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 32.0cm wide and 38.4cm high. The maximum safe pressure inside the vessel has been measured to be 8.30MPa . For a certain reaction the vessel may contain up to 2.92kg of boron trifluoride gas. Calculate the maximum safe operating temperature the engineer should recommend for this reaction. Write your answer in degrees Celsius. Be sure your answer has the correct number of significant digits

Answer 1

Volume of cylindrical vessel = ( Pi/4)*d2*h, d= diameter of vessel = 32 cm , h= height= 38.4 cm

volume of vessel = (22/28)* 32*32*38.4 =30895.54 cm3, 1000CC = 1L, volume of vessel, V= 30895.54/1000 = 30.9 L

boron trifluoride is BF3 and its molar mass = 68 g/mole, mass of BF3= 2.92 kg, converting this mass into gram, mass BF3= 2.92 kg*1000 gm/kg= 2920 gm, n= moles of gas= 2920/68 =42.94 moles

given P= pressure =8.3 Mpa, 1Mpa = 8.9 atm, 8.3Mpa= 8.3 Mpa* 8.9 atm/Mpa= 73.87 atm

assuming ideal gas law is obeyed and R= 0.0821 L.atm/mole.K

T= maximum operating temperature= PV/nR = 73.87* 30.9/ (0.0821* 42.94)=647 K

since K ( kelving)= t( deg.c)+273

t ( deg.c)= 647-273= 374 deg.c, maximum operating temperature