# Heating Curves

Skills to Develop

• Explain what is happening as a system is heated.

A system is an imaginary closed container isolated from its environment. It is isolated so that we can investigate how the system changes as it is disturbed either by transferring mass or energy to and from it. The existence of the container is optional in definition, but in reality a container is used for the isolation.

When the system is heated, energy is transferred into it. In response to the energy it receives, the system changes, for example by increasing its temperature. A plot of the temperature versus time is called the heating curve. One such heating curve is shown here.

When a system contains only one phase (solid, liquid or gas), the temperature will increase when it receives energy. The rate of temperature increase will be dependent on the heat capacity of the phase in the system. When the heat capacity is large, the temperature increases slowly, because much energy is required to increase its temperature by one degree. Thus, the slope of temperature increase for the solid, liquid, and gases are different.

For example, the temperature of a system containing ice below its melting point will increase when heated. However, at 273.15 K, the temperature stops rising. At this temperature, the ice starts to melt, and the heat is used to melt the ice. The melting of ice is called a phase transition. When energy supplied is used for the phase transition the temperature stays constant. After the phase transition is complete, the temperature rise will follow a different rate than that of the solid due to different heat capacity, as shown in the heating curve. A colorful web site for discussing States of Matter also shows the heating curve and phase diagram of water.

For one mole of water (18 g), we have the following data:

• Heat capacity of ice = 37.6 J (K mol)-1.
• Heat capacity of water = 75.3 J (K mol)-1.
• Heat capacity of steam = 35.8 J (K mol)-1 (at constant pressure of 1 atm).
• Melting point = 273.15 K
• Heat of fusion of ice = 6.01 kJ mol-1.
• Boiling point = 373.15 K.
• Heat of vaporization = 40.67 kJ mol-1.
• Heat of sublimation = 46.7 kJ mol-1.

The heating curve given above is sketched according to the above data. In a real experiment, the heat transferred into the system is hardly at a constant rate unless the heat source is at a very high temperature. However, for the sake of simplicity, let us assume the heat flow into the system to be at a constant rate.

Water is a common substance. Ice is the stable phase below 273.15 K. Both solids and liquids coexist at 273.15 K. When heat is put into the system, more solid will melt. Thus, the temperature does not change. The normal boiling point is 373.15 K. As heat is absorbed, some water will boil off but the temperature is kept at 373.15 K. The changes in temperature as a function of time, or as a function of heat absorbed.

For water, the heat of fusion is 6.0 kJ / mol, and that of vaporization is 40.7 kJ/mol. If the heat input is constant, a longer period is needed for one mole of water to evaporate than the time needed for the ice to melt.

In a laboratory, we heat up different materials and plot the temperature as a function of time. Every material has a unique melting point and boiling point. It also has its heat of fusion and heat of vaporization.

### Questions

1. What is the temperature in K when ice and water coexist for a long period of time when the gas phase is at 1.0 atm pressure?

Hint: 273.15 K

Skill -
Describe the melting point.

2. What is the heat of fusion (in kJ/mol) for ice?

Hint: 6.01 kJ/mol

Discussion -
The experimental value is 6.01 kJ/mol which is equivalent to 80 cal/g. Which portion on the heating curve will be affected by the heat of fusion?

3. The heat capacity is the largest for which phase: solid, liquid or gas?

Hint: liquid

Discussion -
From the value given above, the heat capacity for water is larger than that of solid or gas. Heat capacity for gas $$\ce{H2O}$$ varies with temperature.

4. Considering intermolecular forces between molecules, which one has higher heat of vaporization, water or ethyl ether?

Hint: water

Discussion -
More energy is required to separate water molecules due to strong hydrogen bonding. Only weak hydrogen bonding is present in ether. Heats of vaporization for water and ether are 40.67 and 26.0 kJ/mol respectively.

5. Copper (Z = 29) and gold (Z = 79) belong to the same group on the periodic table. Which one of these do you think should have higher boiling point? (copper or gold)

Hint: gold

Discussion -
Gold atoms have more electrons around them. Boiling points: $$\mathrm{Cu = 2868\: K}$$; $$\mathrm{Au = 2933\: K}$$.

6. Copper (Z = 29) and gold (Z = 79) belong to the same group on the periodic table. Which one of these do you think should have higher heat of vaporization? (copper or gold)

Hint: gold

Discussion -
Heat of vaporization: $$\mathrm{Cu = 304\: kJ/mol}$$; $$\mathrm{Au = 310\: kJ/mol}$$.

7. In an experiment a definite amount of water is used. The heat of fusion of the system was found to be 9 kJ. What should be the corresponding heat of vaporization? (Molar heats of fusion and vaporization are 6 and 40 kJ /mol respectively.)

Hint: 60 kJ

Discussion -
40 * 9 / 6 = 60 kJ (Note units are not kJ/mol)

8. A definite amount of ice at 273.15 K is contained in a system, and 15 kJ energy is required to completely melt the ice. The molar heat of fusion for water is 6 kJ/mol. How many moles of ice is used?

Hint: 15/6 = 2.5 mol

Discussion -
The units for the values may cause confusion.