Write balanced chemical equations to correspond to each of the following descriptions: (a) When sulfur trioxide gas reacts with water, a solution of sulfuric acid forms. (b) Boron sulfide, \(B_{2} S_{3}(s),\) reacts violently with water to form dissolved boric acid, \(H_{3} B O_{3},\) and hydrogen sulfide gas. (c) Phosphine, PH \(_{3}(g),\) combusts in oxygen gas to form water vapor and solid tetraphosphorus decaoxide. (d) When solid mercury(II) nitrate is heated, it decomposes to form solid mercury(II) oxide, gaseous nitrogen dioxide, and oxygen.(e) Copper metal reacts with hot concentrated sulfuric acid solution to form aqueous copper(II) sulfate, sulfur dioxide gas, and water.

When substances interact to form new products, we refer to this as a chemical reaction. The essence of a chemical reaction involves breaking old bonds and forming new ones. Each reaction is governed by certain rules that ensure the conservation of mass. This principle dictates that the number of atoms for each element involved must be the same before and after the reaction. This is where we use what is known as a balanced chemical equation.

For instance, in the reaction where sulfur trioxide gas reacts with water to produce sulfuric acid, represented by the equation:
\[SO_3(g) + H_2O(l) \rightarrow H_2SO_4(aq)\]
the equation is balanced as there is an equal number of sulfur, oxygen, and hydrogen atoms on both sides of the reaction. In essence, balanced equations are vital for accurately representing the transformation of reactants to products and for making quantitative predictions about the reactions.

The quantitative relationship between reactants and products in a chemical reaction is known as stoichiometry. It involves using the balanced chemical equations to calculate how much reactant is needed to produce a certain amount of product. In a balanced chemical equation, the coefficients represent the mole ratios of the substances involved.

Take for example the reaction of boron sulfide with water to form boric acid and hydrogen sulfide:
\[B_2S_3(s) + 6H_2O(l) \rightarrow 2H_3BO_3(aq) + 3H_2S(g)\]
The coefficients (1, 6, 2, and 3) tell us the exact ratio in which substances react and are formed. These coefficients are crucial for stoichiometry calculations as they allow us to convert between masses, volumes, and moles of reactants and products. Understanding stoichiometry is essential for performing accurate chemical calculations and for practical applications such as determining the correct proportions for a reaction mixture in industrial processes.

A specific type of chemical reaction is combustion, which usually involves a substance (typically a hydrocarbon) reacting with oxygen to release energy in the form of heat and light, producing water and carbon dioxide in the process. However, combustion doesn't always produce carbon dioxide - it depends on the substance that is burning.

For instance, the combustion of phosphine in oxygen is a reaction that forms water and tetraphosphorus decaoxide, which is represented by the equation:\[4PH_3(g) + 5O_2(g) \rightarrow 6H_2O(g) + P_4O_{10}(s)\]
This balanced chemical equation shows the stoichiometry of the combustion process. It's important to balance combustion equations correctly to understand the amount of oxygen needed for the reaction to occur completely and to predict the quantities of the products formed. Properly understanding combustion reactions has practical applications in various fields, such as engine design, fire safety, and environmental science, where knowing the products of combustion is essential for controlling pollution.