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 57.0 cm wide and 68.4 cm high. The maximum safe pressure inside the vessel has been measured to be7.90 MPa For a certain reaction the vessel may contain up to 11.5 kg of carbon dioxide 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.

The maximum safe operating temperature the engineer should recommend for this reaction is 590. °C (3 significant figures)

Explanation:

1) Data:

a) Cylinder diameter: d = 17.0 cm

b) Cylinder height: H = 20.4 cm

c) p = 2.20 MPa

d) compound: BF₃ gas

e) mass, m = 0.0985 kg

2) Formulae:

a) Volume of a cylinder, V = π r² H

b) Number of moles, n = mass in grams / molar mass

c) Ideal gas equation: pV = nRT

3) Solution:

a) Volume (V)

i) r = d / 2 = 17.0 cm / 2 = 8.50 cm

ii) V = V = π r² H = π (8.50 cm) ² (20.4 cm) = 4,630 cm³ = 4.630 liter

b) Number of moles (n)

i) molar mass BF₃: 67.82 g/mol

ii) n = mass in grams / molar mass = 98.5 g / 67.82 g/mol = 1.452 mol

c) Temperature

i) pressure conversion: 2.20 MPa = 22.21 atm

ii) pV = nRT ⇒ T = pV / (nR)

T  = 22.21 atm × 4.630 liter / (1.452 mol × 0.08206 atm-liter /K-mol(

T = 863 K

T = 863 - 273 °C = 590. °C ← answer

The result is given with 3 significant figures, since that is the number of significant figures used for the data.

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