[beruniy]

One hundred thousands denarii (or 423 kg of gold) cost a vase from mineral A in Ancient Rome. A Painter in 17th century occasionally got from it gas B and Physicist in 19th told an assumption of its composition.
There are experimental data of pressure of its saturated steam and density over a liquid at different temperatures:

T, ^oC                  0          20         40        60        80       100
p, mm m.c.        363,8     773,2     1516    2778     4801     7891
ρ, g/l                2,015     3,170     4,976   7,645    11,44    16,64

and also data of relative density at different temperature in gaseous phase for this matter:

T, ^oC               26,4        29,2        33,1        39,2        47,3        88,1
p, mm m.c.        745        750          750        743         745          741
D, air               1,773      1,578       1,321     1,002       0,823       0,713

1) Determine gas A and mineral B
2) Determine compound and structure of this matter in gaseous phase
3) Describe physical properties and give the examples of chemical properties of this compound (reactions with different classes: simple matters, oxides, salts, hydroxides, acids)
4) What was the names of Painter and Physicist?

Solution

Points 2), 3) and 4) of this task I can solve if I know what the matters A and B. So it is necessary to solve point 1).
I tried to use Mendeleev-Klapeiron equation, through density it becomes following:

M = ρRT/p

But for each occasion I've got... different molar masses! Explain please if it's possible?
I've got the next data:
M, g/mole    94,3    74,9    64,1    57,1    52,5    49,0
It means that during of temperature raising molar mass is decreasing. But it's impossible!
May be, I need to use another equations?

[Borek]

I am afraid your translation is hard to follow. It is not always clear what is the subject of the phrase, it is not always clear what you mean, as you seem to be using words like mineral and matter in a rather random way. When you write steam you mean vapor, that I am sure about.

[beruniy]

I'm very-very sorry for confusion. I mixed up mineral and gas.

1) Determine mineral A and gas B

Yes, steam = vapour.

Gas and matter have the same meaning - it is B. I think that problem says that B has different structures in liquid and gaseous phase. All the data relate to B.

I have  only one question: how is it possible to determine gas B using pressures of its saturated vapour and relative densities?

[Borek]

It means that during of temperature raising molar mass is decreasing. But it's impossible!

It suggests some reaction taking place.

[beruniy]

Do you mean that reaction runs during the phase transition?

B_liq   B_gas
B_gas  C_gas + D_gas

Then the question: why do the different molar masses correspond to each temperature/pressure? It means that each 20 degrees the chemical reaction occurs.

[beruniy]

Using Clapeiron-Clausius equation I calculated ΔH of evaporation of B in temperature range from 0 to 100^oC.

ΔH_ev = 6137 kal/mole

Then I found boiling temperature using equation
ΔH_ev/T_b = 8.75 + 4.57lgT_b

T_b = 305.6 K = 32.4^oC

What have I to do next? How can I use relation "density of saturated vapor - temperature"? How can I find gas? Help please.

[Borek]

Then the question: why do the different molar masses correspond to each temperature/pressure? It means that each 20 degrees the chemical reaction occurs.

No, it means there is an equilibrium which shifts with a temperature. If you have a reaction of the type

2A B

average molar mass of the mixture is a function of temperature.

T_b = 305.6 K = 32.4^oC

Not many gases with boiling points around room temperature and reacting with themselves.

Not that I know what the A is, but I am almost sure what the gas is.

[beruniy]

Thank you very much! Now I know what is it.
NO₂, boiling temperature is 21,5^oC
N₂O₄ 2NO₂
I calculated average molar mass using the first table. I built graph of function
ρ = f(p/T) - the linear dependence, where M/R = tgα. M = 46 g/mole - is for liquid.
But I have next table where relative density is - how can I use it?

My considerations: build a new graph and find M for gas. By this way linear dependence between ρ and T is not observed. So I can't calculate M as tgα of straight line. What have I to do?

[Borek]

I am not convinced you need to make much of the second table - for sure you can use it to check if the changing molar mass range fits the possible outcome of the reaction.