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 55.0cm wide and 66.0cm high. The maximum safe pressure inside the vessel has been measured to be 3.60MPa.For a certain reaction the vessel may contain up to 11.6kg 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.

To solve this problem, we need to use the ideal gas law, which states that the pressure of a gas times its volume is equal to the number of moles of the gas times the gas constant times the temperature of the gas (PV = nR*T).

First, we need to convert the pressure from MPa to Pa, the volume from cm to m, and the mass of sulfur tetrafluoride to moles.

1 MPa = 1,000,000 Pa, so 3.60 MPa = 3.60 * 1,000,000 = 3,600,000 Pa.

The volume of the cylinder is given by the formula V = πr²h, where r is the radius and h is the height. The radius is half the width, so r = 55.0 cm / 2 = 27.5 cm = 0.275 m. The height is 66.0 cm = 0.66 m. So, the volume is V = π*(0.275 m)²*(0.66 m) = 0.157 m³.

The molar mass of sulfur tetrafluoride (SF4) is approximately 108 g/mol. So, 11.6 kg = 11,600 g, which is 11,600 g / 108 g/mol = 107.41 mol.

Now we can use the ideal gas law to solve for the temperature. Rearranging the formula to solve for T gives us T = PV / (nR). The gas constant R is 8.314 J/(mol*K) when the pressure is in Pa and the volume is in m³.

So, T = (3,600,000 Pa * 0.157 m³) / (107.41 mol * 8.314 J/(mol*K)) = 68,400 K.

Finally, we need to convert this temperature from Kelvin to Celsius. The formula to convert from Kelvin to Celsius is C = K - 273.15.

So, the maximum safe operating temperature is 68,400 K - 273.15 = 68,126.85 °C.

Rounding to three significant digits gives us a final answer of 68,100 °C.