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 13.0cm wide and 15.6cm high. The maximum safe pressure inside the vessel has been measured to be 1.90MPa.For a certain reaction the vessel may contain up to 0.0828kg of sulfur hexafluoride 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 ideal gas constant times the temperature of the gas (PV=nRT).

First, we need to convert the pressure from MPa to Pa, the volume from cm^3 to m^3, and the mass of sulfur hexafluoride to moles.

1.90 MPa = 1.90 x 10^6 Pa

The volume of the cylinder is given by the formula V=πr^2h, where r is the radius and h is the height. The radius is half the width, so r = 13.0 cm / 2 = 6.5 cm = 0.065 m. The height is 15.6 cm = 0.156 m. So, the volume is V = π(0.065 m)^2(0.156 m) = 0.000052 m^3.

The molar mass of sulfur hexafluoride (SF6) is approximately 146 g/mol. So, 0.0828 kg = 82.8 g, which is 82.8 g / 146 g/mol = 0.567 moles.

Now we can substitute these values into the ideal gas law and solve for T:

(1.90 x 10^6 Pa)(0.000052 m^3) = (0.567 mol)(8.314 J/(mol·K))T

Solving for T gives T = (1.90 x 10^6 Pa x 0.000052 m^3) / ((0.567 mol)(8.314 J/(mol·K))) = 227.5 K

To convert this to degrees Celsius, we subtract 273.15 from the Kelvin temperature: 227.5 K - 273.15 = -45.65°C

So, the maximum safe operating temperature the engineer should recommend for this reaction is -45.65°C. However, since we need to round our answer to 3 significant digits, the final answer is -45.7°C.