# AP Physics 2 : Ideal Gas Law

## Example Questions

### Example Question #11 : Ideal Gas Law

What is the volume of  of nitrogen gas (diatomic) at and ?

Explanation:

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.

### Example Question #301 : Ap Physics 2

What is the mass of  of helium gas at  and ?

Explanation:

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.

### Example Question #13 : Ideal Gas Law

What is the density of hydrogen gas at  and ?

Explanation:

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.

### Example Question #11 : Ideal Gas Law

What is the mass of of oxygen gas at  and ?

Explanation:

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.

### Example Question #11 : Ideal Gas Law

What is the density of neon gas at  and ?

Explanation:

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.

### Example Question #11 : Ideal Gas Law

What is the volume of  of gaseous water at  and ?

Explanation:

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.

### Example Question #17 : Ideal Gas Law

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?

None of these

Explanation:

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.

### Example Question #11 : Ideal Gas Law

Which of the following graphs shows an incorrect relationship for an ideal gas?

Explanation:

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.

### Example Question #11 : Ideal Gas Law

of gas are heated from to and the pressure increases from to . Determine the volume in the final state.

Explanation:

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:

### Example Question #20 : Ideal Gas Law

How many moles of gas are there in a  container at a temperature of  at atmospheric pressure?