# AP Physics 2 : Ideal Gas Law

## Example Questions

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### Example Question #1 : Ideal Gas Law

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?

Explanation:

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:

### Example Question #43 : Thermodynamics

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?

The volume of the gas will not change

Decrease by a factor of 2

Increase by a factor of 8

Decrease by a factor of 8

Increase by a factor of 2

Decrease by a factor of 8

Explanation:

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.

### Example Question #44 : Thermodynamics

An ideal gas is kept in a  container at  and . How many moles of the gas are in the container?

There is not enough information to determine the number of moles

Explanation:

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.

### Example Question #45 : Thermodynamics

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?

There is not enough information to determine the new volume

Explanation:

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.

### Example Question #2 : Ideal Gas Law

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?

There is no volume change

Explanation:

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 .

### Example Question #3 : Ideal Gas Law

An airship has a volume of . How many kilograms of hydrogen would fit in it at  and ?

None of these

Explanation:

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.

### Example Question #4 : Ideal Gas Law

Assuming ideal gas behavior, find the density of pure oxygen gas at  and .

None of these

Explanation:

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.

### Example Question #5 : Ideal Gas Law

Assuming ideal gas behavior, determine the volume of  of methane gas at  and .

None of these

Explanation:

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.

### Example Question #50 : Thermodynamics

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 .

Explanation:

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:

### Example Question #6 : Ideal Gas Law

How many moles of nitrogen gas are in a  tank with a pressure of  at ?

Explanation:

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.

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