For the process \(\mathrm{A}(l) \longrightarrow \mathrm{A}(g),\) which direction is favored by changes in energy probability? Positional probability? Explain your answers. If you wanted to favor the process as written, would you raise or lower the temperature of the system? Explain.

We are given a process in which substance A changes its state from liquid (l) to gas (g). We need to determine whether this process is favored by energy probability and positional probability.

Energy probability refers to the likelihood of a system adopting a certain energy state. For a system to transition from one state to another, it needs to overcome the potential energy barrier between those states. In the case of a liquid-to-gas transition, the system needs to overcome the intermolecular forces that hold the molecules together in the liquid state. When the energy probability favors the forward reaction (A(l) → A(g)), it means that the system has enough thermal energy to break the intermolecular forces of the liquid state. As a result, the molecules gain freedom to move as a gas. In this case, the forward reaction (liquid to gas) is favored by energy probability. Therefore, energy probability favors the direction from liquid to gas.

Positional probability refers to the likelihood of a particle being found in a certain location or state. For a substance to transition from a more ordered to a less ordered state, the positional probability favors the process. When going from liquid to gas, the substance becomes less ordered and the particles have more freedom to move. As a result, the positional probability favors the forward reaction (A(l) → A(g)) as it allows the particles to occupy more positions in space, increasing the entropy of the system. Therefore, positional probability favors the direction from liquid to gas.

To favor the given process (A(l) → A(g)), we need to ensure that the energy probability and positional probability are favored. As we concluded in steps 2 and 3, both energy and positional probabilities favor the forward reaction. However, we need to know how temperature affects this process. As the forward reaction (A(l) → A(g)) requires energy to break the intermolecular forces, increasing the temperature provides this energy and increases the energy probability for the forward reaction. Therefore, we should raise the temperature of the system to favor the process as written.