[Tobes]

So here goes the problem: Elemental sulfur boils at 445 celcius at 1.00 atm. The density of gaseous sulfur is 4.35g/L. Does sulfur form a monatomic gas under these conditions? if not determine the actual molecular formula of gaseous sulfur in these conditions.

So I thought of using the PV=nRT equation because we are studying gas laws. I put in the given information but the Density confuses me ???. I tried putting in 1L in for the V and solved more n but it doesn't seem right. What am i supposed to do with the 4.35g then? Or maybe I'm just doing everything wrong. Can someone please help me out?

[AWK]

pV=nRT or pV=mRT/M or p=dRT/M since d=m/V

[jdurg]

Ahhhhh, this is a fun one.  

First off, yes, you would use the ideal gas equation of PV=nRT.  You are given the temperature, the pressure, the volume, and the gas constant R (0.0821 L*Atm/K).  The question tells you that at the temperature of 445 Celcius (718 K), the pressure is equal to one atmosphere.  They also say that 4.35 grams is in one liter of the sulfur gas.  So we'll set up the equation as follows:

(1.00 atm)(1.00 L) = n(0.0821 L*atm/K)(718 K)

If we solve for n, the number of moles of gas, we get 0.01696 (Not the right number of significant figures, but oh well).

If we multiply that number by the molecular mass of sulfur (32.1 grams per mole), we get a value of 0.545 grams.

So this is telling us that in .017 moles of gas, we have 0.545 grams of sulfur.  Also remember that the value 'n' in the Ideal Gas Equation is the number of moles of GAS and not the number of moles of atom.  In the ideal gas equation, a mole of oxygen is equal to 1 mole of O2, so the number of moles of oxygen is actually 2.  Since the initial question told us that one liter of sulfur gas weighs 4.35 grams, we see that while we have 0.17 moles of sulfur gas, we must have a greater number of moles of sulfur atoms.  How do we find out the number of atoms per molecule then?

Well we can take the 4.35 grams and divide it by the number of grams we calculated.  So 4.35/0.545 = 7.98 = 8 atoms of sulfur per molecule of gas.  Therefore, sulfur would have the form of S8 molecules as a gas which is correct.

[Tobes]

  thanks! that helped a lot!  

[AWK]

Ahhhhh, this is a fun one.  

So this is telling us that in .017 moles of gas, we have 0.545 grams of

Sulfur gas is not monoatomic!

To Tobes
Calculate approximate M from p=dRT/M, then divide your result by 32.

[jdurg]

Sulfur gas is not monoatomic!

To Tobes
Calculate approximate M from p=dRT/M, then divide your result by 32.

AWK, PLEASE read my entire post.  The ideal gas law PV=nRT uses n as the number of moles of gas.  It doesn't matter if the gas is made up of fifty atoms or one atom.  According to the ideal gas law, one mole of hydrogen molecules is equal to 22.4 Liters of volume at STP.  However, in reality that's two moles of hydrogen atoms because two moles of hydrogen make up one mole of hydrogen gas.

If you go through my entire post, you'll see that I have made note of that and everything I did is completely correct.

[jdurg]

Let's use fluorine gas and helium as examples of calculating the number of atoms per gas molecule.

Density of Helium = 0.1785 g/L
Temperature = 273.15 K
Pressure = 1.0 atm
R = 0.0821
n = 0.044592
n*MM of He (4.00) = 0.1784 grams

0.1785/0.1784 is about equal to 1 so there is one atom per molecule of Helium gas.  Helium is therefore a monatomic gas.

Density of fluorine = 1.7 g/L
Temperature = 273.15 K
Pressure = 1.0 atm
R = 0.0821
n = 0.044592
n*MM of F (19.0) = 0.847 grams.

1.7/0.847 is about equal to 2 so there are two atoms per molecule of Fluorine gas.  Fluorine gas is therefore diatomic.  

If you are given the molecular weight of the substance, the density of the gas, the temperature and the pressure, you can determine if it's diatomic, monatomic, triatomic, etc. etc.