Ideal Gas Law - AP Physics 2
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Suppose that a gas originally at standard temperature and pressure undergoes a change in which its pressure is quadrupled while its temperature is cut in half. What change in volume does the gas experience during this process?
Suppose that a gas originally at standard temperature and pressure undergoes a change in which its pressure is quadrupled while its temperature is cut in half. What change in volume does the gas experience during this process?
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To solve this problem, we'll need to use the ideal gas equation:
We are told that the gas undergoes a change in which its pressure quadruples and its temperature halves. Therefore:
and
Furthermore, we can set the ideal gas equation to solve for volume:
and
If we plug in the values from above, we obtain:
Therefore, we can see that the new volume is 
of its original value.
To solve this problem, we'll need to use the ideal gas equation:
We are told that the gas undergoes a change in which its pressure quadruples and its temperature halves. Therefore:
and
Furthermore, we can set the ideal gas equation to solve for volume:
and
If we plug in the values from above, we obtain:
Therefore, we can see that the new volume is
A balloon is in a room that has a constant pressure of 
and constant temperature of 
. How many moles of air must be put into the balloon for 
of work to be done on the balloon?
A balloon is in a room that has a constant pressure of
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We know that pressure and temperature are constant. Therefore, we can use the following formula for work:
Write out the ideal gas law:
Rearrange for moles:
Substitute in our expression for work:
Now, plug in values for each variable:
We know that pressure and temperature are constant. Therefore, we can use the following formula for work:
Write out the ideal gas law:
Rearrange for moles:
Substitute in our expression for work:
Now, plug in values for each variable:
An ideal gas is kept in a 
container at 
and 
. How many moles of the gas are in the container?
An ideal gas is kept in a
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Because this is an ideal gas, we can use the Ideal Gas Law to determine its state.
The value for 
is sometimes tricky to determine, because it has several values depending on the units being used. The two main values for that are used are:
and 
Because we have units in Liters, and we can convert our temperature and pressure to Kelvin and atmospheres respectively, we use the second value of .
First, let's convert our values to usable units.
Because we're trying to find moles of gas, we can rearrange the ideal gas equation to equal moles, and plug in our values.
Therefore, there are 
of gas in the container.
Because this is an ideal gas, we can use the Ideal Gas Law to determine its state.
The value for
Because we have units in Liters, and we can convert our temperature and pressure to Kelvin and atmospheres respectively, we use the second value of
First, let's convert our values to usable units.
Because we're trying to find moles of gas, we can rearrange the ideal gas equation to equal moles, and plug in our values.
Therefore, there are
At 
, the volume of a gas is 
. The temperature of the gas gets raised to 
with no change in pressure. What is the new volume of the gas?
At
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When the only properties of an ideal gas that are changing are volume and temperature, we use Charles' Law (a derivative of the Ideal Gas Law). Charles' Law is as follows:
We're given all but the new volume, 
. To find the new volume, we rearrange the equation.
The addition of 273.15 is to convert the Celsius units to Kelvin.
When the only properties of an ideal gas that are changing are volume and temperature, we use Charles' Law (a derivative of the Ideal Gas Law). Charles' Law is as follows:
We're given all but the new volume,
The addition of 273.15 is to convert the Celsius units to Kelvin.
The pressure of a sample of gas is 
in a 
sealed, flexible container. If the pressure gets raised to 
at a constant temperature, what is the new volume?
The pressure of a sample of gas is
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Because the only properties of the gas that are changing are the pressure and volume1, we use Boyle's Law, a derivative of the Ideal Gas Law. Boyle's Law states
Since 
can be in atmospheres, and 
can be in Liters, we don't have to convert any units. Instead, we just rearrange the equation to solve for 
, and plug in our numbers.
The new volume is 
.
Because the only properties of the gas that are changing are the pressure and volume1, we use Boyle's Law, a derivative of the Ideal Gas Law. Boyle's Law states
Since
The new volume is
An airship has a volume of 
. How many kilograms of hydrogen would fit in it at 
and 
?
An airship has a volume of
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Use the ideal gas equation:
Convert the volume into liters in order to use our ideal gas constant: 
Rearrange the ideal gas equation to solve for 
, then plug in known values and solve.
Use the ideal gas equation:
Convert the volume into liters in order to use our ideal gas constant:
Rearrange the ideal gas equation to solve for
Assuming ideal gas behavior, find the density of pure oxygen gas at 
and 
.
Assuming ideal gas behavior, find the density of pure oxygen gas at
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For simplicity, we will assume 
.
Rearrange the ideal gas equation to solve for volume.
Plug in known values and solve.
Use volume to solve for density.
For simplicity, we will assume
Rearrange the ideal gas equation to solve for volume.
Plug in known values and solve.
Use volume to solve for density.
Assuming ideal gas behavior, determine the volume of 
of methane gas at 
and 
.
Assuming ideal gas behavior, determine the volume of
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Use the ideal gas equation and rearrange, solving for volume.
Find 
by using the molar mass of methane.
Plug in known values into the rearranged ideal gas equation and solve.
Use the ideal gas equation and rearrange, solving for volume.
Find
Plug in known values into the rearranged ideal gas equation and solve.
A balloon filled is filled with pure nitrogen gas. The balloon is determined to have a volume of 
on a day when the temperature is 
, and the air pressure is 
.
How many nitrogen molecules are present?
A balloon filled is filled with pure nitrogen gas. The balloon is determined to have a volume of
How many nitrogen molecules are present?
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We will use our ideal gas equation.
Where 
is the pressure
is the volume
is the number of moles
is the gas constant
is the temperature in Kelvin
We rearrange the equation to solve for n
A common mistake is using the wrong gas constant, 
. We need to use
We convert our temperture from Celsius to Kelvin
We plug in our values
We then need to multiply by Avogadros number to convert to number of molecules.
We will use our ideal gas equation.
Where
We rearrange the equation to solve for n
A common mistake is using the wrong gas constant,
We convert our temperture from Celsius to Kelvin
We plug in our values
We then need to multiply by Avogadros number to convert to number of molecules.
How many moles of nitrogen gas are in a 
tank with a pressure of 
at 
?
How many moles of nitrogen gas are in a
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We will use the ideal gas equation:
Where 
is the pressure in atm, 
is the volume in liters, 
is the number of moles of gas, 
, and 
is the temperature in Kelvin.
Rearrange the equation to solve for moles:
Plug in known values and solve.
We will use the ideal gas equation:
Where
Rearrange the equation to solve for moles:
Plug in known values and solve.
What is the volume of 
of nitrogen gas (diatomic) at 
and 
?
What is the volume of
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We will use the equation:
Where:
is the pressure in atm
is the volume in liters
is the number of moles of gas
is the temperature in Kelvin.
We need to convert the temperature to Kelvin.
Rearrange our original equation for volume:
We need to find the moles of nitrogen gas. We divide the mass by the molar mass of nitrogen, which is 
.
Plug in our values to our original equation and solve.
We will use the equation:
Where:
We need to convert the temperature to Kelvin.
Rearrange our original equation for volume:
We need to find the moles of nitrogen gas. We divide the mass by the molar mass of nitrogen, which is
Plug in our values to our original equation and solve.
What is the volume of 
of gaseous water at 
and 
?
What is the volume of
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We will use the equation
Where:
is the pressure in atm
is the volume in liters
is the number of moles of gas
is the temperature in Kelvin
We need to convert the temperature to Kelvin
Rearrange our original equation for volume:
We need to find the moles of nitrogen gas. We divide the mass by the molar mass of water, which is 
.
Plug in our values to our rearranged original equation and solve.
We will use the equation
Where:
We need to convert the temperature to Kelvin
Rearrange our original equation for volume:
We need to find the moles of nitrogen gas. We divide the mass by the molar mass of water, which is
Plug in our values to our rearranged original equation and solve.
What is the mass of 
of helium gas at 
and 
?
What is the mass of
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We will use the equation:
Where:
is the pressure in atm
is the volume in liters
is the number of moles of gas
is the temperature in Kelvin
We need to convert the temperature to Kelvin.
Rearrange to solve for moles:
Plug in our values and solve
Then, we need to multiply by the molar mass of helium; recall that helium is not a diatomic gas.
We will use the equation:
Where:
We need to convert the temperature to Kelvin.
Rearrange to solve for moles:
Plug in our values and solve
Then, we need to multiply by the molar mass of helium; recall that helium is not a diatomic gas.
What is the mass of 
of oxygen gas at 
and 
?
What is the mass of
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We will use the equation:
Where:
is the pressure in atm
is the volume in liters
is the number of moles of gas
is the temperature in Kelvin
Rearrange to solve for moles:
Plug in our values and solve
Then, we need to multiply by the molar mass of oxygen gas, which is diatomic.
We will use the equation:
Where:
Rearrange to solve for moles:
Plug in our values and solve
Then, we need to multiply by the molar mass of oxygen gas, which is diatomic.
What is the density of hydrogen gas at 
and 
?
What is the density of hydrogen gas at
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We will use the equation
Where:
is the pressure in atm
is the volume in liters
is the number of moles of gas
is the temperature in Kelvin
We need to convert celsius to Kelvin
Then, we will assume 
to make our calculations easier.
Rearrange for volume:
Plug in our values and solve
Again, assume 
and multiply by the molar mass of hydrogen gas, 
:
We divide mass by volume to get density.
We will use the equation
Where:
We need to convert celsius to Kelvin
Then, we will assume
Rearrange for volume:
Plug in our values and solve
Again, assume
We divide mass by volume to get density.
What is the density of neon gas at 
and 
?
What is the density of neon gas at
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We will use the equation:
Where:
is the pressure in atm
is the volume in liters
is the number of moles of gas
is the temperature in Kelvin
First we need to convert our temperature to Kelvin:
We will assume to make our calculations easier.
Rearrange for volume:
Plug in our values and solve.
Again, assume and multiply by the molar mass of neon 
:
We divide mass by volume to find density.
We will use the equation:
Where:
First we need to convert our temperature to Kelvin:
We will assume
Rearrange for volume:
Plug in our values and solve.
Again, assume
We divide mass by volume to find density.
In a room where the temperature is 
, a football has been inflated to a gauge pressure of 
. The football is then taken to the field, where the temperature is 
. What will the football's gauge pressure be when its temperature becomes equal to the temperature of the air on the field? Assume the air follows the ideal gas law and that the atmospheric pressure that day was 
.
In a room where the temperature is
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Start by converting to Pascals:
For the atmosphere: 
Find the absolute pressure in the football:
Write the ideal gas law for the football in the locker room:
Solve for 
, the constants that won't change as the air cools:
Write the ideal gas law for the football on the field:
Substitute 
from before:
Recognize that the volume does not change, so those terms cancel:
Convert from absolute pressure to gauge pressure:
Start by converting to Pascals:
For the atmosphere:
Find the absolute pressure in the football:
Write the ideal gas law for the football in the locker room:
Solve for
Write the ideal gas law for the football on the field:
Substitute
Recognize that the volume does not change, so those terms cancel:
Convert from absolute pressure to gauge pressure:
Which of the following graphs shows an incorrect relationship for an ideal gas?
Which of the following graphs shows an incorrect relationship for an ideal gas?
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This question is asking for us to identify which graph shows an incorrect relationship between volume, pressure, and temperature of an ideal gas. To distinguish between which graphs are correct, and which one isn't, we'll need to use the ideal gas law.
It's also important to note that each graph in the answer choices shows a linear, positive relationship between the x and y-variables.
The only graph that shows an incorrect relationship is the graph that has 
as the y-axis and 
as the x-axis. From the ideal gas law shown above, we would expect a positive linear relationship of a graph showing 
vs. 
. If we instead have 
vs. 
, the graph would have a negative relationship.
All of the other graphs shown in the remaining answer choices show correct relationships. 
vs. 
gives a positive relationship. Likewise, 
vs. 
gives a positive relationship. And finally, 
vs. 
also gives a positive relationship.
This question is asking for us to identify which graph shows an incorrect relationship between volume, pressure, and temperature of an ideal gas. To distinguish between which graphs are correct, and which one isn't, we'll need to use the ideal gas law.
It's also important to note that each graph in the answer choices shows a linear, positive relationship between the x and y-variables.
The only graph that shows an incorrect relationship is the graph that has
All of the other graphs shown in the remaining answer choices show correct relationships.
How many moles of gas are there in a 
container at a temperature of 
at atmospheric pressure?
How many moles of gas are there in a
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In this question, let's start with what we know and what we want to know. We're given the volume of the gas in a container, as well as the pressure and the temperature. Then, we're asked to find the number of moles of gas that are in this container.
To answer this question, we'll need to make use of the ideal gas equation.
Plugging in the values that we know, we can calculate our answer.
In this question, let's start with what we know and what we want to know. We're given the volume of the gas in a container, as well as the pressure and the temperature. Then, we're asked to find the number of moles of gas that are in this container.
To answer this question, we'll need to make use of the ideal gas equation.
Plugging in the values that we know, we can calculate our answer.
of 
gas are heated from 
to 
and the pressure increases from 
to 
. Determine the volume in the final state.
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Only the final state data will be needed Convert Celsius to Kelvin:
Use the ideal gas law:
Where
is the pressure in 
is the volume in 
is the number of moles
is the gas constant, 
is the temperature in 
Plug in values and solve:
Only the final state data will be needed Convert Celsius to Kelvin:
Use the ideal gas law:
Where
Plug in values and solve: