Question

A chemical engineer must calculate the maximum safe operating temperature of a high-pressure gas reaction vessel. The vessel is stainless-steel cylinder that measures 25.0 cm wide and 30.0 cm high. The maximum safe pressure inside the vessel has been measured to be 6.60 MPa. For a certain reaction the vessel may contain up to 0.800 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.

Answer 1

Maximum safe operating temperature = 370°C

Step-by-step explanation:

Radius of stainless steel vessel = 25.0/2 = 12.5 cm

height of vessel = 30.0 cm

`volume =\pi r^2h`

Substitute the values in the above formula

`volume=3.14 * (1.25\ cm)^2 * 30.0\ cm\\=14718.75\ cm^3\ 0.014718\ m^3`

Maximum safe temperature is calculated by using ideal gas equation

PV = nRT

pressure, P = 6.60 mPa =
`6.60* 10^6\ Pa`

R = 8.314 J/mol.K

`n=(m)/(M)`

molecular mass of CO2 = 44 g/mol

mass of CO2 = 0.800 kg = 800 g

`n=(800\ g)/(44\ g/mol) \\=18.18\ mol`

`6.60* 10^(6) * 0.014718=18.18* 8.314 * T\\T=643\ K`

T (K)=T (°C) + 273.15

643 K = T (°C) + 273.15

T = 643 - 273.15

= 369.85 °C = 370°C

Maximum safe temperature = 370°C