Calculating density of an ideal gas

[kalisious]

Homework Statement

The density of helium gas at T= 0 degrees Celsius is 0.179 kg/m^3. The temperature is then raised to 100 degrees Celsius, but pressure is kept constant Assuming the helium gas is an ideal gas, calculate the new density of the gas.

Homework Equations

PV = nRT

The Attempt at a Solution

I thought that using PV = nRT --> Pm/density = nRT would be sufficient in solving this problem, but when I tried to solve this I found that I needed the mass of the molecule and there was no number of moles expressed for me to solve n, etc. So now I am stuck and not even sure if that is the proper equation to use. This problem seems simple enough, but I have myself all mixed up about it!

 

[Borek]

Assume 1 L initial volume.

It is not necessary - if you will do calculations using symbols only, volume will cancel out. But assuming 1L you can calculate mass of the gas, then new volume, then new density.

 

[cavalier]

Without moles, you can still calculate the ratio of the volume at T=100 C to the volume at T=0 C. Since you how much the volume changes you can find how much the density changes.

Alternately, you can choose an arbitrary amount of grams helium, convert it to moles n, and then plug it into PV=nRT with T=373K to find the volume occupied by that amount of helium. Divide whatever mass you initially chose by whatever volume you get to determine the density at T=100C.

 

[kalisious]

Wouldn't setting it up this way also cancel out pressure along with volume? That would just give me the equation density = mass/volume and then if volume cancels I'm left with density = mass?

 

[kalisious]

Without moles, you can still calculate the ratio of the volume at T=100 C to the volume at T=0 C. Since you how much the volume changes you can find how much the density changes.

Alternately, you can choose an arbitrary amount of grams helium, convert it to moles n, and then plug it into PV=nRT with T=373K to find the volume occupied by that amount of helium. Divide whatever mass you initially chose by whatever volume you get to determine the density at T=100C.

so should I set it up as P₁V₁/T₁ = P₂V₂/T₂?

 

[cavalier]

Yes, but there is only one P throughout the problem since P is constant. You can get rid of it.

 

[kalisious]

Yes, but there is only one P throughout the problem since P is constant. You can get rid of it.

okay, so now I have the mass, but how do I calculate the volume to use when solving for the final density?
when I set this up as density = mass/volume I end up with density being equal to the mass and I KNOW that is not correct!

 

[cavalier]

Density=(mass/volume)(initial volume/final volume)

Unit analysis makes sense.