# An unknown gas shows a density of 2.4g/litre at 273 degree celcius and 140 mm Hg pressure.What is the gram molecular mass of this gas?

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Given

density = 2.4 g/L

Mass = 2.4 g

Volume = 1 Litre

Pressure = 140 mmHg = 0.184 atm

absolute temperature = 273 C + 273 = 546 K

Gas constant = 0.082 `LatmK^-1mol^-1`

molar mass = ?

Formula

`PV = nRT`

`n = (PV)/(RT)`

`n = (0.184*1)/(0.082*546)`

n = 0.00410

n = moles = `(mass)/(molar mass)`

molar mass = mass/moles

Molar mass = `(2.4)/(0.00410)`

Molar mass = 585.3 g/mol

PV = nRT

n = mass / mw

substituting

PV = (mass / mw) RT

rearrainging

mw = (mass / V) RT / P = ρ RT/P

mw = molecular weight, molar mass, etc

ρ = density = mass / V = 2.4 g/L

R = ideal gas constant = 0.08206 Latm/moleK

T = 273C = 273+273 K = 546 K

P = 140 mm Hg = 140 mm Hg x (1 atm / 760 mm Hg) = 0.184 atm

substituting...

mw = (2.4 g/L) x (0.08206 Latm/moleK) x (546 K) / (0.184 atm) = 584.41 g/mole