Phase Changes - Energy Changes - Heating Curves

Phase changes - energy changes - heating curves

Phase Changes - Energy Changes - Heating Curves

 

Many important properties of liquids and solids relate to the ease with which they change from one state to another. Water for example, when heated it evaporates that is changes from liquid to the gas state. In general, each state of matter (solid, liquid, gas)  can change into either of the the other two states. Figure I.1 shows these transformations which are called phase changes or changes of state.

Fig. I.1: Phase changes between the three states of matter and the corresponding energy changes.

What happens when a solid is heated? Typically, it melts to form a liquid. If the heating continues, the liquid at some point boils and forms the vapor phase (gas). This process can be represented by a heating curve: a plot of temperature versus time for a process where energy is added at a constant rate. The heating curve of water is shown in Fig. I.2.

There are five separate zones on the graph (heating curve) of Fig. I.2:

 

Zone 1 (Ice):

As energy flows into the ice, the random vibrations of the water molecules increase as the temperature rises from -20 °C to 0 °C. Eventually, the molecules become so energetic that they break loose from their solid lattice positions and the change from solid to liquid occurs. This is indicated by a plateau at 0 °C on the heating curve. At this temperature, called the melting point, all the added energy is used to break the ice structure by breaking the hydrogen bonds, thus increasing the potential energy of the water molecules. The enthalpy change that occurs at the melting point when a solid melts is called the heat of fusion or enthalpy of fusion ΔΗfus. The temperature remains constant until all the solid has changed to liquid.

The general equation for calculating heat energy required to change the temperature of a solid is:

Q = m * cs * ΔΤ      (1)

Where: Q heat energy (Joules)

cs specific heat of the solid (Joules/g°C)

ΔΤ temperature change (°C)

 

Notes:

Specific heat of a solid cs is the amount of heat energy that changes the temperature of 1.0 g of a solid by 1.0 °C.

Each substance has its own specific heat. The specific heat of ice is for example 2.1 Joules/g°C.

 

Zone 2 (Ice & Water):

In zone 2, the temperature remains constant at 0 °C. At this temperature, called the melting point, all the added energy is used to disrupt the ice structure by breaking the hydrogen bonds and potential energy is increasing. The attractive forces that hold particles in fixed positions in the solid must be overcome to form the liquid. The heat absorbed in this case is called the heat of fusion or enthalpy of fusion and is symbolized ΔΗfusion.

Each substance has its own heat of fusion. The heat of fusion of ice is 340 Joules/g. Exactly the same amount of heat is given up when 1.0 g of water is changed to ice. This heat is called the heat of crystallization.

The general equation for calculating heat energy to change a solid to a liquid is:

Q = m * ΔΗfusion     (2)

Where: Q heat energy (Joules, J)

m mass of solid (g)

ΔH heat or enthalpy of fusion (J/g)

 

Zone 3 (Water):

The temperature is again changing as soon as all the solid (ice in this case) has changed to liquid. Then it begins to increase again starting from 0 °C up to 100 °C. The particles of a liquid are in constant motion and they are not held together as tightly as the particles of a solid. To change the temperature of a liquid heat energy must be added according to equation (1) and where m is the mass of 1.0 g of water in this case, where cs is the specific heat of water (cs)water = 4.2 J/g°C and ΔΤ is the temperature change.

Fig. I.2: The heating curve of water (for a given quantity of water where energy is added at a constant rate). The plateau at the boiling point is longer than the plateau at the melting point because it takes seven times more energy (seven times the heating time) to vaporize liquid water than to melt ice. There are five zones in the heating curve (ice, ice&water, water, water & steam, steam) each one having its own unique formula for calculating heats.

 

Zone 4 (Water & Steam):

At 100 °C the liquid water reaches its boiling point, and the temperature again remains constant as the added energy is used to vaporize the liquid. The heat absorbed is called heat of vaporiza-tion(ΔΗvapor). This heat is increasing the potential energy of the molecules of the liquid. Each substance has its own heat of vaporization. The heat of vaporization for water is 2270 J/g. Exactly the same amount of heat is given up when 1.0 g of water vapor is changed to liquid water. This heat is called the heat of condensation.

The general equation for calculating heat energy to change a liquid to a gas is:

Q = m * ΔΗvapor     (3)

Where: Q heat energy (Joules, J)

m mass of solid (g)

ΔHvapor heat or enthalpy of vaporization (J/g)

 

Notes:

Each substance has its own heat of vaporization. The heat of vaporization for water is 2270 J/g.

 

Zone 5 (Steam):

When all the liquid is changed to vapor the temperature again begins to rise. Note that phase changes are physical changes. No chemical bonds have been broken but intermolecular forces have been overcome. On the average, gaseous molecules are many times further apart from each other than molecules of solids and liquids.

To change the temperature of a gas, heat energy must be added. The amount of heat energy that changes the temperature of 1.0 g of a gas by 1.0 °C is called its specific heat (cs)gas. Each substance has its own specific heat. The specific heat of steam is 2.02 J/g°C.

To change the temperature of a gas heat energy must be added according to equation (1) and where m is the mass of 1.0 g of steam in this case, where cs is the specific heat of steam (cs)steam = 2.02 J/g°C and ΔΤ is the temperature change.

 

Note:

All substances have the same basic heating curve graphs (five zones). The differences are going to be the transition temperatures, and the values for specific heats cs and ΔΗ’s.

Relevant Posts

Free energy, entropy and thermodynamic equilibrium

Gas Laws - Ideal Gas Law

References
  1. P. Atkins, J. de Paula, “Physical Chemistry”, 9th Edition, W. H. Freeman (2009)
  2. I. N. Levine, “Physical Chemistry”, 6th Edition, McGraw-Hill (2008)
  3. S. S. Zumdahl, “Chemical Principles”, 6th Edition, Houghton Mifflin Company (2009)
  4. A. W. Adamson, A. P. Gast, “Physical Chemistry of Surfaces”, John Wiley & Sons (1997
Key Terms
phase changes, changes of state, heating curve, heat of fusion, enthalpy of fusion, ,ΔΗ, , specific heat

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