The maximum safe operating temperature for this reaction is equal to 895°C.
Given the following data:
Scientific data:
Radius, r = [tex]\frac{width}{2} =\frac{22}{2} =11\;cm[/tex]
First of all, we would determine the volume of the stainless-steel cylinder by using this formula:
[tex]V=\pi r^2 h\\\\V = 3.142 \times 11^2 \times 26.4\\\\[/tex]
Volume, V = 10,036.81 [tex]cm^3[/tex].
In liters, we have:
Volume, V = 10.04 Liters.
Next, we would determine the number of moles of dinitrogen monoxide ([tex]N_2F_2[/tex]) gas:
[tex]Number \;of \;moles = \frac {mass}{molar\;mass}\\\\Number \;of \;moles = \frac {537}{66}[/tex]
Number of moles = 8.136 moles.
Now, we can solve for the maximum safe operating temperature by applying the ideal gas equation:
[tex]PV=nRT\\\\T=\frac{PV}{nR} \\\\T=\frac{6.30 \times 10^3 \times 10.04}{8.136 \times 8.314}\\\\T=\frac{60541.2}{67.6427}[/tex]
T = 895.02 ≈ 895°C.
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