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.

523°C

Explanation:

Step 1:

Data obtained from the question.

Diameter (d) = 31.0 cm

Height (h) = 37.2 cm

Pressure (P) = 5.90 MPa

Mass of ClF5 = 3.27 kg

Temperature (T) =?

Step 2:

Determination of the volume of the stainless-steel cylinder.

Volume of cylinder = πr^2h = π/4d^2h

V = π/4 x (31)^2 x 37.2

V = 28077.36 cm3

Converting the volume to L, we have:

1 cm3 = 0.001 L

Therefore, 28077.36 cm3 = 28077.36 x 0.001 = 28.07736 L

Step 3:

Conversion of 5.90 MPa to atm.

1 MPa = 9.869 atm

Therefore, 5.90 MPa = 5.90 x 9.869

= 58.2271 atm

Step 4:

Determination of the number of mole of chiorine pentafluoride gas (ClF5). This is illustrated below:

Molar Mass of ClF5 = 35.5 + (19x5) = 35.5 + 95 = 130.5g/mol

Mass of ClF5 = 3.27kg =3.27x10000

Mass of ClF5 = 3270g

Number of mole = Mass /Molar Mass

Number of mole of ClF5 = 3270/130.5

Number of mole of ClF5 = 25.057 moles

Step 5:

Determination of the temperature.

Applying the ideal gas equation

PV = nRT, the temperature T, can be obtained as follow:

P = 58.2271 atm

V = 28.07736 L

n = 25.057 moles

R (gas constant) = 0.082atm.L/Kmol

T=?

PV = nRT

Divide both side by nR

T = PV /nR

T = (58.2271x28.07736)/(25.057x0.082)

T = 795.68 K

Step 6:

Conversion of Kelvin temperature to celsius temperature.

°C = K - 273

K = 795.68 K

°C = 795.68 - 273

°C = 523°C

Therefore, the maximum safe operating temperature the engineer should recommend is 523°C

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