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Chemical reactions are the processes by which substances interact to form new substances with different properties. Each reaction involves the rearrangement of atoms and is governed by the laws of conservation of mass and energy. This means in a chemical reaction, the total mass of the reactants equals the total mass of the products. Reactions are depicted by chemical equations that represent the identities and quantities of the reactants and products involved.

Writing and balancing these equations requires a clear understanding of the reaction specifics, including the physical state of substances, the reaction conditions, and the stoichiometry of the reaction. In balancing equations, it is crucial to ensure that there is an equal number of atoms for each element on both sides of the equation, reflecting the conservation of matter.

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It is the mathematical aspect of chemistry that pertains to the mass and mole relationships among reactants and products. Understanding stoichiometry allows chemists to predict the quantities needed to react and the amounts produced. When balancing chemical equations, stoichiometry is key in determining the coefficients that make the number of atoms of each element equal on both sides of the equation. It involves the use of mole ratios, derived from the balanced equation, to calculate the mass, volume, or number of particles of substances involved.

The reaction of barium oxide with water is an example of a chemical reaction where a base reacts with water to form a hydroxide. This particular type of reaction is synonymous with the behavior of alkaline earth metals. The balanced equation for this reaction is:
\[ BaO + H_2O \rightarrow Ba(OH)_2 \]
This shows that barium oxide (BaO) combines with water (H₂O) to form barium hydroxide (Ba(OH)₂). In this case, the stoichiometry is straightforward, with a one-to-one-to-one mole ratio among BaO, H₂O, and Ba(OH)₂ respectively. This reaction is important in understanding how basic oxides interact with water, forming hydroxides as products.

Iron(II) oxide reacts with perchloric acid to produce iron(II) perchlorate and water. The balancing of this equation involves adjusting the coefficients to obey the law of conservation of mass. The balanced chemical equation is:
\[ 2FeO + 4HClO_4 \rightarrow 2Fe(ClO_4)_2 + 2H_2O \]
This reaction is a type of acid-base reaction, where iron(II) oxide (a basic oxide) neutralizes perchloric acid. Perchlorates are the salts formed when perchloric acid reacts with bases. Stoichiometry is illustrated here by the different coefficients needed for reactants to ensure that the number of each type of atom is conserved across both sides of the equation.

When sulfur trioxide reacts with water, sulfuric acid is formed. This is a synthesis reaction, which can be represented by the balanced chemical equation seen below:
\[ SO_3 + H_2O \rightarrow H_2SO_4 \]
In this balanced equation, one molecule of sulfur trioxide (SO₃) reacts with one molecule of water (H₂O) to produce one molecule of sulfuric acid (H₂SO₄). It’s an exothermic and highly spontaneous reaction that is significant in the industrial production of sulfuric acid. The stoichiometry is shown here by the straightforward one-to-one ratio of reactants to products, indicating that no further adjustment is necessary for balancing the atoms.

The reaction of carbon dioxide (CO₂) with aqueous sodium hydroxide (NaOH) produces sodium bicarbonate (NaHCO₃). This chemical equation represents a type of reaction known as a neutralization reaction, which occurs between an acid and a base. The balanced chemical equation for this reaction is:
\[ CO_2 + NaOH \rightarrow NaHCO_3 \]
This equation indicates that one mole of CO₂ reacts with one mole of NaOH to produce one mole of NaHCO₃. In terms of stoichiometry, this reaction also illustrates a one-to-one-to-one ratio. Understanding this reaction is critical for many environmental and industrial processes, such as carbon capture and sequestration, and the manufacture of baking soda.