A chemical engineer must calculate the maximum safe operating temperature of a h

Question

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 31.0 cm wide and 37.2 cm high. The maximum safe pressure inside the vessel has been measured to be 5.90 MPa. For a certain reaction the vessel may contain up to 3.27 kg of chiorine pentafluoride 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.

Explanation / Answer

We can use the ideal gas equation PV = nRT for calculating the safe temperature.

Given the maximum safe pressure = 5.90 MPa = 5.90x 9.869 atm [ one MPa = 9.869atm]= 58.23 atm

volume of cylinder is given by pi x r2 xh where pi = 22/7, r = radius of cylinder = 31/2 cm, height = 37.2 cm

Thus Volume = ( 22/7)(31/2)2x 37.2 cm3 =28088.65 cc = 28.088L

number of moles of gas = weight of gas / molar mass = [3.27x1000g]/ 130.5 g/mol = 25.057 mol

Substituting these values in PV=nRT we get temperture as

T = 795.051K = 521.90 o C

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