Choosing the Right Propane Tank for Your Home in Rural Areas

What is the minimum number of hours it would take for a range with 4 burners to consume an entire 400-gallon tank of liquid propane? The minimum number of hours it would take for a range with 4 burners to consume an entire 400-gallon tank of liquid propane is 2666.7 hours.

Understanding the Calculation

The key to solve this problem is that we are given the propane gas consumed in one hour, which gives us the volume consumed at 1 atm and 298 K (25 + 273). Using the gas law, we can calculate the rate of propane consumption per hour:

Using the ideal gas law formula PV = nRT, where n = PV/RT, we can calculate the number of moles of propane consumed per hour:

n = 1 atm x 165 L / (0.08206 L atm / kmol x 298 K) = 6.75 mol propane

Next, we calculate the mass of propane:

6.75 mol x 44 g/mol = 296.88 g

Converting this mass to kilograms:

296.88 g / 1000 g/kg = 0.30 kg

Calculating the volume in liters this mass represents by dividing by the density:

0.30 kg / 0.5077 kg/L = 0.59 L

Converting this to gallons:

0.59 L x 1 gallon / 3.785 L = 0.15 gallon

Finally, we calculate how many hours the 400-gallon propane tank will deliver:

400 gallons / 0.15 gallon/hr = 2666.7 hours

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