# When 3.2 g of Sulphur is vaporized at 450oC and 723 mm pressure, the vapors occupy a volume of 780 ml. What is the molecular formula of sulphur vapours under these conditions? Calculate the vapor density also.

Given-
Mass of sulphur  = 3.2 g
Temperature = 450oC or 723 K
Volume = 780 mL or 0.780 L
Pressure = 723 mm Hg or 0.954 atm ( 1 mm Hg = 0.0013158 atm)
Calculation
Using ideal gas equation -
PV = nRT
​Where P = pressure
V= volume
n = number of moles
R = gas constant (0.082 L atm/ mol. K)
​T = temperature
Putting the values in the given equation -

0.7444 = n $×$ 59.286
n = 0.01255
Now, number of moles  = mass / Molar mass
0.01255 = 3.2 / Molar mass
Molar mass = 254.98008 g mol​-1
We know tha atomic mass of S = 32 g
so dividing by 16 we will get the number of sulfur atoms
number of atoms = 254.98/32
number of atoms  = 7.96 $~$ 8
Thus, Molecular formula will be S8
Vapor density = molecular mass/ 2
vapor density = 127.49

• 36
Given-
Mass of sulphur  = 3.2 g
Temperature = 450oC or 723 K
Volume = 780 mL or 0.780 L
Pressure = 723 mm Hg or 0.9513 atm ( 1 mm Hg = 0.0013158 atm)
Calculation
Using ideal gas equation -
PV = nRT
​Where P = pressure
V= volume
n = number of moles
R = gas constant (0.082 L atm/ mol. K)
​T = temperature
Putting the values in the given equation -

0.7420 = n $×$ 59.286
n = 0.01252
Now, number of moles  = mass / Molar mass
0.01252 = 3.2 / Molar mass
Molar mass = 255.59 g mol​-1
We know the Molar mass of S = 32 g
so dividing by 16 we will get the number of sulphur atoms
number of atoms of S = 255.59/32
number of atoms of S = 7.98 $~$ 8
Thus, Molecular formula will be S8
Vapour density = molecular mass/ 2
vapour density = 127.49

• 13
Given-
Mass of sulphur  = 3.2 g
Temperature = 450oC or 723 K
Volume = 780 mL or 0.780 L
Pressure = 723 mm Hg or 0.954 atm ( 1 mm Hg = 0.0013158 atm)
Calculation -
Using ideal gas equation -
PV = nRT
​Where P = pressure
V= volume
n = number of moles
R = gas constant (0.082 L atm/ mol. K)
​T = temperature
Putting the values in the given equation -
0.954 atm × 0.780L  = n ×0.082 L atm /mol .K × 723K

0.7444 = n    ×   59.286
n = 0.01255
Now, number of moles  = mass / Molar mass
0.01255 = 3.2 / Molar mass
Molar mass = 254.98008 g mol​-1
We know tha atomic mass of S = 32 g
so dividing by 32 we will get the number of sulfur atoms
number of atoms = 254.98/32
number of atoms  = 7.96    ~   8
Thus, Molecular formula will be S8
Vapor density = molecular mass/ 2
vapor density = 127.49
• 15
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