Recall the ideal gas law:

,

where ,

 ,

, 

,

and .

Since the question asks for pressure, rearrange the equation to solve for .

Plug in the given values. Remember that 

Since we are given the volume and the pressure of this sample of gas, we will need to use Boyle's Law, which states that the pressure and volume of a gas, at a constant temperature, are inversely related. As thus, we can then write the following equation:

Since all the answer choices are in units of atmospheres, we will need to convert the given units into atmospheres.

Plug in the given pressures and volume into the equation, and solve for .

Start by finding the number of moles of nitrogen gas by using the ideal gas law:

Rearrange the equation to solve for the variable :

In order to use the ideal gas law, the pressure must have units of atmospheres and the temperature must have units of Kelvin.

Convert the given pressure into atmospheres:

Now, substitute in all the given values in order to find the number of moles of nitrogen gas.

Next, use the stoichiometric ratio given by the chemical equation to find the number of moles of lithium needed to react completely with the nitrogen gas.

Finally, convert the number of moles of lithium to number of grams of lithium.

Avogadro's law states that volume is proportional to moles of gas.  Temperature and pressure are fixed.  Boyle law states that volume of gas is inversely proportional to pressure.  Charles' law states that volume of gas is proportional to temperature.  

Recall the Ideal Gas Law:

Since the question is asking for volume, rearrange the equation to the following:

Also recall that for the Ideal Gas Law equation to work, the temperature must be given in degrees Kelvin, and we will also need the number of moles of gas.

Start by converting the mass of gas into moles:

Don't round the values just yet.

Next, convert the temperature into degrees Kelvin.

Now, plug in all the given values into the equation to solve for volume:

The answer should have  significant figures.

The volume is .

Recall the Ideal Gas Law:

Because we want the amount of gas in the cylinder, we must find the number of moles of oxygen present first. Rearrange the Ideal Gas Law to solve for the number of moles of oxygen.

Plug in the given information to solve for the number of moles.

Now, convert the number of moles to the number of grams by using the molar mass of oxygen gas.

Make sure that your answer has  significant figures.

Use the ideal gas equation

Rearrange to solve for the volume

An ideal gas with a pressure of  is is compressed to  of its original volume, what is the new pressure?

Use Boyle’s law:

You want to solve for the new pressure so isolate :

It compresses to  its original volume so, 

Plug in everything we know:

Cancel  from the numerator and denominator

Use Boyle’s law:

You want to solve for the new pressure so isolate :

It expands to  its original volume, so 

Plug in everything we know:

Cancel  from both the numerator and denominator