Question

3. (a) The schematic temperature dependence of the chemical potential of CO2 is given below. Show how the melting pint (TT) will change when increase the pressure and justify your answer. Draw the new u-T line in the following scheme. (b) If this diagram is for water, repeat the same questions in (a).

Answer 1

This question is related to the phase rule and the phase diagram. A diagram which shows the different phases of a particular system is known as a phase diagram.

The phase diagrams of a pure compound like water and carbon dioxide are for the single-component system, where temperature (T) and pressure (P) are usually the coordinates, which shows the (T, P) conditions for the stable phases.

There are following phase changes during the pressure and temperature changing in the system.

Solid to liquid --------------------> Melting curve

Liquid to Solid --------------------> Freezing curve

Liquid to Gas ----------------------> Vaporization curve

Gas to Liquid ---------------------> Condensation curve

Solid to Gas -----------------------> Sublimation curve

Gas to Solid -----------------------à Deposition curve

Sublimation is the conversion of dry ice CO₂ to gas.

Phase diagram of carbon dioxide

From the diagram 1, where the solid, liquid and gas coexist is called the triple point, the line between the solid and liquid phase is known as melting point line and the line between liquid and gas phase is known as boiling point line.

s / pressure Platon) -Tripple point - temperature T

Diagram 1. Phase diagram of carbon dioxide

At 1 atm if the temperature is increased then it directly goes from solid to the gas phase, therefore, CO₂ sublimes. Comparing to the diagram given in the question the melting point (T_f) of solid CO₂ is the point where it started to become liquid with increasing the temperature but when there is the pressure increases with increasing temperature then the melting point (T_f) of the becomes the triple point in the phase diagram of CO₂.

Point to be noted that at 1 atm the pressure is below the triple point. If the pressure is above the triple point then it will go from solid to liquid to the gas phase.

As the pressure increase, the density of system is increasing because increasing pressure is compacting the atoms together of the system and the atoms started to squeeze into a tighter space, therefore, more mass per unit volume with higher density. Thus increasing the pressure the phase change of CO₂ is from liquid to the solid so it freezes the substance, which means the solid phase is at a higher pressure than a liquid phase. Therefore, in the case of CO_2, the melting point curve has a positive slope the density of solid CO₂ is greater than that of liquid CO₂ at higher pressure.

Phase diagram of water

hapo ansaed tripple poind - Temperature

Diagram 2. Phase diagram of water

Diagram 2 shows that at low temperature, (solid) ice is the stable phase. At high pressure and moderate temperatures, the liquid phase of water is the stable phase, and at low pressure and high temperature, the gas phase (vapour) of water is the stable phase.

The solid phase from the gas phase is separated through the sublimation curve. This line indicates the vapour pressure of ice as a function of temperature (Diagram 2).

The melting point line has a negative slope instead of the positive slope as moving towards the right side the line decrease. This is still going to be through the solid phase, liquid phase and the gas phase and here 1 atm pressure is above the triple point.

Because standard pressure is above the triple point, increasing in temperature ice is going to melt into liquid and if the temperature is increased continuously the liquid will vaporize into a gas so at 1 atm pressure increasing the temperature to get all three phases of water.

If decrease the pressure below the triple point the solid will sublime directly to gas so sublimation occurs when pressure is below the triple point.

The density of Liquid is high at a higher pressure, therefore, it is denser than a solid thus liquid water has a higher density than ice and that is why ice floats in water.