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 44.0 cm wide and 52.8 cm high. the maximum safe pressure inside the vessel has been measured to be 8.40 mpa. for a certain reaction the vessel may contain up to 12.4 kg 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

Explanation:

Step1: Calculate the volume of the cylinder

The volume formula for a cylinder is $V=\pi r^{2}h$. The diameter $d = 44.0$ cm, so the radius $r=\frac{d}{2}=\frac{44.0}{2}=22.0$ cm $ = 0.220$ m, and the height $h = 52.8$ cm $=0.528$ m. Then $V=\pi\times(0.220)^{2}\times0.528\approx0.0801$ m³.

Step2: Calculate the number of moles of sulfur tetrafluoride

The molar - mass of $SF_{4}$ is $M=(32.07 + 4\times19.00)=108.07$ g/mol. The mass of $SF_{4}$ is $m = 12.4$ kg $=12400$ g. The number of moles $n=\frac{m}{M}=\frac{12400}{108.07}\approx115$ mol.

Step3: Use the ideal gas law

The ideal gas law is $PV = nRT$, where $P = 8.40$ MPa $=8.40\times10^{6}$ Pa, $V\approx0.0801$ m³, $n\approx115$ mol, and $R = 8.314$ J/(mol·K). We can solve for $T$: $T=\frac{PV}{nR}$.
Substitute the values: $T=\frac{8.40\times10^{6}\times0.0801}{115\times8.314}\approx698$ K.

Step4: Convert the temperature to Celsius

The conversion formula from Kelvin to Celsius is $t=T - 273.15$. So $t=698 - 273.15\approx425^{\circ}C$.

Answer:

$425^{\circ}C$