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. \(\mathrm{Al}(\mathrm{OH})_{3}(s)+\mathrm{HCl}(a q) \rightarrow \mathrm{AlCl}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(t)\) 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 as follows: a. \(3\mathrm{Ca}(\mathrm{OH})_{2}(a q)+2\mathrm{H}_{3} \mathrm{PO}_{4}(a q) \rightarrow 6\mathrm{H}_{2}\mathrm{O}(l)+\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s)\) b. \(\mathrm{Al}(\mathrm{OH})_{3}(s)+3\mathrm{HCl}(a q) \rightarrow \mathrm{AlCl}_{3}(a q)+3\mathrm{H}_{2} \mathrm{O}(l)\) c. \(2\mathrm{AgNO}_{3}(a q)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{Ag}_{2} \mathrm{SO}_{4}(s)+2\mathrm{HNO}_{3}(a q)\)

Step-by-step solution

Count the number of atoms on both sides

Before balancing, the equation is: \(\mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{H}_{3} \mathrm{PO}_{4}(a q) \rightarrow \mathrm{H}_{2}\mathrm{O}(l)+\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s)\) Number of atoms on the reactants side (left): - Ca: 1 - O: 2 (from OH) - H: 5 (2 from OH and 3 from H3PO4) - P: 1 - O: 4 (from H3PO4) Number of atoms on the products side (right): - H: 2 (from H2O) - O: 9 (1 from H2O and 8 from Ca3(PO4)2) - P: 2 - Ca: 3

Balance the equation

We can adjust the coefficients to balance the equation as follows: \( 3\mathrm{Ca}(\mathrm{OH})_{2}(a q)+2\mathrm{H}_{3} \mathrm{PO}_{4}(a q) \rightarrow 6\mathrm{H}_{2}\mathrm{O}(l)+\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s) \) Now the equation is balanced. #For equation (b)#

Count the number of atoms on both sides

Before balancing, the equation is: \(\mathrm{Al}(\mathrm{OH})_{3}(s)+\mathrm{HCl}(a q) \rightarrow \mathrm{AlCl}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) Number of atoms on the reactants side (left): - Al: 1 - O: 1 - H: 3 (from Al(OH)3) - Cl: 1 Number of atoms on the products side (right): - Al: 1 - Cl: 3 - H: 2 - O: 1

Balance the equation

We can adjust the coefficients to balance the equation as follows: \( \mathrm{Al}(\mathrm{OH})_{3}(s)+3\mathrm{HCl}(a q) \rightarrow \mathrm{AlCl}_{3}(a q)+3\mathrm{H}_{2} \mathrm{O}(l) \) Now the equation is balanced. #For equation (c)#

Count the number of atoms on both sides

Before balancing, the equation is: \(\mathrm{AgNO}_{3}(a q)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{Ag}_{2} \mathrm{SO}_{4}(s)+\mathrm{HNO}_{3}(a q)\) Number of atoms on the reactants side (left): - Ag: 1 - N: 1 - O: 3 (from AgNO3) - H: 2 - S: 1 - O: 4 (from H2SO4) Number of atoms on the products side (right): - Ag: 2 - S: 1 - O: 4 (from Ag2SO4) - H: 1 - N: 1 - O: 3 (from HNO3)

Balance the equation

We can adjust the coefficients to balance the equation as follows: \( 2\mathrm{AgNO}_{3}(a q)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{Ag}_{2} \mathrm{SO}_{4}(s)+2\mathrm{HNO}_{3}(a q) \) Now the equation is balanced.

Key concepts

Stoichiometry

Stoichiometry is a fascinating concept in chemistry that involves the calculation of reactants and products in chemical reactions. It's akin to a recipe in cooking, ensuring that you have the right amounts of ingredients to create a perfect dish. In stoichiometry, we use the balanced chemical equation to understand the relationship between different substances involved in a chemical reaction. This helps in identifying how much of each substance is needed and what quantities are produced.

The key to stoichiometry is the mole, a unit that allows chemists to count particles in a feasible way. By converting masses of substances into moles, one can compare and predict the outcomes of reactions in terms of the number of particles involved. This concept is grounded in the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction, meaning everything at the start of the reaction must be accounted for in the products.

Chemical Reactions

A chemical reaction is a process where reactants transform into products, involving the breaking and forming of bonds. This transformation can manifest in various ways depending on the type of reaction, such as synthesis, decomposition, single replacement, double replacement, and combustion.

In chemical reactions, substances change their identities due to the rearrangement of their atomic structures. This is seen in the change of physical and/or chemical properties. For example, when hydrogen gas reacts with oxygen gas, it produces water – showcasing a clear change from gaseous elements to a liquid compound.

During a chemical reaction, it's crucial to understand the conditions required for the reaction to occur, such as temperature and pressure, which can affect the rate and yield of the reaction. These conditions, along with the nature of the reactants, dictate the pathway and outcome of a chemical reaction. Observing these transformations helps chemists understand the properties and interactions of different substances better.

Coefficients Adjustment

Balancing chemical equations is an essential skill for anyone studying chemistry. It's like solving a puzzle where every piece must fit perfectly for the reaction to proceed as expected. The coefficients in a chemical equation represent the number of units of each substance involved, ensuring the law of conservation of mass is upheld.

The process involves first counting the number of atoms for each element on both sides of the equation and then adjusting the coefficients to make these counts equal. It often requires patience and practice, as sometimes an initial guess may not work, and adjustments are necessary to balance the equation properly.

Key points to remember when balancing equations include:

• Only adjust coefficients, never the subscripts in a chemical formula.
• Tackle one element at a time, starting with those present in fewer compounds and moving to those in more.
• Check your work by recounting each element to ensure balance.

By mastering this method, you can accurately predict how substances react and the quantities that result from chemical reactions.