Respuesta :
The density of the N₂O at 325 K and 113.0 kPa is 1.84 kg m⁻³.
Explanation :
Density (kg/m³) = mass (kg) / Volume (m³)
d = m/V (1)
Ideal gas law,
PV = nRT (2)
Where,
P is the pressure of the gas (Pa)
V is the volume of the gas (m³)
n is the number of moles of gas (mol)
R is the universal gas constant ( 8.314 J mol⁻¹ K⁻¹)
T is temperature in Kelvin.
n = m/M (3)
Where,
n is number of moles
m is mass and M is molar mass.
From (2) and (3),
PV = (m/M) RT
By rearranging,
P = (m/VM)RT (4)
From (1) and (4)
P = (dRT) / M
The given data,
P = 1.12 atm = 1.12 x 101325 Pa = 113484 Pa
d = ?
R = 8.314 J mol⁻¹ K⁻¹
T = 325 K
M = 44.0 g/mol = 44.0 x 10⁻³ kg/mol
By substitution,
113484 Pa = (d x 8.314 J mol⁻¹ K⁻¹ x 325 K) / 44.0 x 10⁻³ kg/mol
⇒d = (113484 Pa x 44.0 x 10⁻³ kg/mol) / (8.314 J mol⁻¹ K⁻¹ x 325 K)
⇒d = 1.84 kg m⁻³
Hence, the density of the N₂O at 325 K and 113.0 kPa is 1.84 kg m⁻³.
It is assumed that "N₂O gas has an ideal gas behavior".
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