Answer : 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) and 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 = 113.0 kPa = 113.0 x 10³ 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,
113.0 x 10³ Pa = (d x 8.314 J mol⁻¹ K⁻¹ x 325 K) / 44.0 x 10⁻³ kg/mol
d = (113.0 x 10³ 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.
Assumption made is "N₂O gas has an ideal gas behavior".
