# AP Physics 2 : Ideal Gas Law

## Example Questions

### Example Question #21 : Ideal Gas Law

A sealed container with an adjustable volume goes from  to . If the initial pressure was , what will be the final pressure, assuming temperature stays constant?

None of these

Explanation:

Using

Solving for

Plugging in values

### Example Question #22 : Ideal Gas Law

How many oxygen molecules are there in a  tank at  and ?

None of these

Explanation:

Using ideal gas law:

Converting Celsius to Kelvin and plugging in values:

### Example Question #23 : Ideal Gas Law

By what factor does the volume of an ideal gas change if its temperature increases by 50% and pressure quadruples?

Explanation:

We will use the ideal gas law to solve this problem:

We are asked to find the change in volume, so let's rearrange for that:

Then applying this to the initial and final scenarios:

Then taking the ratio of scenario 2 to scenario 1:

Where:

Substituting these in, we get:

### Example Question #61 : Thermodynamics

A mixture of gas has a volume of , a pressure of , and is at a temperature of . If the gas mixture is 80% nitrogen and 20% oxygen, how many moles of nitrogen are there?

Explanation:

We will begin with the ideal gas law for this problem:

Then rearranging for total moles:

Then multiplying by 80% to get the number of moles of nitrogen:

### Example Question #25 : Ideal Gas Law

In a  rigid, sealed container, there is 1 mole of an ideal gas. The container is initially at . If the gas is heated to , what is the new pressure in the container?

Explanation:

To determine the answer, we must do several steps with the ideal gas law:

For this problem, the pressure and temperature are the only things to change. Therefore, we can rearrange the equation to account for this.

However, we don't know what the value of P1 is just yet. To determine it, we must use the values we do know to solve for the initial pressure.

Now, we have P1. Using this, along with T1 and T2, we can solve for P2.

### Example Question #26 : Ideal Gas Law

If a container of  of oxygen gas undergoes an isobaric expansion in which its volume is doubled at a pressure of , what happens to the gas's temperature?

The temperature is doubled

The temperature is reduced by a quarter

The temperature remains the same

The temperature is halved

The temperature is doubled

Explanation:

In this question, we're given a situation in which a gas with certain defined parameters is undergoing an isobaric expansion. We're asked to determine how the temperature changes.

An isobaric expansion refers to a process in which a container expands while maintaining a constant pressure. In this problem, we're going to need to use the ideal gas law.

Based on the process described in the question stem, we know that the number of moles of gas will remain the same. Furthermore, we know the pressure remains constant. And, of course, the ideal gas constant stays the same as well. Thus, we can lump all the constants together.

Therefore, the only variables that will be changing during this process are the temperature and the volume. Consequently, we can set up a before and after expression.

Since we're solving for the final temperature, , let's go ahead and isolate that term.

Since we know the volume doubles, we can conclude that . We can plug this into the equation to obtain:

Canceling common terms, we obtain:

Thus, we see that the final temperature is twice as much as the initial temperature. We could have concluded this fairly easily without the math, since we know that temperature and volume are directly proportional to one another. If one doubles, the other will also double (assuming all other variables remain constant).

### Example Question #27 : Ideal Gas Law

sealed metal container is being tested. It is filled with atmosphere at  and . Previous tests indicate that it can reach  before failure. Determine what temperature the air inside would need to rise up to to reach that pressure.

None of these

Explanation:

Using

So

Solving for

Converting to Kelvin and plugging in values

### Example Question #28 : Ideal Gas Law

If a sample of gas whose density is  is at a pressure of  and a temperature of , what is the molar mass of this gas?

Explanation:

For this question, we're given various parameters with regards to a gas, including its pressure, temperature, and density. We're asked to solve for the gas's molar mass.

To solve this problem, we'll need to make use of the ideal gas law.

Using this expression, we'll need to manipulate it in order to account for the density of the gas. To do that, we'll have to define moles in an alternative way.

Combining these two expressions....

And rearranging further....

Leads us to a term for density.

Now, we can isolate the term for molar mass.

Then we just need to plug in the values from the question stem to find the molar mass.