# Change of State

## Explore the energy required to convert a substance between gas, liquid, and solid

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Change of State

Credit: User:Mark.murphy/Wikipedia

Before the internal combustion engine was invented, steam engines were the power source for ships, locomotives, tractors, lumber saws, and most industrial machines. Coal or wood was burned to boil water into steam, which ran the engine.

### Change of State

Most substances may exist in any of the three common states of matter. In the gaseous state, the molecular motion has completely overcome any attraction between the particles and the particles are totally separate from each other. There are large spaces between the particles and they move large distances between collisions. In the liquid state, the molecular motion and the molecular attractions are more balanced. While the particles stay more or less in contact with each other, they are still free to move and can slide past one another easily. In the solid state, the attractive forces dominate. The particles are pulled together into a tightly packed pattern which does not allow the particles to pass each other. The molecular motion in this form is essentially reduced to vibration in place. Increasing the temperature of a substance means increasing the molecular motion (kinetic energy) of the molecules in the substance. The phase in which a substance exists is the result of a competition between attractive forces and molecular motion.

Credit: Christopher Auyeung
Source: CK-12 Foundation

For most substances, when the temperature of the solid is raised high enough, the substance changes to a liquid, and when the temperature of the liquid is raised high enough, the substance changes to a gas. We typically visualize a solid as tiny particles in constant motion held together by attractive forces. As we add heat to the solid, the motion, or the kinetic energy, of the particles increases. At some temperature, the motion of the particles becomes great enough to overcome the attractive forces. The thermal energy that was added to the solid up to this point was absorbed by the solid as kinetic energy, increasing the speed of the molecules. The lowest temperature at which the particles are able to exist in the liquid form is called the melting point.

In order for the molecules to actually separate from each other, more energy must be added. This energy, called heat of fusion or heat of melting, is absorbed by the particles as potential energy as the solid changes to a liquid. Recognize that, once the temperature of a solid has been raised to the melting point, it is still necessary for the solid to absorb additional thermal energy in the form of potential energy as the molecules separate.

The boiling point of a liquid is the temperature at which the particles have sufficient molecular motion to exist in the form of a gas. Once again, however, in order for the particles to separate to the gaseous form, they must absorb a sufficient amount of potential energy. The amount of potential energy necessary for a phase change to gaseous form is called the heat of vaporization. Consider the heating curve shown below.

Credit: Christopher Auyeung
Source: CK-12 Foundation

The heating curve shown is for water but other substances have similarly shaped heating curves. Suppose you begin with solid water (ice) at -30°C and add heat at a constant rate. The heat you add in the beginning will be absorbed as kinetic energy and the temperature of the solid will increase. When you reach a temperature of 0°C (the melting point for water), the heat you add is no longer absorbed as kinetic energy. Instead, the added heat is absorbed as potential energy and the particles separate from each other. During the flat part of the curve labeled “melting”, heat is being added constantly but the temperature does not increase. At the left edge of this flat line, the water is solid; by the time enough heat has been added to get to the right edge, the water is liquid, but maintains the same temperature. Once all the water is in the liquid form, the added heat will once again be absorbed as kinetic energy and the temperature will increase again. During the time labeled “water being heated as a liquid”, all the added heat is absorbed as kinetic energy.

When a temperature of 100°C (the boiling point of water) is reached, the added heat is once again absorbed as potential energy and the molecules separate from liquid form into gaseous form. When all the substance has been converted into gas, the temperature will again begin to rise.

 Substance Heat of Fusion, \begin{align*}\underline{H_f \ (J/kg)}\end{align*} Heat of Vaporization, \begin{align*}\underline{H_v \ (J/kg)}\end{align*} Copper \begin{align*}2.05 \times 10^5\end{align*} \begin{align*}5.07 \times 10^6\end{align*} Gold \begin{align*}6.30 \times 10^4\end{align*} \begin{align*}1.64 \times 10^6\end{align*} Iron \begin{align*}2.66 \times 10^5\end{align*} \begin{align*}6.29 \times 10^6\end{align*} Methanol \begin{align*}1.09 \times 10^5\end{align*} \begin{align*}8.78 \times 10^5\end{align*} Water \begin{align*}3.34 \times 10^5\end{align*} \begin{align*}2.26 \times 10^6\end{align*}

When the temperature of a substance is changing, we can use the specific heat to determine the amount of heat that is being gained or lost. When a substance is changing phase, we can use the heat of fusion or heat of vaporization to determine the amount of heat being gained or lost. When a substance freezes from liquid to solid, the amount of heat given off is exactly the same as the amount of heat absorbed when the substance melts from solid to liquid. The equations for heat gained or lost are given here:

The heat gained or lost during a temperature change: \begin{align*}Q = mc \Delta t\end{align*}.

The heat gained or lost during a phase change of solid to liquid: \begin{align*}Q = mH_f\end{align*}.

The heat gained or lost during a phase change of liquid to gas: \begin{align*}Q = mH_v\end{align*}.

### Examples

#### Example 1

5000 Joules of heat is added to ice at 273 K. All the heat goes into changing solid ice into liquid water. How much ice is melted?

\begin{align*}m=\frac{Q}{H_f}=\frac{5000 \ J}{3.34 \times 10^5 \ J/kg}=0.0150 \ kg\end{align*}

#### Example 2

Beginning with 1.00 kg of ice at -20.0°C, heat is added until the substance becomes water vapor at 130.0°C. How much heat was added? The specific heat of ice is \begin{align*}2108 \ J/kg^\circ C\end{align*}, the specific heat of liquid water is \begin{align*}4187 \ J/kg^\circ C\end{align*}, and the specific heat of water vapor is \begin{align*}1996 \ J/kg^\circ C\end{align*}.

5 steps:

1. Calculate the heat required to raise the sample from -20.0°C to 0°C.
2. Calculate the heat required to melt the sample.
3. Calculate the heat required to raise the sample from 0°C to 100°C.
4. Calculate the heat required to vaporize the sample.
5. Calculate the heat required to raise the sample from 100°C to 130°C.

The solution is the sum of these steps.

\begin{align*}1. Q_{HS} = mc_{\text{ice}} \Delta t = (1.00 \ kg)(2108 \ J/kg.^\circ C)(20.0^\circ C) = 42160 \ J\end{align*}

\begin{align*}2. Q_{\text{Melt}} = mH_f = (1.00 \ kg)(334000 \ J/kg) = 334000 \ J\end{align*}

\begin{align*}3. Q_{HL} = mc_{\text{water}} \Delta t = (1.00 \ kg)(4187 \ J/kg.^\circ C)(100.0^\circ C) = 418700 \ J\end{align*}

\begin{align*}4. Q_{\text{Vap}} = mH_v = (1.00 \ kg)(2260000 \ J/kg) = 2260000 \ J\end{align*}

\begin{align*}5. Q_{\text{HV}} = mc_{\text{vapor}} \Delta t = (1.00 \ kg)(1996 \ J/kg.^\circ C)(30.0^\circ C) = 59880 \ J\end{align*}

\begin{align*}\text{Total Heat} = 3.11 \times 10^6 \ J\end{align*}

### Summary

• Most substances may exist in any of the three common states of matter, solid, liquid, or gas.
• The phase in which a substance exists is the result of a competition between attractive forces and molecular motion.
• The potential energy absorbed by a solid as it changes to a liquid is called the heat of fusion or the heat of melting.
• The amount of potential energy necessary for a phase change to gaseous form is called the heat of vaporization.
• The heat gained or lost during a temperature change is given by, \begin{align*}Q = mc \Delta t\end{align*}.
• The heat gained or lost during a phase change of solid to liquid is given by, \begin{align*}Q = mH_f\end{align*}.
• The heat gained or lost during a phase change of liquid to gas is given by, \begin{align*}Q = mH_v\end{align*}.

### Review

1. A 200 g sample of water at 60.0°C is heated to water vapor at 140.0°C. How much heat was absorbed?
2. A 175 g lump of molten lead at its melting point (327°C) is placed into 55.0 g of water at 20.0°C. The specific heat of lead is \begin{align*}130 \ J/kg \cdot ^\circ C\end{align*} and the \begin{align*}H_f\end{align*} of lead is 20,400 J/kg.
1. When the lead has become solid but is still at the melting point, what is the temperature of the water?
2. When the lead and the water have reached equilibrium, what is the temperature of the mixture?

### Explore More

Use this video to answer the questions that follow.

1. For water, which takes more energy, melting or evaporating?
2. When are there two phases present at the same time in the pot?

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http://www.slideshare.net/angel4all1/specific-heat-and-phase-change-ditto

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