Calculate the density of br2(g) at 59.9oc and 1.00 atm pressure

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".

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