Chemistry-temperature

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 19.0 cm wide and 22.8cm high. The maximum safe pressure inside the vessel has been measured to be 7.90 MPa . For a certain reaction the vessel may contain up to 0.577 kg of dinitrogen difluoride gas. Calculate the maximum safe operating temperature the engineer should recommend for this reaction. Write your answer in degrees Celsius. report your answer in the correct number of significant digits.

Answer 1

This ultimately comes down to a problem involving the Ideal Gas Law, PV = nRT. But before we can use this, we will first have to determine the volume (V) of the container, and the number of moles (n) of gas that are present. The maximum safe pressure (P) is provided (7.90 MPa), and R is the gas constant (8.314 LkPa/Kmol). We will want to convert the pressure to kPa in order to agree with the units of R.

Volume of a cylinder = π r² h = (3.1416)(9.5 cm)²(22.8 cm) = 6464 cm³ = 6464 mls = 6.464 L

Moles of dinitrogen difluoride (N₂F₂) = g / molar mass = 577 g / 66.01 g/mol = 8.741 moles

Pressure = 7.90 MPa x 1000 kPa / MPa = 7900 kPa

R = 8.314 LkPa/Kmol

Temperature in Kelvin = ?

Solving the Ideal Gas Law for T we have...

PV = nRT

T = PV/nR = (7900 kPa)(6.464 L) / (8.741 mols)(8.314 LkP/Kmol)

T = 702.70 K

Converting this to degrees C we have...

702.70 C - 273.15 = 429.55

Rounding to 3 significant figures ...

T = 430.ºC

So, one might say that the maximum SAFE operating temperature would be something less than 430.ºC just to be on the "safe side".