products in a chemical reaction. It's fundamental to the practice of balancing chemical equations because it tells us how much of each substance is involved in the reaction. In simple terms, stoichiometry is like a recipe: for a chemical reaction to proceed correctly, one needs the right proportion of ingredients (reactants) to make the desired product.

Let's consider exercise (a) as an example. We needed to figure out the right amounts of lithium (Li) and nitrogen (N₂) to produce lithium nitride (Li₃N). Using stoichiometry, we calculated that 6 moles of lithium react with 1 mole of nitrogen to produce 2 moles of lithium nitride. This ratio (6:1:2) is essential in ensuring the amounts of reactants and products adhere to the law of conservation of mass.

Chemical Reaction

A chemical reaction is a process by which substances, known as reactants, transform into different substances, known as products. During the reaction, bonds between atoms in the reactants are broken and new bonds are formed to create the products. The process can involve a range of phenomena: light, heat, color changes, or gas production, for example.

In exercise (b), when titanium tetrachloride (TiCl₄) reacts with water (H₂O), we see a transformation where titanium dioxide (TiO₂) and hydrochloric acid (HCl) are formed. It illustrates how starting materials morph into new substances, a marvel that is encountered from industrial processes down to the cellular level in biology.

Law of Conservation of Mass

The law of conservation of mass states that mass in an isolated system is neither created nor destroyed by chemical reactions or physical transformations. According to the law, the mass of the reactants in a chemical equation must equal the mass of the products. This principle is the cornerstone of chemical equation balancing, as it ensures that atoms are neither lost nor gained during a reaction.

Reflecting on exercise (c), balancing the decomposition of ammonium nitrate (NH₄NO₃) into nitrogen (N₂), oxygen (O₂), and water vapor (H₂O) requires that we account for all atoms involved. Although they rearrange to form different molecules, the total count of each type of atom remains the same before and after the reaction, in accordance with the law of conservation of mass.