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 21.0cm wide and 25.2cm high. The maximum safe pressure inside the vessel has been measured to be 4.00MPa. For a certain reaction the vessel may contain up to 0.474kg 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.

Explanation:

Volume of cylinder = πr²h where r is radius of cylinder, h is height of cylinder

r = d/2 = 21/2 = 10.5 cm; h = 25.2 cm

volume of cylinder = (22 * 10.5 cm * 10.5 cm * 25.2 cm) / 7

volume = 8731.8 cm³ = 8.7318 L

Using the ideal gas equation, PV = nRT

P = 4.00 MPa = 4.0 * 10³ kPa, V = 8.7318 L, R = 8.314 L.kPa/mol.K,

n = mass / molar mass

where mass = 0.474 kg or 474 g, molar mass of BF₃= 68 g/mol

n = 474 g / 68 g/mol = 6.9706 moles

making T subject of formula in the ideal gas equation;

T = PV/nR

T = (4.0 * 10³ kPa * 8.7318 L)/(6.9706 mol * 8.314 L.kPa/mol.K)

T = 602.675 K

T in °C =  K - 273.15

T = 602.675 -273.15 = 329.5 °C

T = 330 °C