The triple point of water is the unique condition at which ice, liquid water and water vapour coexist in equilibrium. Which of the following pressure–temperature pairs corresponds to this triple point?

Introduction / Context:
This thermodynamics question concerns the triple point of water. The triple point is an important reference in temperature scales and phase diagrams because it represents the unique combination of pressure and temperature at which solid, liquid and gaseous phases of a substance coexist in equilibrium. For water, this point is used in defining the Kelvin temperature scale.

Given Data / Assumptions:

• The question is specifically about water and its triple point.
• Several pressure–temperature combinations are offered, including values at 1 atmosphere and 4.58 Torr.
• We assume standard phase diagram information for pure water.
• Pressure units include atmosphere (atm) and Torr (approximately equivalent to mm of mercury).

Concept / Approach:
The triple point of water is experimentally determined to occur at a temperature of 0.01 degrees Celsius (273.16 K) and at a pressure of about 611 pascals, which is approximately 4.58 mm of mercury or 4.58 Torr. This point is not at 1 atmosphere; normal melting and boiling points at 1 atm are different from the triple point. Therefore, options that quote 1 atm as the pressure cannot represent the triple point of water. Only the combination of about 4.58 Torr and 0.01 degrees Celsius matches the physical definition.

Step-by-Step Solution:
1) Recall that the triple point temperature of water is approximately 0.01°C, not exactly 0°C.2) The triple point pressure is much lower than standard atmospheric pressure and is roughly 611 Pa, which corresponds to about 4.58 Torr.3) Examine each option: pairs that include 1 atm cannot be correct, because triple point is at low pressure.4) Option a (1 atm, 0°C) corresponds roughly to the normal freezing point of water, not the triple point.5) Option b (1 atm, 0.01°C) is also at 1 atm and is not the triple point; at 1 atm, water would exist mainly as solid or liquid depending on the exact conditions.6) Option d (4.58 Torr, 0.01°C) matches both the known triple point pressure and temperature of water.7) Therefore, the triple point of water corresponds to 4.58 Torr and 0.01°C.

Verification / Alternative check:
International definitions of the Kelvin scale historically referenced the triple point of water at exactly 273.16 K (0.01°C) and at a specific equilibrium vapour pressure of about 611 Pa over ice water mixture. Converting 611 Pa to Torr gives roughly 4.58 Torr. Phase diagrams of water mark this point where the solid liquid and vapour coexist. It is distinct from the normal melting point at 0°C and 1 atm, and from the normal boiling point at 100°C and 1 atm. These references confirm that the correct pair is 4.58 Torr and 0.01°C.

Why Other Options Are Wrong:
1 atm and 0°C: Represents the normal freezing point of water but not the triple point; only solid and liquid phases are relevant there.
1 atm and 0.01°C: Still at 1 atm, water will not have all three phases in equilibrium at this point.
1 atm and 0 K: This is physically impossible for liquid water; 0 K is absolute zero where all thermal motion stops.
760 Torr and 100°C: This pair corresponds approximately to the normal boiling point of water at 1 atm, not the triple point.

Common Pitfalls:
Students often confuse the triple point with the normal melting point at 0°C and 1 atm because both involve solid and liquid water. However, the triple point also includes vapour, and occurs at a much lower pressure. Another mistake is to memorise 0°C without remembering the 0.01°C correction and the specific low pressure. A good strategy is to recall that triple point is a special calibration point at 0.01°C and about 4.58 Torr, not at 1 atmosphere.

Final Answer:
The triple point of water occurs at 4.58 Torr and 0.01°C, where ice, liquid water and water vapour coexist in equilibrium.