chemistry question

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 37.0cm

 wide and 44.4cm

 high. The maximum safe pressure inside the vessel has been measured to be 8.90MPa

.

For a certain reaction, the vessel may contain up to 

9.01kg

 of sulfur tetrafluoride 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.

temperature:

°C

Answer 1

Find the volume of the cylinder:

V = h π r² (44.4 cm)(3.14)(18.5 cm)²

h = height = 44.4 cm

r = radius = 1/2 37.0 cm = 18.5 cm

V = (44.4 cm)(3.14)(18.5 cm)²

V = 47,739 cm³ = 4.77 L

Using the ideal gas law PV = nRT we can find the temperature (T) for the given conditions, but first we will need to find the moles (n) of gas.

Sulfur tetrafluoiride gas = SF₄ with a molar mass of 108 g / mol

moles SF₄ = 9.01 kg x 1000 g / kg x 1 mol / 108 g = 83.4 moles of SF₄

Before plugging values into the ideal gas law equation, we must first convert 8.90 MPa to atm

8.90 MPa x 1000 kPa/1 MPa x 1 atm / 101.325 kPa = 87.8 atm

Now plugging this into the ideal gas law equation, and solving for T, we have...

PV = nRT

T = PV / nR = (87.8 atm)(4.77 L) / (83.4 mols)(0.0821 Latm/Kmol)

T = 61.16K

Converting this to ºC

61.16K - 273.15 = -211.98ºC = -212ºC