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 stainless-steel cylinder that measures 25.0 cm wide and 30.0 cm high. The maximum safe pressure inside the vessel has been measured to be 6.60 MPa. For a certain reaction the vessel may contain up to 0.800 kg of carbon dioxide 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

Volume of cylinder = pi x r2 x h  = 3.14 x (25/2)cm^2 x 30cm = 14725.78 cm^3 or 0.01472578m^3

Now, using ideal gas law, PV = nRT

P = 6.60E6Pa

V = 0.01472578m^3

n= no. of moles = mas staken/ molar mass of CO2 = 800g/44g/mol = 18.18moles

R =  8.314 J/mol.K

So, (6.60x10^6 ) x 0.01472578  = 18.18 x 8.314 xT

T = 643K = 643-273.15 = 369.85oC = 370 oC = maximum safe operating temperature

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