using the ideal equation of state

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 17.0cm wide and 20.4cm high. The maximum safe pressure inside the vessel has been measured to be 1.70 MPa. For a certain reaction the vessel may contain up to 0.0995kg of dinitrogen difluoride 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.

Answer 1

Since this is a question dealing with a gas (dinitrogen difluoride, N₂F₂), we should look to using the ideal gas law, PV = nRT. The trick is to find all the right variables, and then solve for T, temperature.

V = volume in liters, which we can calculate from the width and height of the cylinder.

V = π h r² = (3.1416)(20.4 cm)(8.5)² = 4630 cm³ = 4630 mls = 4.630 L = V

P = pressure in kPa = 1.70 MPa x 1000 kPa/MPa = 1700 kPa (note units for R that follow)

R = gas constant = 8.314 L-kPa/Kmol

n = moles = 0.0995 kg N₂F₂ x 1000 g/kg x 1 mol / 66g = 1.508 mols

T = ? in Kelvin

Solving for T, we have...

T = PV/nR = (1700 kPa)(4.630 L) / (1.508 mol)(8.314 LkPa/Kmol)

T = 628 K

Converting to ºC we have...

T = 628 - 273 = 355ºC