Reef Chemistry Question of the Day #242 Density of a gas vs a liquid

[Randy Holmes-Farley]

Reef Chemistry Question of the Day #242

Curiously, the density of a gas and density of a liquid do not necessarily track together when you look at different chemicals. In other words, the features that determine the density of the two phases are different.

Let's take the following four liquids at room temperature and pressure:

1. Bromine (Br2) molecular weight = 159.8 g/mmole
2. Water (H2O) molecular weight = 18.0 g/mole
3. n-Butane (C4H10) molecular weight = 58.1 g/mole
4. n-Dodecane (C12H26) molecular weight = 170.3 g/mole

The liquid densities rank as follows, from low to high:

n-Butane (0.6 g/mL) < n-Dodecane (0.75 g/mL) < water (1 g/mL) < Bromine (3.1 g/mL)

What is the rank order of the density of the gas phase (each chemical alone in the gas) at a constant temperature and pressure?

A. Bromine < Water < Butane < Dodecane
B. Water < butane < Dodecane < Bromine
C. Butane < Dodecane < Bromine < Water
D. Water < Butane < Bromine < Dodecane

Note that I have given you everything you need to answer the problem. No lookups needed. All you need to do is determine what attribute of a molecule determines its gas phase density at a fixed pressure and temperature.

Good luck!































.

 

[jsker]

A

 

[sghera64]

Answer is D.

PV = nRT. So,

n/V = P/RT

Since Pressure and RT are constant then n/V will be too for all the gases. If we take 1L, it will contain the same number of moles (n) in every case - - assuming these follow the ideal gas law.

If each 1L sample of gas has the same number of moles, we can order them by their density using their molecular weight. That is, n * gm/mole = gm. Thus, n/V * M.W. gives us density (gm/L). Using the molecular weights, we find that their rank order of density will correspond to the rank order of their M.W. with Dodecane being the most dense and water the least dense.

 

[CircleCityBill]

B.

PV = nRT. So,

n/V = P/RT

Since Pressure and RT are constant then n/V will be too for all the gases. If we take 1L, it will contain the same number of moles (n) in every case - - assuming these follow the ideal gas law.

If each 1L sample of gas has the same number of moles, we can order them by their density using their molecular weight. That is, n * gm/mole = gm. Thus, n/V * M.W. gives us density (gm/L). Using the molecular weights, we find that their rank order of density will correspond to the rank order of their M.W. with Bromine being the most dense and water the least dense.

I agree with the logic, but I believe dodecane has a higher MW.

 

[sghera64]

I agree with the logic, but I believe dodecane has a higher MW.

You are correct. I had to correct my post (while you were reading the original errored one).

 

[Alfrareef]

I’ll go with B. Under similar conditions (P,V,T), more molar weight should give more gas density. The mmole almost got me...

 

[anit77]

I agree. It's B.

 

[redfishbluefish]

Assuming they are all ideal gasses, they occupy the same volume per mole. So simply use their molecular weights.........accordingly, the answer is D.

 

[Randy Holmes-Farley]

And the answer is...

What is the rank order of the density of the gas phase (each chemical alone in the gas) at a constant temperature and pressure?


D. Water < Butane < Bromine < Dodecane

The interesting thing here (to me) is how the factors that determine liquid density and gas density differ so much.

In a liquid, essentially all the space is taken up by atoms of one sort or another, and it turns out that heavy atoms (say, gold) do not take up all that much more space than lighter atoms (say lithium). Hence, the density of a liquid (or a solid) is generally higher if you have more heavy elements in it. In our example, bromine is heavier than anything else, and its liquid is the densest. Meanwhile, carbon and hydrogen are the lightest elements we are discussing, and so butane and dodecane are the least dense liquids.

In a gas, however, most of the space is empty between molecules. At a fixed pressure there are an equal number of molecules present in any gas. So the density is only driven by the molecular weight of the molecule. I selected dodecane because, despite being made of light atoms, it weighs a lot (more than Br2) and so has the highest gas density. Water, even with its heavier oxygen atom, has a much lower gas density than butane just because its molecular weight is much lower.

Happy Reefing!

 

[Alfrareef]

Don’t understand why isn’t B. If the question it’s presented with Bromine unit g/mmole (milimole) which means it’s roughly 1 thousand heavier than dodecane.

 

[sghera64]

Don’t understand why isn’t B. If the question it’s presented with Bromine unit g/mmole (milimole) which means it’s roughly 1 thousand heavier than dodecane.

I noticed that too, but realized it would be very in conventional to use those units especially when all the others did not. Figured it was a typo. But if not, I believe you would be correct

 

[Alfrareef]

I noticed that too, but realized it would be very in conventional to use those units especially when all the others did not. Figured it was a typo. But if not, I believe you would be correct

Also, but since Randy didn’t correct that in al these days and he stated we have everything needed to solve the question...
Never mind. Fun its learning while participating...

 

[Randy Holmes-Farley]

Sorry, the molecular weight of Br2 is 159.8 g/mole, not g/mmole. [emoji3]

 

[Alfrareef]

Sorry, the molecular weight of Br2 is 159.8 g/mole, not g/mmole. [emoji3]

So, I still get the A++

 

[Randy Holmes-Farley]

So, I still get the A++

Yes.

 

[Alfrareef]

Yupi!!!!