Consider these changes: (a) \(\mathrm{Hg}(l) \longrightarrow \mathrm{Hg}(g)\) (b) \(3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{O}_{3}(g)\) (c) \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(s) \longrightarrow \mathrm{CuSO}_{4}(s)+5 \mathrm{H}_{2} \mathrm{O}(g)\) (d) \(\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{HF}(g)\) At constant pressure, in which of the reactions is work done by the system on the surroundings? By the surroundings on the system? In which of them is no work done?

Understanding the influence of a change in the number of moles of gas during a chemical reaction is essential for analyzing work done by or on the system. A mole represents a specific quantity of particles, specifically Avogadro's number, which is approximately 6.022 x 10²³ particles. When a gas-phase reaction results in an increase in the number of moles of gas, as seen in the conversion of liquid mercury (Hg(l)) to gaseous mercury (Hg(g)) or the dehydration of CuSO₄·5H₂O(s) to CuSO₄(s) and water vapor (H₂O(g)), the reaction system does work to push the surroundings back, causing expansion. Conversely, a decrease in moles, such as the reaction of O₂(g) to O₃(g), leads to contraction, where the surroundings do work on the system. In reactions where the mole count of gas remains constant, like the formation of HF from H₂ and F₂, no net work is done because the volume change is negligible.

This concept becomes particularly important when dealing with gases' behavior under different pressure and temperature conditions, as guided by the ideal gas law, PV=nRT, where P is pressure, V is volume, n is moles, R is the gas constant, and T is temperature.

Phase transitions involve changing a substance from one state of matter to another, such as solid to liquid, liquid to gas, or vice versa. In our exercise, the transitions of mercury from liquid to gas (Hg(l) to Hg(g)) and the dehydration of copper sulfate pentahydrate (CuSO₄·5H₂O) exemplify phase changes resulting in the increase of gas moles. During a phase change, energy is either absorbed or released in the form of heat, known as enthalpy. Additionally, if a transition leads to the formation of gases, as mentioned earlier, it may involve work being done due to the change in volume.

It's noteworthy to highlight that phase transitions are not always accompanied by a change in moles of gas—a melted ice cube, from ice (solid) to water (liquid), does not alter the mole count but still constitutes a phase change.

In thermodynamics, the 'system' refers to the part of the universe we focus on, typically a set of substances involved in a reaction. Everything else is the 'surroundings.' When discussing work in chemical reactions, we specifically consider the system's ability to do work on the surroundings or the surroundings doing work on the system. This interaction is governed by the laws of thermodynamics.

First Law of Thermodynamics

The first law, also known as the law of energy conservation, states that the total energy of an isolated system remains constant; it can neither be created nor destroyed, only transformed or transferred. This principle is crucial when considering that during a reaction, the energy change in the system must be equal to the energy exchanged with the surroundings, whether in the form of work or heat.

The expansion and contraction of gases are directly linked to work in thermodynamics. When a gas expands, as in reactions (a) and (c) from the exercise, it exerts force over the displacement of a boundary, such as the walls of a container, thus performing work on the surroundings. This phenomenon is often visualized in a piston where gas expansion pushes the piston outward.

Work Done by Expansion

The work done by an expanding gas is calculated by the integral of the pressure over the volume change, represented as \( w = -\int P_{ext}(dV) \), where \( P_{ext} \) is the external pressure and \( dV \) is the differential change in volume.

Conversely, when gases contract, like in reaction (b), the surroundings do work on the system by pushing the boundaries inwards, which compresses the gases. This concept is crucial for understanding not only chemical processes in closed environments but also those that occur in our atmosphere, automotive engines, and even biological systems.