Thermodynamics and Phases - GRE
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Which of the following assumptions is not made by the ideal gas law?
Which of the following assumptions is not made by the ideal gas law?
Under the ideal gas law, we assume that the interactions between the molecules are very brief and that the forces involved are negligible. The assumption that the molecules obey Coulomb's law when interacting with each other is not necessary; rather, an ideal gas must disregard Coulomb's law.
The ideal gas law assumes only Newtonian mechanics, disregarding any intermolecular or electromagnetic forces.
Under the ideal gas law, we assume that the interactions between the molecules are very brief and that the forces involved are negligible. The assumption that the molecules obey Coulomb's law when interacting with each other is not necessary; rather, an ideal gas must disregard Coulomb's law.
The ideal gas law assumes only Newtonian mechanics, disregarding any intermolecular or electromagnetic forces.
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Which of the following is relevant for real gases, but irrelevant for ideal gases?
I. Volume of gas particles
II. Intermolecular forces between gas particles
III. Volume of container
Which of the following is relevant for real gases, but irrelevant for ideal gases?
I. Volume of gas particles
II. Intermolecular forces between gas particles
III. Volume of container
There are two main assumptions for an ideal gas (and a few smaller assumptions). First, the gas particles of the ideal gas must have no molecular volume. Second, the gas particles must exert no intermolecular forces on each other; therefore, forces such hydrogen bonding, dipole-dipole interactions, and London dispersion forces are irrelevant in ideal gases. Other small assumptions of ideal gases include random particle motion (no currents), lack of intermolecular interaction with the container walls, and completely elastic collisions (a corollary of zero intermolecular forces).
For real gases, however, these assumptions are invalid. This means that the real gas particles have molecular volume and exert intermolecular forces on each other.
Recall that the volume in the ideal gas law is the volume of the free space available inside the container. For ideal gases, the free space volume is equal to the volume of the container because the gas particles take up no volume; however, for real gases, the free space volume is the volume of the container minus the volume of the gas particles. Though the exact values of free space volume will differ, the volume of the container is important for both real and ideal gases.
There are two main assumptions for an ideal gas (and a few smaller assumptions). First, the gas particles of the ideal gas must have no molecular volume. Second, the gas particles must exert no intermolecular forces on each other; therefore, forces such hydrogen bonding, dipole-dipole interactions, and London dispersion forces are irrelevant in ideal gases. Other small assumptions of ideal gases include random particle motion (no currents), lack of intermolecular interaction with the container walls, and completely elastic collisions (a corollary of zero intermolecular forces).
For real gases, however, these assumptions are invalid. This means that the real gas particles have molecular volume and exert intermolecular forces on each other.
Recall that the volume in the ideal gas law is the volume of the free space available inside the container. For ideal gases, the free space volume is equal to the volume of the container because the gas particles take up no volume; however, for real gases, the free space volume is the volume of the container minus the volume of the gas particles. Though the exact values of free space volume will differ, the volume of the container is important for both real and ideal gases.
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Consider a real gas with a constant amount and a constant pressure. It has a temperature of 
and a volume of 
. If you double the temperature, what will happen to the volume?
Consider a real gas with a constant amount and a constant pressure. It has a temperature of
This question can be solved using either Charles's law or the ideal gas law (converted into the combined gas law).
Charles's Law: 
Ideal Gas Law: 
The question states that the pressure and moles 
are held constant; therefore, the volume and temperature are directly proportional. If the question were asking about an ideal gas, the volume would double when you double the temperature
The volume would double for an ideal gas; however, the question is asking about a real gas. To find the correct relationship between volume and temperature we need to look at the equation for real gas volume. Remember that the volume we are concerned with is the volume of the free space in the container, given by the container volume minus the volume of the gas particles. The equation for real gas volume accounts for the volume of the container and the volume of the gas particles. For a real gas, the volume is given as follows:
In this equation, 
is the number of moles of gas particles and 
is the bigness coefficient. This equation implies that the volume of free space for a real gas is always less than the volume for an ideal gas; therefore, doubling the temperature will produce a volume that is less than the predicted volume for an ideal gas. Our answer, then, must be less than double the initial volume.
Note that for an ideal gas the bigness coefficient, 
, would be zero and the volume of free space 
would be equal to the volume of the container 
. This occurs because the volume of the gas particles is negligible for an ideal gas.
This question can be solved using either Charles's law or the ideal gas law (converted into the combined gas law).
Charles's Law:
Ideal Gas Law:
The question states that the pressure and moles
The volume would double for an ideal gas; however, the question is asking about a real gas. To find the correct relationship between volume and temperature we need to look at the equation for real gas volume. Remember that the volume we are concerned with is the volume of the free space in the container, given by the container volume minus the volume of the gas particles. The equation for real gas volume accounts for the volume of the container and the volume of the gas particles. For a real gas, the volume is given as follows:
In this equation,
Note that for an ideal gas the bigness coefficient,
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What is the freezing point of a 2M solution of 
in water?
What is the freezing point of a 2M solution of
First, we need to calculate the molality because that is what we use in our equation for freezing point depression. We can get that from the molarity without knowing exactly how many liters or grams we have. We just have to know what we have one mole per liter. The weight of water is one kilogram per liter, so this allows us to make this conversion.
The molality is 2m. The van't Hoff factor is 3, as we get one calcium ion and two chloride ions per molecule during dissociation.
We can now plug the values into the equation for freezing point depression.
This gives us our depression of 
. The normal freezing point of pure water is 
, which means our new freezing point is 
.
First, we need to calculate the molality because that is what we use in our equation for freezing point depression. We can get that from the molarity without knowing exactly how many liters or grams we have. We just have to know what we have one mole per liter. The weight of water is one kilogram per liter, so this allows us to make this conversion.
The molality is 2m. The van't Hoff factor is 3, as we get one calcium ion and two chloride ions per molecule during dissociation.
We can now plug the values into the equation for freezing point depression.
This gives us our depression of
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How much sodium chloride has been added to four liters of water if the freezing point of the solution is 
?
Sodium chloride has a molar mass of 
.
How much sodium chloride has been added to four liters of water if the freezing point of the solution is
Sodium chloride has a molar mass of
We can determine how much sodium chloride was added to the water using the freezing point depression equation.
The normal freezing point of wtaer is 0 degrees Celsius, so we know that the temperature of the solution has changed by 2.5 degrees. Since sodium chloride will generate two ions per molecule in solution, the van't Hoff factor will be 2. Based on the density of water, we can determine that 4 liters of water weighs 4 kilograms.
We can determine how much sodium chloride was added to the water using the freezing point depression equation.
The normal freezing point of wtaer is 0 degrees Celsius, so we know that the temperature of the solution has changed by 2.5 degrees. Since sodium chloride will generate two ions per molecule in solution, the van't Hoff factor will be 2. Based on the density of water, we can determine that 4 liters of water weighs 4 kilograms.
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What is the freezing point of a 2M solution of in water?
What is the freezing point of a 2M solution of
First, we need to calculate the molality because that is what we use in our equation for freezing point depression. We can get that from the molarity without knowing exactly how many liters or grams we have. We just have to know what we have one mole per liter. The weight of water is one kilogram per liter, so this allows us to make this conversion.
The molality is 2m. The van't Hoff factor is 3, as we get one calcium ion and two chloride ions per molecule during dissociation.
We can now plug the values into the equation for freezing point depression.
This gives us our depression of . The normal freezing point of pure water is , which means our new freezing point is .
First, we need to calculate the molality because that is what we use in our equation for freezing point depression. We can get that from the molarity without knowing exactly how many liters or grams we have. We just have to know what we have one mole per liter. The weight of water is one kilogram per liter, so this allows us to make this conversion.
The molality is 2m. The van't Hoff factor is 3, as we get one calcium ion and two chloride ions per molecule during dissociation.
We can now plug the values into the equation for freezing point depression.
This gives us our depression of
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How much sodium chloride has been added to four liters of water if the freezing point of the solution is ?
Sodium chloride has a molar mass of .
How much sodium chloride has been added to four liters of water if the freezing point of the solution is
Sodium chloride has a molar mass of
We can determine how much sodium chloride was added to the water using the freezing point depression equation.
The normal freezing point of wtaer is 0 degrees Celsius, so we know that the temperature of the solution has changed by 2.5 degrees. Since sodium chloride will generate two ions per molecule in solution, the van't Hoff factor will be 2. Based on the density of water, we can determine that 4 liters of water weighs 4 kilograms.
We can determine how much sodium chloride was added to the water using the freezing point depression equation.
The normal freezing point of wtaer is 0 degrees Celsius, so we know that the temperature of the solution has changed by 2.5 degrees. Since sodium chloride will generate two ions per molecule in solution, the van't Hoff factor will be 2. Based on the density of water, we can determine that 4 liters of water weighs 4 kilograms.
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Use the following values for water as needed.
If burning wood releases 
of heat energy per gram of wood consumed, what mass of wood must be consumed to heat 
of water from 
to 
, and then to convert it to water vapor?
Use the following values for water as needed.
If burning wood releases
There are two processes requiring added heat in this problem:
1. Raising the temperature of the liquid water from 
to 
(use 
)
2. Boiling the water at a constant temperature of 
(use 
)
To use either of these equation, we need to find the mass of the water using the relation between mass, density, and volume.
Use this mass with the given specific heat and temperatures to find the heat for part 1 of the process.
Then, use the mass with the given heat of vaporization to find the energy needed to convert the water to water vapor.
Sum the energies for step 1 and step 2.
This is the total amount of energy needed from the burning wood. Use stoichiometry to find the grams of wood needed to produce this amount of energy.
There are two processes requiring added heat in this problem:
1. Raising the temperature of the liquid water from
2. Boiling the water at a constant temperature of
To use either of these equation, we need to find the mass of the water using the relation between mass, density, and volume.
Use this mass with the given specific heat and temperatures to find the heat for part 1 of the process.
Then, use the mass with the given heat of vaporization to find the energy needed to convert the water to water vapor.
Sum the energies for step 1 and step 2.
This is the total amount of energy needed from the burning wood. Use stoichiometry to find the grams of wood needed to produce this amount of energy.
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Calculate the specific heat of 
of metal that requires 
of heat energy to raise its temperature from 
to 
?
Calculate the specific heat of
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
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What was the final temperature of water if a 
sample of water absorbs 
of heat energy and heats up from 
? (specific heat of water is 
)
What was the final temperature of water if a
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
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An 
metal at 
was put into 
of water at 
. The final temp of the water and metal was 
. Assuming heat was not lost to the surroundings find the specific heat of the metal? The specific heat of water is 
.
An
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Heat is transferred from the metal to the water.
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Heat is transferred from the metal to the water.
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Calculate the final temperature when a 
sample of metal (specific heat of the metal=
) at 
is placed into 
of water at 
. (specific heat of water is 
)
Calculate the final temperature when a
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Heat is transferred from the metal to the water.
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Heat is transferred from the metal to the water.
Compare your answer with the correct one above
How much heat is absorbed when 
of water goes from 
to 
? (Specific heat of water= 
)
How much heat is absorbed when
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Compare your answer with the correct one above
Calculate the specific heat of 
of metal that requires 
of heat energy to raise its temperature from 
to 
?
Calculate the specific heat of
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Compare your answer with the correct one above
What was the final temperature of the water if a 
sample of water absorbs 
of heat energy and heats up from 
? (specific heat of water is 
)
What was the final temperature of the water if a
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Rearranging gives,
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Rearranging gives,
Compare your answer with the correct one above
A 
metal at 
was placed in 
of water at 
. The final temp of the water and metal was 
. Assuming heat was not lost to the surroundings find the specific heat of the metal? The specific heat of water is .
A
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Heat is transferred from the metal to the water.
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Heat is transferred from the metal to the water.
Compare your answer with the correct one above
Calculate the final temperature when a 
sample of metal (specific heat of the metal=
) at 
is placed into 
of water at 
. (Specific heat of water is 
)
Calculate the final temperature when a
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Heat is transferred from the metal to the water.
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Heat is transferred from the metal to the water.
Compare your answer with the correct one above
How much heat is absorbed when 
of water goes from 
to 
? (Specific heat of water = 
)
How much heat is absorbed when
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Rearranging gives,
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Rearranging gives,
Compare your answer with the correct one above
What was the final temperature of the water if a 
sample of water absorbs 
of heat energy and heats up from 
? (specific heat of water= 
)
What was the final temperature of the water if a
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Rearranging gives,
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Rearranging gives,
Compare your answer with the correct one above
A 
metal at 
was placed in 
of water at 
. The final temp of the water and metal was 
. Assuming heat was not lost to the surroundings find the specific heat of the metal? The specific heat of water is .
A
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Heat is transferred from the metal to the water.
Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings.
Heat is transferred from the metal to the water.
Compare your answer with the correct one above