(a) What is the significance of the triple point in a phase diagram? (b) Could you measure the triple point of water by measuring the temperature in a vessel in which water vapor, liquid water, and ice are in equilibrium under $101.32 \mathrm{kPa}$ of air? Explain.

The triple point in a phase diagram is a unique point where all three phases (solid, liquid, and gas) of a substance coexist in thermodynamic equilibrium. It signifies the specific temperature and pressure conditions necessary for all three phases to be present simultaneously. It is important because at this triple point, very small changes in temperature and/or pressure can cause a substance to spontaneously change phase.

In this scenario, liquid water, water vapor, and ice are in equilibrium under an air pressure of 101.32 kPa. However, the presence of air complicates the system, as the pressure we are measuring is not the partial pressure of the water vapor but the total air pressure in the vessel. The triple point of water occurs at a very specific temperature and pressure (0.01 °C and 611.657 Pa). When the pressure within the vessel is 101.32 kPa (which includes the partial pressure of the water vapor and the partial pressure of air), the equilibrium with ice, liquid, and vapor would be different than what is needed for the triple point. Therefore, it is not possible to directly measure the triple point of water under these conditions. To accurately measure the triple point of water, all other gases must be removed so that only water is present in the system.