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A cylindrical tank, 6 inches in diameter and 1.2 meters long, is filled with methane gas at a pressure of 80 psig and 65°F. How many kilograms of methane gas are filled in the tank?

Answer :

Final answer:

The cylindrical tank is filled with approximately 0.0108 kilograms of methane gas.

Explanation:

To calculate the mass of methane gas in the tank, we need to follow these steps:

  1. Calculate the volume of the cylindrical tank using its diameter and length.
  2. Convert the volume from cubic meters to liters.
  3. Convert the pressure from psig to pascals.
  4. Convert the temperature from Fahrenheit to Kelvin.
  5. Use the ideal gas law equation PV = nRT to calculate the number of moles of methane gas.
  6. Convert the number of moles to kilograms using the molar mass of methane gas.

Let's calculate each step:

  1. The radius of the tank is half of the diameter, so the radius is 6 inches / 2 = 3 inches = 0.0762 meters.
  2. The volume of a cylinder is given by V = πr^2h, where r is the radius and h is the height. Plugging in the values, we get V = π(0.0762 meters)^2 * 1.2 meters = 0.0277 cubic meters.
  3. Converting the volume to liters, we get 0.0277 cubic meters * 1000 liters/cubic meter = 27.7 liters.
  4. Converting the pressure from psig to pascals, we get 80 psig * 6894.76 pascals/psig = 551,580 pascals.
  5. Converting the temperature from Fahrenheit to Kelvin, we get (65°F - 32) * 5/9 + 273.15 = 291.48 Kelvin.
  6. Using the ideal gas law equation PV = nRT, we can rearrange it to solve for n (number of moles): n = PV / RT. Plugging in the values, we get n = (551,580 pascals) * (27.7 liters) / ((8.314 J/(mol·K)) * (291.48 Kelvin)) = 0.674 moles.
  7. Finally, to convert moles to kilograms, we multiply by the molar mass of methane gas: 0.674 moles * 16.04 grams/mole * (1 kilogram / 1000 grams) = 0.0108 kilograms.

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