Balance the following equations: (a) \(\mathrm{PCl}_{5}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{POCl}_{3}(l)+\mathrm{HCl}(a q)\) (b) \(\mathrm{Cu}(s)+\mathrm{HNO}_{3}(a q) \longrightarrow \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(I)+\mathrm{NO}(g)\) (c) \(\mathrm{H}_{2}(g)+\mathrm{I}_{2}(s) \longrightarrow \mathrm{HI}(s)\) (d) \(\operatorname{Fe}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)\) (e) \(\mathrm{Na}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g)\) (f) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}(s) \longrightarrow \mathrm{Cr}_{2} \mathrm{O}_{3}(s)+\mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) (g) \(\mathrm{P}_{4}(s)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{PCl}_{3}(l)\) (h) \(\mathrm{PtCl}_{4}(s) \longrightarrow \operatorname{Pt}(s)+\mathrm{Cl}_{2}(g)\)

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It's a mathematical way of describing the conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. In practice, stoichiometry involves using balanced chemical equations to calculate the amounts of reactants needed or products formed.

For instance, if you're baking cookies and the recipe calls for two eggs for every cup of flour, stoichiometry is like the 'recipe' for chemical reactions, telling you how much of each reactant you need to end up with a certain amount of product. In balancing chemical equations, we ensure that the number of atoms for each element in the reactants side is equal to that in the products side. This balancing act reflects the stoichiometric relationship and is essential for any further calculations related to the reaction.

A chemical reaction is a process where reactants transform into products through breaking and forming of chemical bonds. The substances involved can change states, colors, or temperatures, and new substances with different properties from the initial reactants emerge.

Understanding chemical reactions is crucial because they are the fundamental processes that allow us to create new materials and obtain energy. When writing out a chemical reaction, reactants are usually written to the left of an arrow with products on the right side. For a reaction to be balanced, it must adhere to the law of conservation of mass. This particularly means altering coefficients, not subscripts in the chemical formulas, to ensure that the same number of each type of atom appears on both sides of the equation. The balanced chemical equations provide a visual representation of this conservation.

Reaction stoichiometry describes the quantitative relationship between reactants and products in a chemical reaction. It builds on the concept of stoichiometry by specifically focusing on the ratio in which reactants combine and the ratio of products formed.

Understanding reaction stoichiometry is essential for predicting the outcome of reactions and for scaling reactions up or down, such as in industrial processes or laboratory experiments. Using coefficients derived from the balanced chemical equations, we can convert between the amounts of one reactant or product to another, determine the limiting reactant, and calculate the theoretical yield of a reaction. It's like a detailed map that tells you not only how to get from point A to point B but also tells you how much fuel you’ll need and what you’ll see along the way.