When you take an ice cube out of the freezer, it doesn't melt instantly. Even though room temperature (~20 °C) is much higher than the freezing point of water (0 °C). It will take some time before the ice completely melts. This is because the ice has to absorb a set amount of heat until it turns to water.
In this article, we will be learning about how energy/heat is transferred during a phase change, and how to calculate it.
- This article is about the enthalpy of phase changes.
- First, we will refresh your memory on phases and phase changes.
- Next, we will look at a phase change diagram
- Then, we will learn about the enthalpy of phase change for water.
- Lastly, we will learn how to calculate the enthalpy of a phase change and work on some examples.
Phase Change of Matter
Before we dive into the enthalpy side of things, let's brush up on what a phase and phase change are.
Matter can exist in any of these three phases/states:
- Solid.
- Liquid.
- Gas.
Depending on the amount of energy within a species, it will be in one of these states as seen in figure 1 below:
Fig. 1-Different states of matter
In a solid,the particles are in close and constant contact with one another in fixed positions. They only have enough energy to vibrate in place.
In a liquid, the particles are still in close and constant contact but have enough energy to switch positions with each other.
In a gas particles are far apart and move freely. They only come into contact with one another when they occasionally collide.
When a substance switches between these phases, that is called a phase change.
A phase change is a physical process where a substance changes from one state to another. This change occurs at set temperatures called the boiling point and melting point.
The boiling point is the temperature where a liquid gains enough energy to overcome the interactions between particles and become a gas OR where a gas loses enough energy to become a liquid (instead called the condensation point).
The melting point is the temperature where a solid gains enough energy to become a liquid OR a liquid loses enough energy to become a solid (instead called the freezing point).
There are 6 phase changes in total:
- Melting (solid --> liquid).
- Solidifying/Fusion (liquid --> solid).
- Boiling (liquid --> gas).
- Condensing (gas --> liquid).
- Sublimation (solid --> gas).
- Deposition (gas --> solid).
Phase changes that are caused by a gain of heat are the changes where a substance goes to a state higher in energy (ex: solid --> liquid). However, phase changes caused by a release of heat are the changes where a substance goes to a state lower in energy (ex: liquid --> solid).
Phase Change Diagram
Let's look at a phase change diagram for water:
Fig.2-Phase change of water diagram
There are 2 key sections of this graph:
- -40-0 °C
- Water is in the form of ice at -40 °C. Once it reaches 0 °C (melting point), the ice starts to convert to water. As more heat is added, the temperature doesn't change since that energy is being used to convert the ice to water. Once the phase change is complete (all ice is now water), any extra heat will increase the temperature
- 0 °C-100 °C
- As heat is added, the temperature of the water will increase. Once it reaches 100 °C (boiling point), the water starts to convert to steam. Like before, the heat added won't change temperature, but instead it will aid in the phase change. Once the phase change is complete, the extra heat will increase the temperature.
During a phase change, both states exist (i.e. the transformation isn't complete). Once the phase change ends, the substance only exists in one state.
Now let's move on to looking at enthalpy.
Enthalpy of Phase Change Water
For every compound/element, the amount of heat it takes for a phase change to occur is different. These amounts are called the heat of fusion (ΔHfus) and the heat of vaporization (ΔHvap).
The heat/enthalpy of fusion (ΔHfus) is the amount of energy it takes for a substance to convert from a solid to a liquid, OR it is the amount of energy released when a liquid turns into a solid.
The heat of vaporization (ΔHvap) is the amount of energy it takes for a substance to convert from a liquid to a gas, OR it is the amount of energy released when a gas turns into a liquid.
Often when we talk about phase changes, we are referring to water. We constantly see water change phase in our daily life, such as boiling water when cooking or seeing dew form on grass.
Here are the enthalpies of the phase changes for water:
- ΔHfus=334 J/g (solid --> liquid)
- ΔHfus=(-)334 J/g (liquid --> solid)
- ΔHvap=2260 J/g (liquid --> gas)
- ΔHvap=(-)2260 J/g (gas --> liquid)
When a substance goes to a higher energy state, ΔH is positive. This is because the system is gaining heat. This is also called endothermic.
When a substance goes to a lower energy state, ΔH is negative. Since the system is releasing heat, it is exothermic.
Adding these values to the phase diagram from before, it would look like this:
Fig. 3-Phase diagram of water with heat enthalpies for 1 g.
The heat of fusion/vaporization is how much heat it takes for the phase change to occur once we have hit the melting/boiling point. It is the energy it takes for the entire phase change to occur.
The energy it takes for a substance to boil is always going to be much greater than the energy it takes to melt. This is because, for a substance to become a gas, the forces between particles need to be severed. Going from a solid to a liquid, these forces are only slightly weakened, so it takes less energy to do so.
Enthalpy of Phase Change Equation
The heat required/released for a phase change depends on two things:
- Mass/amount (greater mass/more moles=higher energy)
- The forces between particles (the stronger the forces between particles, the harder it will be to force the particles apart (higher energy))
Because of this, the formula for the heat change is:
$$\text{heat}=m*\Delta H_{x}\,or\,\text{heat}=n*\Delta H_{x}$$
Where m is the mass of the species, n is the number of moles of the species, and \(\Delta H_{x}\) is the heat of fusion or heat of vaporization
Example of Enthalpy for Phase Changes
It takes 2,412J to vaporize a sample of liquid ethanol (C2H5OH). If the ΔHvap=838 J/g and the density=0.789 g/mL, how many milliliters of ethanol were in the sample?
Since we are given the enthalpy in J/g, we will be using this formula:
$$\text{heat}=m*\Delta H_{vap}$$
Our first step is to divide the heat required by the enthalpy to get the mass in grams.
$$\text{heat}=m*\Delta H_{vap}$$
$$\frac{\text{heat}}{\Delta H_{vap}}=m$$
$$\frac{2,412\,J}{838\frac{J}{g}}=2.88\,g$$
Since we want the volume in mL, our last step is to divide by the density.
$$\frac{2.88\,g}{0.789\frac{g}{mL}}=3.65\,mL$$
Now let's do a problem where the phase change is exothermic.
When a solid sample of mercury (Hg) melts, 6,213 J of energy is released. If the ΔHfus=-2,301 J/mol and the molar mass of mercury is 201 g/mol, how many grams of mercury are in the sample?
Since we are given our enthalpy in J/mol, we will be using this formula:
$$\text{heat}=n*\Delta H_{fus}$$
We need to first divide our heat released by the enthalpy of fusion. However, we need to make sure the heat is negative. This is because heat is being released, so the system is losing heat (this also will cancel the negative from the enthalpy value).
$$\text{heat}=n*\Delta H_{fus}$$
$$\frac{\text{heat}}{\Delta H_{fus}}=n$$
$$\frac{-6,213\,J}{-2,301\frac{J}{mol}}=2.70\,mol$$
To get the mass in grams, we multiply the molar amount by the molar mass.
$$2.70\,mol*201\frac{g}{mol}=543\,g$$
Enthalpy for Phase Changes - Key takeaways
- A phase change is a physical process where a substance changes from one state to another. This change occurs at set temperatures called the boiling point and melting point.
- The heat/enthalpy of fusion (ΔHfus) is the amount of energy it takes for a substance to convert from a solid to a liquid, OR it is the amount of energy released when a liquid turns into a solid.
- The heat of vaporization (ΔHvap) is the amount of energy it takes for a substance to convert from a liquid to a gas, OR it is the amount of energy released when a gas turns into a liquid.
- The heat required/released for a phase change depends on two things
- Mass/amount
- The forces between particles
- The formula for the heat change is:
$$\text{heat}=m*\Delta H_{x}\,or\,\text{heat}=n*\Delta H_{x}$$ Where m is the mass of the species, n is the number of moles of the species, and \(\Delta H_{x}\) is the heat of fusion or heat of vaporization
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