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. $\mathrm{AgNO}_{3}(a q)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{Ag}_{2} \mathrm{SO}_{4}(s)+\mathrm{HNO}_{3}(a q)$

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: \(3Ca(OH)_{2}(aq) + 6H_{3}PO_{4}(aq) \rightarrow 6H_{2}O(l) + Ca_{3}(PO_{4})_{2}(s)\)

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: \(Al(OH)_{3}(s) + 3HCl(aq) \rightarrow AlCl_{3}(aq) + 3H_{2}O(l)\)

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: \(2AgNO_{3}(aq) + H_{2}SO_{4}(aq) \rightarrow Ag_{2}SO_{4}(s) + 2HNO_{3}(aq)\)