A chemical engineer must calculate the maximum safe operating temperature of a high-pressure gas reaction vessel. The vessel is a stainless-steel cylinder that measures 39.0cm wide and 46.8cm high. The maximum safe pressure inside the vessel has been measured to be 5.30MPa. For a certain reaction the vessel may contain up to 7.20kg of sulfur hexafluoride gas. Calculate the maximum safe operating temperature the engineer should recommend for this reaction. Write your answer in degrees Celsius. Round your answer to 3 significant digits.

Maximum safe operating temperature = 450 °C

Explanation:

First, the volume of the cylindrical vessel is determined using the formula:

v = πr²h

Radius, r, of stainless steel vessel = width or diameter / 2

r = 39.0 cm / 2 = 19.5 cm

height of vessel = 46.8 cm

volume of cylinder = 22/7 × 19.5² × 46.8 = 55929.343 cm³ = 0.05593 m³

Using the ideal gas equation to calculate the maximum safe temperature

PV = nRT

pressure, P = 5.30 MPa = 5.30 × 10⁶ Pa

R = 8.314 J/mol.K

n = mass of gas/ molar mass of gas

molar mass of SF₆ = 146 g/mol

mass of Sf₆ = 7.20 kg = 7200 g

n = 7200/146 = 49.315 moles

T = PV/nR

T = (5.30 × 10⁶ × 0.05593) / (49.315 × 8.314)

T = 722.98 K

T in °C = 714.98 - 273.15 = 449.83 °C

Therefore, maximum safe operating temperature = 450 °C