Question

Balance the following equations: a. \(\mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{H}_{3} \mathrm{PO}_{4}(a q) \rightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s)\) b. \(\mathrm{Al}(\mathrm{OH})_{3}(s)+\mathrm{HCl}(a q) \rightarrow \mathrm{AlCl}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) c. \(\mathrm{AgNO}_{3}(a q)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{Ag}_{2} \mathrm{SO}_{4}(s)+\mathrm{HNO}_{3}(a q)\)

Short answer

The balanced equations are: a. \(3Ca(OH)_{2}(aq) + 6H_{3}PO_{4}(aq) \rightarrow 6H_{2}O(l) + Ca_{3}(PO_{4})_{2}(s)\) b. \(Al(OH)_{3}(s) + 3HCl(aq) \rightarrow AlCl_{3}(aq) + 3H_{2}O(l)\) c. \(2AgNO_{3}(aq) + H_{2}SO_{4}(aq) \rightarrow Ag_{2}SO_{4}(s) + 2HNO_{3}(aq)\)

Step-by-step solution

Balancing Equation a

1. Write down the unbalanced equation: \(Ca(OH)_{2}(aq) + H_{3}PO_{4}(aq) \rightarrow H_{2}O(l) + Ca_{3}(PO_{4})_{2}(s)\) 2. Balance calcium (Ca): There are 3 Ca atoms in the product side, so multiply the reactant side by 3: \(3Ca(OH)_{2}(aq) + H_{3}PO_{4}(aq) \rightarrow H_{2}O(l) + Ca_{3}(PO_{4})_{2}(s)\) 3. Balance oxygen (O), hydrogen (H), and phosphorus (P): a. Balance oxygen by multiplying water by 6: \(3Ca(OH)_{2}(aq) + H_{3}PO_{4}(aq) \rightarrow 6H_{2}O(l) + Ca_{3}(PO_{4})_{2}(s)\) b. Balance hydrogen by multiplying \(H_{3}PO_{4}\) by 6: \(3Ca(OH)_{2}(aq) + 6H_{3}PO_{4}(aq) \rightarrow 6H_{2}O(l) + Ca_{3}(PO_{4})_{2}(s)\) c. Balance phosphorus by checking if the product side is balanced; thankfully, it is. 4. The balanced equation is: \(3Ca(OH)_{2}(aq) + 6H_{3}PO_{4}(aq) \rightarrow 6H_{2}O(l) + Ca_{3}(PO_{4})_{2}(s)\)

Balancing Equation b

1. Write down the unbalanced equation: \(Al(OH)_{3}(s) + HCl(aq) \rightarrow AlCl_{3}(aq) + H_{2}O(l)\) 2. Balance aluminum (Al): There is 1 Al atom on both sides, so it is initially balanced. 3. Balance oxygen (O), hydrogen (H), and chlorine (Cl): a. Balance oxygen and hydrogen by multiplying hydrochloric acid (HCl) by 3: \(Al(OH)_{3}(s) + 3HCl(aq) \rightarrow AlCl_{3}(aq) + H_{2}O(l)\) b. Balance chlorine by checking if the product side is balanced; thankfully, it is. 4. The balanced equation is: \(Al(OH)_{3}(s) + 3HCl(aq) \rightarrow AlCl_{3}(aq) + 3H_{2}O(l)\)

Balancing Equation c

1. Write down the unbalanced equation: \(AgNO_{3}(aq) + H_{2}SO_{4}(aq) \rightarrow Ag_{2}SO_{4}(s) + HNO_{3}(aq)\) 2. Balance silver (Ag): There are 2 Ag atoms in the product side, so multiply the reactant side by 2: \(2AgNO_{3}(aq) + H_{2}SO_{4}(aq) \rightarrow Ag_{2}SO_{4}(s) + HNO_{3}(aq)\) 3. Balance oxygen (O), hydrogen (H), nitrogen (N), and sulfur (S): a. Balance oxygen by multiplying nitric acid (HNO_{3}\) by 2: \(2AgNO_{3}(aq) + H_{2}SO_{4}(aq) \rightarrow Ag_{2}SO_{4}(s) + 2HNO_{3}(aq)\) b. Balance hydrogen, nitrogen and sulfur by checking if the reactants and products sides are balanced; thankfully, they are. 4. The balanced equation is: \(2AgNO_{3}(aq) + H_{2}SO_{4}(aq) \rightarrow Ag_{2}SO_{4}(s) + 2HNO_{3}(aq)\)

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves the calculation of reactants and products in chemical reactions. Imagine it like a recipe! Just as you need the right amount of each ingredient to bake a cake, stoichiometry ensures you have the correct proportions of each substance involved in a chemical reaction for it to proceed correctly.

When balancing chemical equations, stoichiometry helps chemists determine the exact amount of each reactant needed and the exact amount of product that will be produced. This ensures that we understand how substances interact and transform during reactions. In the exercises given, the balanced equations are achieved by adjusting the coefficients (the numbers in front of molecules) to make sure there are equal numbers of each type of atom on both sides of the equation.

• Helps calculate quantities in reactions.
• Ensures the reaction proceeds with no shortages or excess.
• Involves using balanced chemical equations.

Conservation of Mass

The principle of conservation of mass is a key concept in chemistry which states that mass in an isolated system is neither created nor destroyed by chemical reactions or physical transformations. When we balance chemical equations, we rely on this principle to make sure that the mass of the reactants equals the mass of the products.

In simpler terms, when a chemical reaction happens, the amount of matter stays the same before and after the reaction. We can picture atoms as tiny building blocks that rearrange themselves during a reaction, but the total count of these blocks remains constant.

• Matter cannot appear or disappear.
• Ensures the same number of atoms of each element is present in reactants and products.
• Guides the balancing of chemical equations.

Chemical Reactions

Chemical reactions are processes where substances (the reactants) interact to form new substances (the products). These reactions are everywhere around us, from digesting food to burning fuel. An understanding of chemical reactions requires knowing both the reactants involved and the products formed.

Each reaction has its distinct equation that represents the reactants converting into products. For a reaction to occur, bonds between atoms in the reactants must break, and new bonds must form to create the products. In chemical equation balancing, it's important to represent these processes accurately, showing the right amount of each particle involved.

• Transforms chemicals from reactants to products.
• Involves breaking and forming bonds.
• Balancing equations reflects the exact transformation.