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 50.0cm wide and 60.0cm high. The maximum safe pressure inside the vessel has been measured to be 7.40MPa. For a certain reaction the vessel may contain up to 19.2kg of sulfur hexafluoride 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

Answer:

525°C is the maximum safe operating temperature the engineer should recommend for this reaction.

Explanation:

Volume of the cylindrical container = V = $\pi r^2h$

Height of the vessel = h =60.0 cm

Diameter of the vessel = d = 50.0 cm

Radius of the vessel = r = 0.5d = 25.0 cm

$V=3.14\times (25.0 cm)^2\times 60.0 cm=117,809.72 cm^3=117,809.72mL$

$1 cm^3=1 mL$

1 mL = 0.001 L

117,809.72 mL = 117,80972 L ≈ 118 L

Pressure of the gas in vessel = P = 7.40 MPa = $7.40\times 10^6 Pa$

$1 MPa = 10^6 Pa$

1 atm = 101325 Pa

$P=\frac{7.40\times 10^6}{101325} atm=73.0 atm$

Mass sulfur hexafluoride gas = 19.2 kg = 19200 g

1 kg = 1000 g

Moles of sulfur hexafluoirde = $\frac{19200 g}{146 g/mol}=131.5 mol$

Temperature of the gas in vessel = T

Using an ideal gas equation :

$PV=nRT$

$T=\frac{PV}{nR}=\frac{73.0 atm\times 118 L}{0.0821 atm L/mol K\times 131.5 mol}$

T = 797.8 ≈ K 798 K

T = 798 - 273°C = 525°C

525°C is the maximum safe operating temperature the engineer should recommend for this reaction.