We have now discussed the properties of matter in its three states: solid, liquid, and gas. In each case, we have talked about the average kinetic energy of the molecules in that state and about changes in average kinetic energy as the temperature is changed. We have also talked about changes from one state to another.

The energy necessary to transform a substance from a solid below its melting point to a gas above its boiling point can be determined by calculating the energy required for each change involved and summing these energies. Figure 10.10 plots the energy required for such a series of changes. In this change, pressure was held constant at 1 atm, so the melting and boiling points of the substance are the normal ones.

Note carefully the shape of the graph. Although the length and slopes of the segments differ between compounds, the general shape will stay the same. The temperatures for the horizontal segments are the melting point and the boiling point of the substance, and the lengths of these segments depend on its molar heat of fusion and molar heat of vaporization. The slopes of the other segments of the graph depend on the specific heats of the substance: the first segment on the specific heat of the solid, the second on the specific heat of the liquid, and the third on the specific heat of the gas.

Note that the sloping segments represent a change in temperature and therefore a change in kinetic energy, whereas the horizontal segments represent no change in temperature and therefore no change in kinetic energy. These segments do represent a change in the potential energy of the sample as bonds are broken.

The amount of energy required to change a sample from one state and temperature to another state and temperature can be calculated if the various physical constants are known for that substance.

FIGURE 10.10 The change in temperature of a sample as heat energy is added and the sample changes from a solid to a liquid to a gas.

Example: How much energy (in joules) is needed to change 55.0 g ice at -5°C to steam at 110°C? Specific heat of ice = 2.05 J/g°C Specific heat of liquid water = 4.184 J/g°C Specific heat of steam = 2.01 J/g°C Molar heat of fusion of water = 6.02 kJ/mol Molar heat of vaporization of water = 40.7 kJ/mol Solution The answer to this problem is obtained by calculating the energy change for each segment of the graph and then finding the total enery change. In this solution, the letter of each step corresponds with a lettered segment of the figure. a. To raise the temperature of ice from -5 C to 0 C, a 5-degree change in the temperature of the solid, the equation is b. To melt the ice at 0 C: c. To raise the temperature of liquid water form 0 C to 100 C: d. To vaporize liquid water at 100 C: e. to heat water vapor (steam) from 100 C to 110 C: The sum of these energy changes is the total amount of energy required by the change: ?J = 0.564 kJ + 18.4 kJ + 23.0 kJ + 124.4 kJ + 1.1 kJ = 167.5 kJ Correcting to three significant figures: ? J = 168 kJ