How much work (in J) is involved in a chemical reaction if the volume decreases from 5.00 to 1.26 L against a constant pressure of 0.857 atm?

Understanding the work-energy principle is crucial for studying the behavior of systems in chemistry, especially during chemical reactions or physical processes such as expansion or compression of gases. In simple terms, work is done when a force causes a displacement. In the context of chemistry, we often refer to the work done by or on a system as the energy transferred when a system expands or contracts against an external pressure.

The work-energy principle in chemistry can be translated to the relationship between work and the internal energy of a system. When work is done on a system, such as compressing a gas, energy is transferred to the system, increasing its internal energy. Conversely, when a system does work on its surroundings, for instance by expanding against an external pressure, it loses energy. The formula to calculate this work is given by the equation, \[W = -P \Delta V\] where 'W' is the work done, 'P' is the external pressure, and '\Delta V' is the change in volume. The sign convention is such that work is considered positive when done on the system, and negative when the system does work on the surroundings.

Pressure-volume work, often abbreviated as P-V work, is one specific type of work encountered in chemical processes and thermodynamics. It occurs when the volume of a system changes in the presence of an external pressure. For gaseous reactions or transitions, this is the most common form of work encountered.

In our exercise, the chemical reaction caused the volume to decrease, implying that the surroundings did work on the system. To calculate this pressure-volume work, you need two critical pieces of information: the external pressure and the change in volume during the process. It's important to note that P-V work is scalar and thus does not depend on the path but only on the initial and final states of the system.

To correctly ascertain the work done, it's essential to align the units of pressure and volume. Ideally, the pressure should be in Pascals (Pa) and the volume in cubic meters (m3). Consistent units ensure an accurate calculation of work in Joules, as was demonstrated in the step-by-step solution of our exercise.

The behavior of gases during a process that involves a change in volume can be precisely described by the gas laws. These laws, which include Boyle's Law, Charles's Law, and Avogadro's Law, help us predict how gases react to changes in volume, temperature, and pressure. In the realm of work calculation, Boyle's Law is particularly relevant, as it describes the inverse relationship between pressure and volume at a constant temperature for a fixed amount of gas.

Considering Boyle's Law, when a gas is compressed (decreasing volume), its pressure increases if temperature is constant, and similarly, when a gas expands, its pressure decreases. This physical property plays a crucial role in understanding how work is done in terms of the gas laws. If you know the initial and final states of the gas regarding pressure and volume, you can calculate the work performed without knowing the path taken between these states.

In our example, although the gas laws themselves were not explicitly used in the calculation, the underlying concept applies; the volume change dictates the work done, adhering to the principles presented by these fundamental laws.