The molar mass of the material : 47 g/mol
In general, the gas equation can be written
[tex]\large{\boxed{\bold{PV=nRT}}}[/tex]
where
P = pressure, atm
V = volume, liter
n = number of moles
R = gas constant = 0.082 l.atm / mol K
T = temperature, Kelvin
[tex]\tt PV=\dfrac{mass}{molar~mass}RT\\\\molar~mass=\dfrac{mRT}{PV}\\\\molar~mass=\dfrac{0.075\times 0.082\times 343}{1\times 0.045}=46.876\approx 47[/tex]
The molar mass of the material has been 46.93 grams.
The gas been assumed to be an ideal gas. For an ideal gas:
Pressure × Volume = moles × R constant × Temperature.
Moles can be given as:
Moles = [tex]\rm \dfrac{weight}{molecular\;weight}[/tex]
Ideal gas equation can be given in terms of moles as:
Pressure × Volume = [tex]\rm \dfrac{weight}{molecular\;weight}[/tex] × R constant × Temperature.
Pressure = 1 atm
Volume = 0.045 L
Weight = 0.075 grams
R = 0.08206 L.atm/mol.K
Temperature = 70[tex]\rm ^\circ C[/tex] = 343.15 K
Substituting the values:
1 × 0.045 = [tex]\rm \dfrac{0.075}{molecular\;weight}[/tex] × 0.08206 × 343.15
0.045 = [tex]\rm \dfrac{0.075}{molecular\;weight}[/tex] × 28.1588
Molecular weight = 46.93 grams.
The molar mass of the material has been 46.93 grams.
For more information about the molar mass, refer to the link:
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