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 = 1 atm
= 101325 pa
d = ?
R = 8.314 J mol⁻¹ K⁻¹
T = (59.9 273) K = 332.9 K
M = 159.808 g/mol = 159.8 x 10⁻³ kg/mol
By substitution,
101325 Pa = (d x 8.314 J mol⁻¹ K⁻¹ x 332.9 K) / 159.8 x 10⁻³ kg/mol
d = (101325 Pa x 159.8 x 10⁻³
kg/mol) / (8.314 J mol⁻¹ K⁻¹ x 332.9 K)
d = 5.85 kg m⁻³
Hence, the density
of the Br₂ at 59.9 °C and 1 atm is 5.85 kg m⁻³.
Assumption made
is "Br₂ gas has an ideal
gas behavior".
