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 41.0cm wide and 49.2cm high. The maximum safe pressure inside the vessel has been measured to be 3.70MPa. For a certain reaction the vessel may contain up to 2.50kg of dinitrogen difluoride gas.

Required:
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

`T=2.78x10^3 \°C`

Step-by-step explanation:

Hello,

In this case, considering that the safe temperature may be computed via the ideal gas law as we now the pressure, mass and volume via the dimensions:

`V=\pi r^2 h=\pi *(41.0cm)^2*49.2cm=2.60x10^5cm^3*(1L)/(1000cm^3) =260L`

The pressure in atm is:

`P=3.70MPa*(1x10^6Pa)/(1MPa) (1atm)/(101325Pa) =36.5atm`

And the moles considering the mass and molar mass (66 g/mol) of dinitrogen difluoride (N₂F₂):

`n_(N_2F_2)=2.50kg*(1000g)/(1kg)*(1mol)/(66g) =37.9mol`

In sich a way, by applying the ideal gas equation, which is not the best assumption but could work as an approximation due to the high temperature, the temperature, with three significant figures, will be:

`T=(PV)/(nR)=(36.5Pa*260L)/(37.9mol*0.082(atm*L)/(mol*K) )\\ \\T=3053.6K-273.15\\\\T=2.78x10^3 \°C`

Best regards.