Consider a vessel with a movable piston. A reaction takes place in the vessel at constant pressure and a temperature of \(200 \mathrm{~K}\). When reaction is complete, the pressure remains the same and the volume and temperature double. Which of the following balanced equations best describes the reaction? (a) \(\mathrm{A}+\mathrm{B}_{2} \longrightarrow \mathrm{AB}_{2}\) (b) \(\mathrm{A}_{2}+\mathrm{B}_{2} \longrightarrow 2 \mathrm{AB}\) (c) \(2 \mathrm{AB}+\mathrm{B}_{2} \longrightarrow 2 \mathrm{AB}_{2}\) (d) \(2 \mathrm{AB}_{2} \longrightarrow \mathrm{A}_{2}+2 \mathrm{~B}_{2}\)

The ideal gas law is a fundamental equation in chemistry that relates the pressure (P), volume (V), temperature (T), and the amount of gas in moles (n) in a simple yet powerful relationship: PV = nRT. Here, R is the ideal gas constant. The law provides a means to predict one property of a gas if the other three are known.

The law is particularly useful in stoichiometry because it helps us understand how gases will behave under different conditions of temperature and pressure. For example, in our exercise, we keep pressure constant and scrutinize the effects of volume and temperature on the amount of gas, which allows us to deduce changes in moles. The ideal gas law underpins many chemical calculations and is essential for understanding gas behavior during reactions like the one we're examining.

In the exercise solution, the law is applied after determining the stoichiometric relationship between reactants and products, helping us to conclude that the volume and temperature doubling (while pressure remains constant) implies the moles of gas must double too, leading us to the correct equation that represents the reaction.

The mole concept is a bridge between the microscopic world of atoms and molecules, and the macroscopic world we can measure. One mole refers to Avogadro’s number (approximately 6.022 x 10²³) of particles, be they atoms, molecules, ions, or others. It becomes hugely valuable when dealing with chemical equations and reactions.

In stoichiometry, the mole concept allows us to calculate amounts of reactants needed or products formed. The exercise at hand required an understanding of how moles are involved in the balancing of chemical equations, by comparing the total mole count before and after the reaction. This comparison gives insights into the changes occurring in a system and whether the equation aligns with the physical changes such as volume and temperature alterations, as mentioned in the ideal gas law.

The step by step solution showcases the process of equating the moles of reactants and products to find the equation that fits the new conditions post-reaction. Through this approach, we engage the mole concept to unravel the right chemical reaction that matches the observed changes.

Chemical equilibrium occurs in a reversible chemical reaction when the rate of the forward reaction equals the rate of the reverse reaction, leading to constant concentrations of the reactants and products. It's dynamic because the reactions continue to occur, but there's no net change in concentration of each engaged species.

In relation to our textbook problem, understanding chemical equilibrium is necessary even though the equilibrium concept doesn't directly apply because we are considering a complete reaction. However, the notion of balancing equations—the core of stoichiometry—is similar to achieving equilibrium in the sense that both concepts involve proportions and ratios of reactants and products.

The exercise improvement advice emphasizes ensuring a thorough explanation of the equilibrium concepts, even if in the context of a problem that doesn't involve a reaction at equilibrium. It's important because it prepares students to think about the balance and relative quantities of chemicals in all reactions, which is the essence of stoichiometry and helpful when they encounter true equilibrium problems.