What effect does an increase in pressure have on each of these systems at equilibrium? (a) \(\mathrm{A}(s) \rightleftharpoons 2 \mathrm{~B}(s)\) (b) \(2 \mathrm{~A}(l) \rightleftharpoons \mathrm{B}(l)\) (c) \(\mathrm{A}(s) \rightleftharpoons \mathrm{B}(g)\) (d) \(\mathrm{A}(g) \rightleftharpoons \mathrm{B}(g)\) (e) \(\mathrm{A}(g) \rightleftharpoons 2 \mathrm{~B}(g)\) The temperature is kept constant. In each case, the reacting mixture is in a cylinder fitted with a movable piston.

When examining the effects of pressure on equilibrium, it's essential to understand that a change in pressure can shift the position of equilibrium in a reaction.

This phenomenon is guided by Le Chatelier's Principle, which states that if an external change is imposed on a system at equilibrium, the system will adjust in a way that counteracts this change. In the context of pressure, for gas-phase reactions, an increase in pressure will shift the equilibrium toward the side of the reaction with fewer gas molecules. This is because an increase in pressure effectively reduces the volume available for the gaseous molecules, and by shifting toward the side with fewer molecules, the system tries to relieve the applied pressure.

However, it's crucial to note that this only applies to gas-phase reactions. For reactions involving solids or liquids, known as condensed phases, changes in pressure have negligible effects, as the particles in these phases are incompressible or marginally compressible and adding pressure doesn't significantly change the volume.

The response of a chemical equilibrium to an external change, such as pressure, is highly dependent on the phase of the reacting substances.

For instance, solids and liquids are virtually incompressible, so altering the pressure does not lead to a significant volume change and, therefore, does not shift the equilibrium. On the contrary, gases are highly compressible, and a pressure change will lead to a volume change significant enough to shift the equilibrium according to Le Chatelier's Principle. For a reaction between a solid and a gas, like in the example of \(\mathrm{A}(s) \rightleftharpoons \mathrm{B}(g)\), increasing the pressure will favor the production of gas if it results in fewer gas molecules than the reactants, as in this case.

Gas phase reactions are particularly susceptible to changes in pressure. In these reactions, the equilibrium can be described by the Ideal Gas Law (PV=nRT), which indicates the direct relationship between pressure (P) and the number of moles of gas (n) when temperature (T) and volume (V) are constant.

Using Le Chatelier's Principle, a reaction with equal moles of gas on both sides, such as \(\mathrm{A}(g) \rightleftharpoons \mathrm{B}(g)\), will not experience a shift in equilibrium with a pressure change, as there's no difference in the number of moles of gas that the change in pressure can leverage.

In the case of a reaction where a different number of moles of gas are present on each side, such as \(\mathrm{A}(g) \rightleftharpoons 2 \mathrm{~B}(g)\), an increase in pressure will drive the equilibrium to the side with fewer moles of gas. This is the system's attempt to lower the pressure, in accordance with the principle.

Le Chatelier's Principle finds applications across various industries, particularly in the field of chemical engineering and industrial chemistry where reactions are designed to favor the production of desired products.

For example, in the Haber process for the synthesis of ammonia, manufacturers manipulate pressure to increase the yield of ammonia. Understanding how pressure affects chemical equilibrium allows us to control reactions for maximum efficiency, or to predict how a system will respond to environmental changes, which is fundamental in environmental chemistry when considering how gases respond to changes in atmospheric pressure.