A chemical engineer must calculate the maximum safe operating temperature of a h

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 38.0 cm wide and 45.6 cm high. The maximum safe pressure inside the vessel has been measured to be 5.10 MPa. For a certain reaction the vessel may contain up to 2.13 kg of carbon dioxide 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.

Explanation / Answer

given

pressure = 5.10 x 10^6 Pa

now

volume of cylinder = pi x r2 x h

given

2r = 38

r = 19 cm = 0.19 m

h = 45.6 cm = 0.456 m

So

volume = pi x (0.19)^2 x 0.456

volume = 0.05169 m3

now

moles = mass / molar mass

so

moles of C02 = 2.13 x 1000 / 44

moles of C02 (n) = 48.41

now

we know that

PV = nRT

so

5.1 x 10^6 x 0.05169 = 48.41 x 0.0821 x T

T = 66330 K

T = 66330 - 273

T = 66060 C

so

the safe operating temperature is 66.06 x 10^3 C

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