## Heat Capacities and Transformations

For chemical reactions and phase transformations, the energy absorbed or liberated is measured as heat. The standard international unit for reporting heat is the joule (rhymes with school), which is defined as the energy needed to raise the temperature of 1 gram of water at 14.5°C by a single degree. The term kilojoule refers to 1,000 joules. Another unit of energy is the calorie, which is equal to 4.187 J. Conversely, a joule is 0.239 calories. The translation of calories to joules, or kilocalories to kilojoules, is so common in chemical calculations that you should memorize the conversion factors.

If a substance is heated without a change of state, the amount of heat required to change the temperature of 1 gram by 1°C is called the specific heat capacity of the substance. Similarly, the molar heat capacity is the amount of heat needed to raise the temperature of 1 mole of a substance by 1°C. Table 1 shows the heat capacities of several elements and compounds. As an example of the use of the heat capacity values, calculate the joules required to heat 1 kilogram of aluminum from 10°C to 70°C. Multiply the grams of metal by the 60°C increase by the specific heat capacity:

1,000 grams × 60°C × 0.891 cal/deg‐g = 53,472 joules

It, therefore, requires 53.47 kilojoules of energy to heat this particular piece of aluminum. Conversely, if a kilogram of the same metal cooled from 70° to 10°C, 53.47 kJ of heat will be released into the environment.

You will realize that there is an abrupt change of energy when one state of matter is transformed into another. A considerable amount of energy is required to transform a low energy state to a higher energy state, like melting a solid to a liquid or vaporizing a liquid to a gas. The same quantity of energy is released upon the reverse transformation from a high energy state to a lower energy state, like condensing a gas to a liquid or freezing a liquid to a solid. Table 2 shows these energy values for H 2O. Bear in mind that such transformations of state are isothermal; that is, they take place without any change in temperature of the substance. It takes 333.9 joules to change 1 gram of ice at 0°C to 1 gram of water at 0°C; the 333.9 joules are used to rearrange the molecules, which is done by overcoming intermolecular forces, from the crystalline order in the solid to the more irregular order in the liquid.

The data in the two previous tables permit some complex calculations of energy for changes of both state and temperature. Take a mole of water vapor at 100°C and cool it to ice at 0°. The energy released, which must be removed by the refrigeration process, comes from three distinct changes listed in Table 3. You should make sure that you understand how each of the values in the third column is obtained. For example, the 7,540 joules is the molar heat capacity of water (75.40 j/deg) multiplied by the 100‐degree change in temperature.

Notice especially that of the total heat released in this example, only 13.9% comes from lowering the temperature. Most of the heat comes from the two transformations of state—condensation and crystallization. For H 2O, the fact that the heat of condensation is almost seven times greater than the heat of crystallization may be interpreted as meaning that the molecular description of the liquid state is much more like the solid than the gas.

• Use the data for H 2O in the above tables to calculate the joules required to change 100 grams of ice at –40°C to water at 20°C.