All MCAT Physical Resources
Example Questions
Example Question #2 : Thermodynamics Of Phase Changes
The following diagram shows the temperature of a substance as constant heat is supplied. Suppose the substance began in a solid state.
What is the freezing point of the substance?
B
D
X
Y
X
Freezing point is always a temperature, meaning it must correspond to a single point on the y-axis. During the freezing/melting process, heat is absorbed/released from the system without any change in temperature. This results in the temperature plateau at the freezing point.
While the substance is freezing during interval B, the freezing point is the temperature at which it freezes, X.
Example Question #1 : Thermodynamics Of Phase Changes
The following diagram shows the temperature of a substance as constant heat is supplied. Suppose the substance began in a solid state.
The slope of the graph is zero at intervals B and D because __________.
no phase changes are taking place at these intervals
the heat that is supplied is being used to overcome intermolecular forces
no energy is being supplied to the system
the substance is undergoing fusion at these intervals
the heat that is supplied is being used to overcome intermolecular forces
During intervals B and D, fusion and vaporization are taking place, respectively. Instead of raising the temperature of the substance, the energy that is added during these phase changes is used to overcome intermolecular forces. The energy breaks the attraction between particles, allowing them to separate and gain the properties of a higher energy phase (liquid or gas).
When the slope is not zero, the phase is steady and the added heat energy is used to increase the molecular kinetic energy of the particles, resulting in a temperature increase.
Example Question #2 : Thermodynamics Of Phase Changes
The molar heats of fusion and vaporization for water are given below:
A certain amount of snow is formed in the atmosphere, and of energy is released. How much water was solidified?
Use the given molar heat of fusion to calculate the amount of snow formed. Remember that heats of fusion and solidification are opposite processes, so the magnitudes of molar heats of fusion and solidification are the same and signs are opposite. This indicates that fusion (melting) is endothermic, while solidification is exothermic.
The given change in energy will be negative, since the question states that it is released from the system into the atmosphere.
Convert moles to grams, and grams to pounds.
Example Question #3 : Thermodynamics Of Phase Changes
The molar heats of fusion and vaporization for water are given below:
of water solidify and of water vaporize within a closed system. What is the change in energy of the surroundings?
of energy is absorbed from the surroundings
of energy is absorbed from the surroundings
of energy is released to the surroundings
The system experiences no overall change in energy
of energy is absorbed from the surroundings
We must use the given heats of fusion and vaporization to calculate the energy change involved in these two processes.
First, calculate the energy change when of water solidifies. Convert the mass to moles and multiply by the heat released during freezing. This value will be equal in magnitude, but opposite in sign to the heat of fusion.
From this calculation we find that of heat is released into the surroundings (a negative sign denotes an exothermic process).
Next, find the energy change associated with the vaporization of of water, using the given heat of vaporization:
We find that of energy is absorbed when this quantity of water is vaporized.
Adding the two together we find a total of .
Since this is a positive number, that means that the energy is absorbed from the surroundings (endothermic).
Example Question #1 : Thermodynamics Of Phase Changes
The enthalpy of fusion for water is .
The specific heat capacity for ice is .
The specific heat capacity for water is .
How much heat is necessary to raise of water from to ?
Solving this problem means solving for three steps.
1. The heat needed to raise the temperature from –20oC to 0oC.
2. Melting the ice (changing phases).
3. Raising the water temperature from 0oC to 50oC.
Steps 1 and 3 are both solved by the equation .
Step 2 is solved using the enthalpy of fusion, and is multiplied by the number of grams being melted: .
Combining the steps, we get the following expression.
Example Question #5 : Thermodynamics Of Phase Changes
The molar heats of fusion and vaporization for water are given below:
Which of the following is not true?
It takes to melt two moles of water
The heat of condensation is
Solidification is an exothermic process
Vaporization is an endothermic process
The heat of condensation is
Vaporization and condensation refer to the transition from liquid to gas and from gas to liquid, respectively. Fusion and freezing, in contrast, refer to the transition from solid to liquid and from liquid to solid, respectively. Vaporization (boiling) and fusion (melting) each require an input of energy, making them endothermic processes with positive changes in enthalpy. Condensation and freezing result in a decrease in energy and an output of enthalpy, making them exothermic.
The given enthalpy of fusion tells us that are consumed for every mole of water. If two moles of water are present, then are consumed during melting.
Enthalpy of vaporization will be equal and opposite the enthalpy of condensation. Since condensation is exothermic, heat will be released and the change in enthalpy must be negative (not positive).
Heat of condensation:
Example Question #6 : Thermodynamics Of Phase Changes
The molar heats of fusion and vaporization for water are given below:
Given the following information, which substance would be expected to have an intermolecular force strength similar to that of water?
Substance |
ΔHfus |
ΔHvap |
Acetone |
5.72 kJ/mol |
29.1 kJ/mol |
Ethanol |
4.60 kJ/mol |
43.5 kJ/mol |
Hydrogen |
0.12 kJ/mol |
0.90 kJ/mol |
Ammonia |
5.65 kJ/mol |
23.4 kJ/mol |
Ethanol and ammonia
Hydrogen
Acetone and ammonia
Ethanol
Ethanol
Intermolecular forces play a key role in determining the energy required for phase changes. Strong intermolecular forces result in more resistance to changes that result in greater distance between molecules (greater entropy), as the forces cause the molecules to "stick" to one another. When a liquid is vaporized, the strength of the intermolecular force is overcome; similar heats of vaporization indicate similar intermolecular forces. A similar concept governs the transition from solid to liquid. If two compounds share similar enthalpies of fusion and vaporization, then they likely have similar intermolecular forces.
In the given table, ethanol enthalpy values are most similar to those of water, meaning it likely has similar intermolecular forces.
Example Question #2 : Thermodynamics Of Phase Changes
The following diagram shows the temperature of a substance as constant heat is supplied. Suppose the substance began in a solid state.
If of the substance begins at interval E and ends at interval C, the substance __________ and energy is __________.
condenses . . . absorbed
condenses . . . released
vaporizes . . . released
solidifies . . . released
condenses . . . released
Plateaus in the graph represent phase changes: period B shows the transitions between solid and liquid, and period D shows the transitions between liquid and gas. When the substance transitions through period D, it undergoes either vaporization (C to E transition) or condensation (E to C transition). If the substances starts out at interval E and ends at interval C, then it has undergone condensation.
Condensation involves transition from a high energy gas to a lower energy liquid, and has a net decrease in heat energy and temperature. This heat release is known as an exothermic process.
Example Question #11 : Thermodynamics Of Phase Changes
The molar heats of fusion and vaporization for water are given below:
Which of the following explains why the heat of vaporization is much greater than the heat of fusion?
More heat is required to vaporize a given quantity of water
Liquids are in constant motion and hold more energy than solids
The difference in kinetic energy of gas and liquid molecules is higher than the difference between solid and liquid molecules
Vaporization is an endothermic process while fusion is an exothermic process
The difference in kinetic energy of gas and liquid molecules is higher than the difference between solid and liquid molecules
Notice that most of these are true statements (the only incorrect statement is that fusion is an exothermic process). The key is finding the statement that best explains why the heat of vaporization is greater than the heat of fusion. Essentially, we are looking for the reason why a transition from liquid to gas requires more energy than a transition from solid to liquid.
It is true that more heat is required to vaporize a given quantity of water, but the reason for this can be found on a molecular level. Gas molecules have a relatively high kinetic energy. The large difference in kinetic energies between the states accounts for the difference in heats of fusion and vaporization. Solids are the lowest energy state, followed by liquids, and then gases. The difference in energy between equal amounts of solid and liquid is given by the heat of fusion, while the difference in energy between equal amounts of liquid and gas is given by the heat of vaporization. The discrepancy in energy is reflected in the difference between these two heat quantities.
Example Question #11 : Phase Changes
A scientist prepares an experiment to demonstrate the second law of thermodynamics for a chemistry class. In order to conduct the experiment, the scientist brings the class outside in January and gathers a cup of water and a portable stove.
The temperature outside is –10 degrees Celsius. The scientist asks the students to consider the following when answering his questions:
Gibbs Free Energy Formula:
ΔG = ΔH – TΔS
Liquid-Solid Water Phase Change Reaction:
H2O(l) ⇌ H2O(s) + X
The scientist prepares two scenarios.
Scenario 1:
The scientist buries the cup of water outside in the snow, returns to the classroom with his class for one hour, and the class then checks on the cup. They find that the water has frozen in the cup.
Scenario 2:
The scientist then places the frozen cup of water on the stove and starts the gas. The class finds that the water melts quickly.
After the water melts, the scientist asks the students to consider two hypothetical scenarios as a thought experiment.
Scenario 3:
Once the liquid water at the end of scenario 2 melts completely, the scientist turns off the gas and monitors what happens to the water. Despite being in the cold air, the water never freezes.
Scenario 4:
The scientist takes the frozen water from the end of scenario 1, puts it on the active stove, and the water remains frozen.
In scenario 1, the Gibbs Free Energy and Keq of the Liquid-Solid Water Phase Change Reaction, as the reaction begins, is best characterized as __________.
undefined and decreasing, respectively
positive and increasing, respectively
negative and increasing, respectively
zero and decreasing, respectively
negative and decreasing, respectively
negative and increasing, respectively
As scenario 1 begins, the reaction is spontaneous as written, and so the Gibbs Free Energy is negative. Additionally, the Van't Hoff equation proves that Keq increases with decreasing temperature in exothermic reactions. As this reaction is exothermic and placed in low-temperature conditions, the relative abundance of the products will become the prevailing state. Keq, therefore, increases.
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