Question

Consider the vaporization of liquid water to steam at a pressure of 1 atm. (a) Is this process endothermic or exothermic? (b) In what temperature range is it a spontaneous process? (c) In what temperature range is it a nonspontaneous process? (d) At what temperature are the two phases in equilibrium?

Short answer

(a) The vaporization of liquid water to steam is an endothermic process. (b) The temperature range for a spontaneous process is above 373.15 K (100 °C). (c) The temperature range for a nonspontaneous process is below 373.15 K (100 °C). (d) The two phases are in equilibrium at 373.15 K (100 °C).

Step-by-step solution

(a) Identify the process: Endothermic or Exothermic?

In order to determine whether the process is endothermic or exothermic, let's consider the nature of the phase transition. The vaporization of liquid water into steam involves an increase in energy since the molecules in the gas phase have more kinetic energy than those in the liquid phase. As energy is needed in this process, we can conclude that this process is endothermic.

(b) Spontaneous process temperature range

A spontaneous process is one that occurs naturally without requiring any external energy input. In the case of vaporization, it will be spontaneous at temperatures where there is enough thermal energy to overcome the intermolecular forces holding the water molecules together in the liquid phase. At 1 atm pressure, the boiling point of water is 100°C (373.15 K). Above this temperature, the vaporization process occurs spontaneously because the thermal energy exceeds the energy needed to break intermolecular bonds. So, the spontaneous temperature range is above 373.15 K (100 °C).

(c) Nonspontaneous process temperature range

A nonspontaneous process is one that does not occur naturally and requires additional energy input to occur. In the case of vaporization, nonspontaneous processes will occur at temperatures below the boiling point of water. This is because the thermal energy in the system is insufficient to overcome the intermolecular forces holding water molecules together in their liquid phase. So, the nonspontaneous temperature range is below 373.15 K (100 °C).

(d) Temperature of two phases in equilibrium

When two phases are in equilibrium, their rates of change are balanced, and no net change in the phases is observed. In the case of vaporization, the liquid phase and the gas phase are in equilibrium at the boiling point of water for a given pressure. At 1 atm pressure, the boiling point of liquid water is 100°C (373.15 K). Hence, the two phases are in equilibrium at 373.15 K (100 °C).