7.3: Phase Changes

Skills to Develop

• The Learning Objective of this Module is to determine the heat associated with a phase change.

Depending on the surrounding conditions, normal matter usually exists as one of three phases: solid, liquid, or gas.

A phase change is a physical process in which a substance goes from one phase to another. Usually the change occurs when adding or removing heat at a particular temperature, known as the melting point or the boiling point of the substance. The melting point is the temperature at which the substance goes from a solid to a liquid (or from a liquid to a solid). The boiling point is the temperature at which a substance goes from a liquid to a gas (or from a gas to a liquid). The nature of the phase change depends on the direction of the heat transfer. Heat going into a substance changes it from a solid to a liquid or a liquid to a gas. Removing heat from a substance changes a gas to a liquid or a liquid to a solid.

Two key points are worth emphasizing. First, at a substance’s melting point or boiling point, two phases can exist simultaneously. Take water (H₂O) as an example. On the Celsius scale, H₂O has a melting point of 0°C and a boiling point of 100°C. At 0°C, both the solid and liquid phases of H₂O can coexist. However, if heat is added, some of the solid H₂O will melt and turn into liquid H₂O. If heat is removed, the opposite happens: some of the liquid H₂O turns into solid H₂O. A similar process can occur at 100°C: adding heat increases the amount of gaseous H₂O, while removing heat increases the amount of liquid H₂O (Figure \(\PageIndex{1}\)).

Figure \(\PageIndex{1}\): The Boiling Point of Water. Nucleate boiling of water over a kitchen stove burner. Image used with permission from Wikipedia.

Water is a good substance to use as an example because many people are already familiar with it. Other substances have melting points and boiling points as well.

Second, the temperature of a substance does not change as the substance goes from one phase to another. In other words, phase changes are isothermal (isothermal means “constant temperature”). Again, consider H₂O as an example. Solid water (ice) can exist at 0°C. If heat is added to ice at 0°C, some of the solid changes phase to make liquid, which is also at 0°C. Remember, the solid and liquid phases of H₂O can coexist at 0°C. Only after all of the solid has melted into liquid does the addition of heat change the temperature of the substance.

Enthalpy, H, is a quantity that is similar to energy and has the same units. The change in enthalpy (ΔH) is equal to the amount of heat gained when pressure is constant, so enthalpy change and heat are often used interchangeably.

For each phase change of a substance, there is a characteristic quantity of heat needed to perform the phase change per gram (or per mole) of material. The heat of fusion (ΔH_fus) is the amount of heat per gram (or per mole) required for a phase change that occurs at the melting point. The heat of vaporization (ΔH_vap) is the amount of heat per gram (or per mole) required for a phase change that occurs at the boiling point. If you know the total number of grams or moles of material, you can use the ΔH_fus or the ΔH_vap to determine the total heat being transferred for melting or solidification using these expressions:

\[\text{heat} = n \times ΔH_{fus} \label{Eq1a}\]

where \(n\) is the number of moles and \(ΔH_{fus}\) is expressed in energy/mole or

\[\text{heat} = m \times ΔH_{fus} \label{Eq1b}\]

where \(m\) is the mass in grams and \(ΔH_{fus}\) is expressed in energy/gram.

For the boiling or condensation, use these expressions:

\[\text{heat} = n \times ΔH_{vap} \label{Eq2a}\]

where \(n\) is the number of moles) and \(ΔH_{vap}\) is expressed in energy/mole or

\[\text{heat} = m \times ΔH_{vap} \label{Eq2b}\]

where \(m\) is the mass in grams and \(ΔH_{vap}\) is expressed in energy/gram.

Remember that a phase change depends on the direction of the heat transfer. If heat transfers in, solids become liquids, and liquids become solids at the melting and boiling points, respectively. The associated values for enthalpy change and heat are positive if heat is gained.

\[\text{solid } \rightarrow \text{ liquid (positive heat of fusion)} \label{Eq3}\]

\[\text{liquid } \rightarrow \text{ gas (positive heat of vaporization)} \label{Eq4}\]

If heat transfers out, liquids solidify, and gases condense into liquids. The values of enthalpy change and heat will be negative for the reverse directions.

\[\text{liquid } \rightarrow \text{ solid (negative heat of fusion)} \label{Eq5}\]

\[\text{gas } \rightarrow \text{ liquid (negative heat of vaporization)} \label{Eq6}\]

Example \(\PageIndex{1}\)

How much heat is necessary to melt 55.8 g of ice (solid H₂O) at 0°C? The heat of fusion of H₂O is 79.9 cal/g.

SOLUTION

We can use the relationship between heat and the heat of fusion (Eq. \(\PageIndex{1}\)b) to determine how many joules of heat are needed to melt this ice:

heat = m × ΔH_fus

\(\mathrm{heat = (55.8\: \cancel{g})\left(\dfrac{79.9\: cal}{\cancel{g}}\right)=4,460\: cal}\)

Example \(\PageIndex{2}\)

Determine the heat associated when 5.00 grams of liquid water at 99.5°C are placed in a freezer until becoming ice (solid H₂O) at -13.5°C? Use 1440 cal/mol as the heat of fusion of H₂O, plus specific heats of 1.00 cal/g°C for liquid and 0.502 cal/g°C for solid.

SOLUTION

We can use heat = mcΔT to find the heat to bring the liquid from 99.5°C to 0°C. Heat = (5.00g)(1.00 cal/g°C)(-99.5°C) = -498 cal

We can use heat = n × ΔH_fus to determine how many calories of heat must be removed to freeze the ice.

The molar mass of water is 16.0+1.0+1.0 = 18.0 g/mol. (5.00 g)/(18.0 g/mol) = 0.278 moles

Heat = (0.278 mol)(-1440 cal/mol) = -400. cal (Note that heat must be removed to freeze, so the value is negative.)

We can use heat = mcΔT to find the heat to bring the solid from 0°C to -13.5°C. Heat = (5.00g)(0.502 cal/g°C)(-13.5°C) = -34.0 cal

The sum of these values is -932 cal. The water LOST 932 calories of heat.

 

Table \(\PageIndex{1}\) lists the heats of fusion and vaporization for some common substances. Note the units on these quantities; when you use these values in problem solving, make sure that the other variables in your calculation are expressed in units consistent with the units in the specific heats or the heats of fusion and vaporization.

Table \(\PageIndex{1}\): Heats of Fusion and Vaporization for Selected Substances

Substance	ΔHfus (cal/g)	ΔHvap (cal/g)
aluminum (Al)	94.0	2,602
gold (Au)	15.3	409
iron (Fe)	63.2	1,504
water (H2O)	79.9	540
sodium chloride (NaCl)	123.5	691
ethanol (C2H5OH)	45.2	200.3
benzene (C6H6)	30.4	94.1

Looking Closer: Sublimation

There is also a phase change where a solid goes directly to a gas:

\[\text{solid} \rightarrow \text{gas} \label{Eq7}\]

This phase change is called sublimation. Each substance has a characteristic heat of sublimation associated with this process. For example, the heat of sublimation (ΔH_sub) of H₂O is 620 cal/g.

We encounter sublimation in several ways. You may already be familiar with dry ice, which is simply solid carbon dioxide (CO₂). At −78.5°C (−109°F), solid carbon dioxide sublimes, changing directly from the solid phase to the gas phase:

\[\mathrm{CO_2(s) \xrightarrow{-78.5^\circ C} CO_2(g)} \label{Eq8}\]

Solid carbon dioxide is called dry ice because it does not pass through the liquid phase. Instead, it does directly to the gas phase. (Carbon dioxide can exist as liquid but only under high pressure.) Dry ice has many practical uses, including the long-term preservation of medical samples.

Even at temperatures below 0°C, solid H₂O will slowly sublime. For example, a thin layer of snow or frost on the ground may slowly disappear as the solid H₂O sublimes, even though the outside temperature may be below the freezing point of water. Similarly, ice cubes in a freezer may get smaller over time. Although frozen, the solid water slowly sublimes, redepositing on the colder cooling elements of the freezer, which necessitates periodic defrosting (frost-free freezers minimize this redeposition). Lowering the temperature in a freezer will reduce the need to defrost as often.

Under similar circumstances, water will also sublime from frozen foods (e.g., meats or vegetables), giving them an unattractive, mottled appearance called freezer burn. It is not really a “burn,” and the food has not necessarily gone bad, although it looks unappetizing. Freezer burn can be minimized by lowering a freezer’s temperature and by wrapping foods tightly so water does not have any space to sublime into.

Concept Review Exercises

1. Explain what happens when heat flows into or out of a substance at its melting point or boiling point.
2. How does the amount of heat required for a phase change relate to the mass of the substance?

Answers

1. The energy goes into changing the phase, not the temperature.

2. The amount of heat is a constant per gram of substance.

Key Takeaway

• There is an energy change associated with any phase change.

Exercises

1. How much energy is given off if 43.8 g of liquid gold, Au, solidifies at its melting point of 1,064°C? (You will need one of the values from Table 7.3.1.) Is this energy change a positive or negative value?

2. What mass of ice can be melted by 558 cal of energy? (You will need one of the values from Table 7.3.1.)

3. What is the heat of vaporization of a substance if 10,776 cal are required to vaporize 5.05 g? Express your final answer in joules per gram.

4. If 1,650 cal of heat are required to vaporize a sample that has a heat of vaporization of 137 cal/g, what is the mass of the sample?

5. What is the heat of vaporization of gold in kilocalories per mole? (Start with the appropriate value in Table \(\PageIndex{1}\), then convert the units)

Answers

1. 670. calories are given off (released) when liquid turns to solid (exothermic), which means the change in energy is – 670. cal 
2. 6.98 g
3. 8,930 J/g
4. 12.0 g
5. 80.6 kcal/mol