In which of the following systems is(are) work done by the surroundings on the system? Assume pressure and temperature are constant. a. \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) b. \(\mathrm{CO}_{2}(s) \longrightarrow \mathrm{CO}_{2}(g)\) c. \(4 \mathrm{NH}_{3}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\) d. \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\) e. \(\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaCO}(s)+\mathrm{CO}_{2}(g)\)

Understanding how chemical reactions involve work requires a grasp on the basics of thermochemistry. In the context of chemical reactions, work is often related to changes in volume against an external pressure. When a reaction occurs in a container at constant pressure, the system either expands, doing work on the surroundings, or contracts, with the surroundings doing work on the system.

Take for example the sublimation of solid carbon dioxide. We can represent this phase change as a chemical reaction: CO₂(s) → CO₂(g). The carbon dioxide starts as a solid (dry ice) and ends as a gas, expanding into the available volume which shows the system doing work on the surroundings by pushing the atmospheric pressure back. Conversely, reactions that lead to a reduction in the volume of gas, such as the synthesis of sulfur trioxide, 2 SO₂(g) + O₂(g) → 2 SO₃(g), imply that the surroundings are compressing the system, thus doing work on it.

Grasping this concept is pivotal, especially when dealing with the idea that a negative change in gas moles suggests work being done on the system, while a positive change indicates the system is doing work on the surroundings. This phenomenon is tied to the conservation of energy and the first law of thermodynamics, where the work can either be an input or output of the system.

The change in moles of gas during a chemical reaction is a critical component that affects work. When the number of moles of gaseous products is less than the number of moles of gaseous reactants, the overall volume tends to decrease, as seen in the reaction where ammonia and oxygen form nitrogen dioxide and water vapor: 4 NH₃(g) + 7 O₂(g) → 4 NO₂(g) + 6 H₂O(g).

It's important to note that only gases are considered in this calculation, mainly because gases are compressible and can expand to fill their containers, which is not the case with solids or liquids. An understanding of the ideal gas law, PV=nRT, also ties into these concepts, as 'n' (the number of moles of gas) directly influences the pressure (P) and volume (V) of the system at a given temperature (T) and gas constant (R).

For students, the challenge is often in counting the moles correctly and keeping in mind that while solids and liquids do undergo volume changes, these are generally negligible in the context of work done by or on the system under constant pressure conditions.

In thermochemistry, the system refers to the part of the universe we are focusing on, typically the reactants and products of a chemical reaction. The surroundings are everything outside the system, which could include the rest of the reaction vessel, the room, or even the entire universe. The interaction between a system and its surroundings often involves energy exchange, which can take the form of work or heat.

When considering our system, it is crucial to determine whether it is open, closed, or isolated. These terms describe whether the system can exchange energy or matter with its surroundings: open systems exchange both, closed systems exchange only energy, and isolated systems exchange neither. Most chemical reactions studied in classrooms are assumed to occur in closed systems at constant pressure.

For instance, the decomposition of calcium carbonate into calcium oxide and carbon dioxide gas, CaCO₃(s) → CaO(s) + CO₂(g), shows a system producing more gas moles, therefore pushing against the surroundings. This concept is vital in predicting the direction in which work is performed and is a fundamental consideration in chemical thermodynamics that gives us insights into energy requirements or releases during reactions.