Determine the gas if the pressure of its saturated steam is known

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SUMMARY

The discussion focuses on determining the identity of gas B and mineral A based on experimental data of saturated steam pressure and density at various temperatures. The Mendeleev-Klapeiron equation, M = ρRT/p, was employed to calculate molar masses, revealing inconsistencies as temperatures increased. Participants emphasized the need for clarity on the relationship between gas and matter, noting that gas B exhibits different structures in liquid and gaseous phases. The conversation highlights the importance of accurate data interpretation in physical chemistry.

PREREQUISITES
  • Understanding of the Mendeleev-Klapeiron equation
  • Familiarity with concepts of saturated steam pressure
  • Knowledge of gas density and relative density calculations
  • Basic principles of physical chemistry and phase transitions
NEXT STEPS
  • Research the application of the Mendeleev-Klapeiron equation in real-world scenarios
  • Explore methods for determining gas identities using pressure and density data
  • Investigate the physical properties of gases and their behavior under varying temperatures
  • Study the relationship between molecular structure and phase behavior in gases
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Chemists, physicists, and students in physical chemistry, particularly those interested in gas behavior, phase transitions, and the application of thermodynamic equations.

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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?
 
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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?
 
Dear sirs,
I've detected an error in my post. I am sorry.

I mixed up mineral and gas.

1) Determine mineral A and gas B

I also want to say that 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?