Question

(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 1 atm of air? Explain.

Short answer

The triple point in a phase diagram is a unique temperature and pressure at which all three phases (solid, liquid, and gas) of a substance coexist in equilibrium. It is significant as it helps determine other specific properties and phase transitions of the substance. However, measuring the triple point of water under 1 atm of air is not possible since its triple point occurs at \(0.01^{\circ}\)C and \(6.1173 \, \text{mbar}\). To measure it correctly, the pressure must be adjusted to the exact triple point value.

Step-by-step solution

1. Explain the significance of the triple point in a phase diagram

The triple point of a substance is a unique temperature and pressure at which all three phases (solid, liquid, and gas) coexist in equilibrium. In a phase diagram, it's represented as a point where the solid-liquid, solid-gas, and liquid-gas phase boundaries converge. The triple point is significant because it's the only set of conditions where all three phases can be in equilibrium simultaneously. Additionally, phase diagrams use the triple point of a substance as a reference point to determine other specific properties and phase transitions.

2. Discuss if we can measure the triple point of water under the given conditions

According to the given experimental setup, we are supposed to measure the triple point of water by maintaining water vapor, liquid water, and ice in equilibrium under 1 atm of air. However, it's important to note that the equilibrium at the triple point depends on both the pressure and temperature conditions. For water, the triple point occurs at a temperature of \(0.01^{\circ}\)C and a pressure of \(6.1173 \, \text{mbar}\) (millibar), which is much lower than 1 atm (\(1013.25 \, \text{mbar}\)). Hence, under 1 atm of air, it will not be possible to maintain all three phases in equilibrium at their triple point. We would have to adjust the pressure to the exact value of the triple point of water to be able to measure it correctly.