All AP Physics 2 Resources
Example Questions
Example Question #1 : Properties Of Ideal Gases
Under which of the following conditions would a gas be expected to deviate the least from ideal behavior?
Low pressure and high temperature
Low pressure and low temperature
High pressure and high temperature
High pressure and low temperature
Low pressure and high temperature
When talking about gases, it's convenient to talk about gases that behave ideally. The ideal gas law, , generally only holds true for gases that behave ideally. Once gases begin to deviate from ideal behavior, this equation begins to lose its accuracy in its power to predict.
There are a number of assumptions that are made when referring to gases that behave ideally, and these assumptions constitute what is known as the kinetic molecular theory of gases. In this model, there are a total of 5 assumptions:
1. Individual gas particles are very tiny points of mass that essentially have no volume (i.e. the volume of a gas is equal to the volume of free space in the container).
2. These gas particles are neither attracted to, nor repelled by, other gas particles (i.e. there are no intermolecular forces acting between gas particles).
3. Each of these gas particles are continuously moving in random directions.
4. All of these gas particles collide with each other, such that no energy is gained or lost by each collision (i.e. each collision is completely elastic).
5. At a given temperature, the average kinetic energy for a given sample of gas is the same as any gas (i.e. the identity of the gas does not matter) and the average kinetic energy of the sample of gas is directly related to the absolute temperature.
Now that we know what the assumptions are, let's go ahead and see how pressure and temperature affect ideal behavior, since these two parameters show up in each of the answer choices.
Temperature
When the temperature of a gas is lowered, the average kinetic energy of the sample of gas also decreases. Consequently, each gas particle making up the solution is expected to slow down. When this happens, the gas particles become more available for interacting with other gas particles, which increases the likelihood for intermolecular forces to begin playing a role. This violates one of the assumptions of kinetic molecular theory. When individual gas particles begin to attract one another, the pressure that the gas exerts on the wall of its container becomes less than what the ideal gas law equation would predict.
Thus, we would expect a high temperature to cause the least deviation from ideal behavior. In other words, a high temperature would increase the average kinetic energy of the sample of gas, and when all of the gas particles are shooting around at greater speeds, they have less of an opportunity to interact with other gas particles.
Pressure
When the pressure of a gas is increased, we also see deviations from ideal behavior. Remember that one of the assumptions of kinetic molecular theory is that the individual gas particles are very tiny points of mass that essentially have no volume, which means that the volume of the gas as predicted by the ideal gas law is essentially equal to the volume of the container. But, we of course know that real gases do not have zero volume and instead, each individual gas particle takes up a small amount of volume. As the external pressure becomes greater and greater, the volume of the container decreases as well. This, in turn, causes each gas particle to comprise a greater fraction of the container. Consequently, at high enough pressures, a real gas will take up a significant fraction of the container's volume, meaning that the volume of the real gas will be greater than what is predicted by the ideal gas law.
When external pressures are kept low, the volume of the container is sufficiently large enough that the volume of gas takes up a negligible fraction of the container. Thus, low external pressures will be expected to cause the least deviation from the ideal gas law.
In summary, it's important to remember the following:
- At high pressures, the actual volume of gas particles makes the real volume higher than the predicted volume.
- At low temperatures, intermolecular forces make the actual pressure lower than the predicted pressure.
Example Question #31 : Thermodynamics
In an enclosed space capsule, the temperature increases from to . Determine the ratio of the final to initial pressures: .
Convert to
Use Gay-Lussac's law:
Plug in values:
Example Question #11 : Properties Of Ideal Gases
Determine the average velocity of radon gas atoms at
Using the equation for the root-mean-square speed:
is the temperature in Kelvin
is the molar mass of the gas, in kilograms per mole
Converting Celsius to Kelvin and plugging in values:
Example Question #31 : Thermodynamics
A balloon is filled with nitrogen at a temperature of to a pressure of . If the temperature is increased to and the pressure is increased to , by what factor does the density of the nitrogen increase by?
We will start with the ideal gas law for this problem:
Since the problem statement is asking us for a change in density, we will need to manipulate the ideal gas law to get this unit. We will start by multiplying both sides of the expression by the molecular weight of nitrogen:
Now rearranging we get:
We can apply this to both scenarios, with density, pressure, and temperature being the only changing variables:
Dividing the second expression by the first and eliminating common variables, we get:
Plugging in our values and making sure our temperatures are in Kelvin, we get:
Example Question #32 : Thermodynamics
How would raising the temperature from to change the average velocity of gas molecules?
Very slight increase
None of these
The velocity would remain unchanged
Decrease the velocity
Double the velocity
Very slight increase
Using
is the temperature in Kelvin
is the gas constant
is the molar mass in kilograms
Converting to Kelvin:
It can be seen that this increase in temperature would lead to a very modest increase in velocity.
Example Question #35 : Thermodynamics
Determine the average velocity of helium gas atoms at .
None of these
Use the following equation to find the average velocity:
Where
is the temperature in Kelvin
is the molar mass of the gas, in kilograms
Converting Celsius to Kelvin and plugging in values:
Example Question #11 : Properties Of Ideal Gases
Determine the average velocity of chlorine molecules at .
None of these
Using
is the temperature in Kelvin
is the gas constant
is the molar mass in kilograms
Converting to Kelvin and plugging in values:
Example Question #37 : Thermodynamics
Determine the root mean square velocity of oxygen gas at
Since the gas is at absolute zero, it will stop
Using,
Where
is the Boltzmann constant,
is the temperature, in Kelvin
is the mass of a single molecule, in kilograms
Finding mass of a single oxygen molecule:
Plugging in values:
Example Question #12 : Properties Of Ideal Gases
Determine the root mean square velocity of chlorine gas at .
None of these
Using,
Where
is the Boltzmann constant,
is the temperature, in Kelvin
is the mass of a single molecule, in kilograms
Finding mass of a single chlorine molecule:
Plugging in values:
Example Question #281 : Ap Physics 2
The concept of an ideal gas is useful when using equations to predict the behavior of gasses under a variety of conditions. However, many gasses do not demonstrate ideal behavior. Which of the following is a characteristic of a gas that is not ideal?
All of the collisions between the gas particles are assumed to be elastic, such that energy is completely conserved
The gas particles do not interact with each other, with the exception of collisions
Each individual gas particle is assumed to be a tiny point of space with negligible volume compared to the size of its container
Each gas particle is assumed to be so small that its mass is neglibible
Each gas particle is in constant motion
Each gas particle is assumed to be so small that its mass is neglibible
For this question, we're asked to identify a statement that is false with respect to ideal gasses. Let's look at each.
There are a number of assumptions that are put into place when defining an ideal gas, together which are called the kinetic molecular theory of ideal gasses.
For one, each gas particle is assumed to exert no attractive or repulsive forces with any other gas particle. As these particles move in constant motion, they continuously collide both with themselves and with the wall of their container. Each of these collisions is assumed to be perfectly elastic, such that no energy is lost or gained from the collision and energy is perfectly maintained. Furthermore, the size of the individual gas particles is assumed to be so tiny as to be negligible. What this means is that the overall amount of space taken up by the gas particles is negligible with respect to the amount of space in the container.
Although the volume of each gas particle is assumed to be negligible, the same cannot be said about their mass. Each particle has a characteristic mass that is dependent on the identity of the gas.
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