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Homes in rural areas where natural gas service is not available often rely on propane to fuel kitchen ranges. The propane is stored as a liquid, and the gas to be burned is produced as the liquid evaporates. Suppose an architect has hired you to consult on the choice of a propane tank for such a new home. The propane gas consumed in 1.0 hour by a typical range burner at high power would occupy roughly 165 L at 25°C and 1.0 atm, and the range chosen by the client will have 4 burners. If the tank under consideration holds 500 gallons of liquid propane, what is the minimum number of hours it would take for the range to consume an entire tank of propane? The density of liquid propane is 0.5077 kg/L.

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sebassandin

Answer:

[tex]t=808.9h[/tex]

Explanation:

Hello,

In this case, the moles consumed in one our by 4 burners turns out:

[tex]n=\frac{165L*1atm}{0.082\frac{atm*L}{mol*K}*298.15K}*4=27.0\frac{mol}{h}[/tex]

Now, 500 gallons of propane are available and equivalent to the following amount in moles (propane's molar mass is 44g/mol):

[tex]n_{available}=500galC_3H_8*\frac{3.785LC_3H_8}{1galC_3H_8}*\frac{0.5077kgC_3H_8}{1LC_3H_8}*\frac{1000gC_3H_8}{1kgC_3H_8}*\frac{1molC_3H_8}{44gC_3H_8} \\n_{available}=21836.9molC_3H_8[/tex]

Finally, the time for the 4 burners to burn the 500 gallons of propane result in:

[tex]t=\frac{21836.9mol}{27.0mol/h} \\\\t=808.9h[/tex]

Best regards.

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