a chemical engineer must calculate the maximum safe operating temperature of a high - pressure gas reaction…

Explanation:

Step 1: Determine the volume of the cylinder

The vessel is a cylinder, so we use the formula for the volume of a cylinder, ( V = \pi r^2 h ). The diameter is 57.0 cm, so the radius ( r = \frac{57.0}{2} = 28.5 ) cm. The height ( h = 68.4 ) cm. [ V=\pi\times(28.5)^2\times68.4 ] [ V=\pi\times812.25\times68.4 ] [ V\approx3.1416\times812.25\times68.4 ] [ V\approx3.1416\times55557.9 ] [ V\approx174500\space cm^3 = 174.5\space L \quad (\text{since } 1\space L = 1000\space cm^3) ]

Step 2: Calculate moles of chlorine pentafluoride (( ClF_5 ))

Molar mass of ( ClF_5 ): ( Cl = 35.45 \space g/mol ), ( F = 19.00 \space g/mol ), so molar mass ( M = 35.45 + 5\times19.00 = 35.45 + 95.00 = 130.45 \space g/mol ). Mass ( m = 9.44 \space kg = 9440 \space g ). Moles ( n=\frac{m}{M}=\frac{9440}{130.45}\approx72.37\space mol )

Step 3: Use the ideal gas law ( PV = nRT ) to find temperature ( T )

Pressure ( P = 2.30 \space MPa = 2300 \space kPa ) (since ( 1 \space MPa = 1000 \space kPa )), ( V = 174.5 \space L ), ( n = 72.37 \space mol ), ( R = 8.314 \space \frac{L\cdot kPa}{mol\cdot K} ) [ T=\frac{PV}{nR} ] [ T=\frac{2300\times174.5}{72.37\times8.314} ] [ T=\frac{401350}{599.7} ] [ T\approx669.3\space K ]

Step 4: Convert Kelvin to Celsius

( T(^\circ C)=T(K)-273.15 ) [ T(^\circ C)=669.3 - 273.15 = 396.15\approx396^\circ C ]

Answer:

( 396^\circ \text{C} )