Homes in rural areas where natural gas service is not availa

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 400 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 hours 3 item attempts

Solution

we have to calculate how many moles are in 165 L at 25 C,

temperature in kelvin = 25 + 273.15 = 298.15 Kelvin

P * V = n * R * T; where

P is pressure

V is volume

R is gas constant : 0.082 atm L / K mol

T is Temperature (Kelvin or Fahrenheit)

Rearrange the equation to get

n = P * V / (R*T) = moles

n = 1 * 165 / (0.082 * 298.15) = 6.75 moles of propane

so you require 1 hour to burn 6.75 moles of propane

you have 400 gallons , 1 gallon has 3.785 liters so multiply:

400 * 3.78 = 1514.16 liters available

calculate the kg of propane using the density

density = mass / volume

mass = density * volume

mass = 0.5077 *1514.16 = 768.739 kg of propane = 768 739 grams of propane

calculate the moles of propane available

molar mass propane = 44.1 g / mol

moles = 768 739 grams of propane / 44.1 = 17431.72 moles of propane

so divide total moles by the moles consumed in 1 hour

17431.72 / 6.75 moles of propane = 2582.477 hours required for 1 burner

you have 4 burners so

2582.477 / 4 = 645.62 hours

*only 1 question at a time please =)