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. \(A g N O_{3}(a q)+H_{2} S O_{4}(a q) \rightarrow A g_{2} S O_{4}(s)+H N O_{3}(a q)\)

Short answer

The balanced equations are: a. \(3Ca(OH)_2(aq) + 2H_3PO_4(aq) \rightarrow 6H_2O(l) + Ca_3(PO_4)_2(s)\) b. \(Al(OH)_3(s) + 3HCl(aq) \rightarrow AlCl_3(aq) + 3H_2O(l)\) c. \(2AgNO_3(aq) + H_2SO_4(aq) \rightarrow Ag_2SO_4(s) + 2HNO_3(aq)\)

Step-by-step solution

Count atoms on both sides of the equation

List the number of atoms of each element on both sides. Currently, we have: - Reactants: - 1 Ca - 2 O - 2 H - 3 H - 1 P - 4 O - Products: - 2 O - 2 H - 3 Ca - 2 P - 8 O

Add coefficients to balance atoms by elements

Begin by balancing the least common atoms first. In this case, let's start with calcium (Ca). Add a coefficient of 3 in front of \(Ca(OH)_2\): \(3Ca(OH)_2(aq) + H_3PO_4(aq) \rightarrow H_2O(l) + Ca_3(PO_4)_2(s)\) Now, balance the phosphate (P) atoms by adding a coefficient of 2 in front of \(H_3PO_4\): \(3Ca(OH)_2(aq) + 2H_3PO_4(aq) \rightarrow H_2O(l) + Ca_3(PO_4)_2(s)\) Finally, balance the hydrogen (H) and oxygen (O) atoms by adding a coefficient of 6 in front of \(H_2O\): \(3Ca(OH)_2(aq) + 2H_3PO_4(aq) \rightarrow 6H_2O(l) + Ca_3(PO_4)_2(s)\) #b. Balancing the equation involving \(Al(OH)_3\), \(HCl\), \(AlCl_3\), and \(H_2O\)# The given equation is: \(Al(OH)_3(s) + HCl(aq) \rightarrow AlCl_3(aq) + H_2O(l)\)

Count atoms on both sides of the equation

List the number of atoms of each element on both sides. Currently, we have: - Reactants: - 1 Al - 3 O - 3 H - 1 H - 1 Cl - Products: - 1 Al - 3 Cl - 1 O - 2 H

Add coefficients to balance atoms by elements

Begin by balancing the chlorine (Cl) atoms; add a coefficient of 3 in front of \(HCl\): \(Al(OH)_3(s) + 3HCl(aq) \rightarrow AlCl_3(aq) + H_2O(l)\) With this step, all atoms are already balanced. #c. Balancing the equation involving \(AgNO_3\), \(H_2SO_4\), \(Ag_2SO_4\), and \(HNO_3\)# The given equation is: \(AgNO_3(aq) + H_2SO_4(aq) \rightarrow Ag_2SO_4(s) + HNO_3(aq)\)

Count atoms on both sides of the equation

List the number of atoms of each element on both sides. Currently, we have: - Reactants: - 1 Ag - 1 N - 3 O - 2 H - 1 S - 4 O - Products: - 2 Ag - 1 S - 4 O - 1 H - 1 N - 3 O

Add coefficients to balance atoms by elements

Begin by balancing the silver (Ag) atoms; add a coefficient of 2 in front of \(AgNO_3\): \(2AgNO_3(aq) + H_2SO_4(aq) \rightarrow Ag_2SO_4(s) + HNO_3(aq)\) With this step, all atoms are already balanced.

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with determining the quantities of reactants and products involved in chemical reactions. It's like the recipe for a chemical reaction, telling chemists the exact proportions of ingredients needed to make a certain amount of product.

In the context of balancing chemical equations, stoichiometry provides the theoretical basis for understanding how different amounts of reactants are consumed and products are formed. A balanced equation represents the conservation of mass and shows a direct relationship between the substances involved in a reaction. By mastering stoichiometry, students can predict the amounts of substances consumed and produced in a reaction, ensuring no atoms are lost or gained in the process. It’s crucial in fields like pharmaceuticals, where precise amounts of chemicals need to be combined to create medicines.

Chemical Reactions

Chemical reactions are processes where substances interact to form new substances with different properties. There are various types of reactions, including synthesis, decomposition, single replacement, and double replacement, among others.

Each type of reaction follows a general pattern that helps in predicting the products. For example, in a synthesis reaction, elements or simple compounds combine to form a more complex compound. Understanding the types of chemical reactions helps in predicting how different substances will behave when mixed together, which is a key aspect of designing experiments and analyzing results. The analysis of the steps in the provided problems showcases how different compounds like calcium hydroxide and phosphoric acid react to form a new substance, highlighting the transformative power of chemical reactions.

Coefficients in Chemical Equations

The coefficients in chemical equations represent the number of moles (or molecules) of each substance involved in a chemical reaction. They are essential in ensuring that the law of conservation of mass is followed since atoms cannot be created or destroyed during a chemical reaction.

Adding appropriate coefficients before the chemical formulas in an equation balances the number of atoms on both sides, ensuring that the reaction adheres to stoichiometric principles. As seen in the textbook problems, adjusting the coefficients leads to a balanced equation, which is indicative of a reaction that can theoretically occur under the right conditions. Understanding how to manipulate these coefficients is vital for accurately representing what happens during a reaction, and is a foundational skill for anyone studying or working in a chemistry-related field.