Gas Stoichiometry Word Problem

Question

Diesel fuel produces 10.17 kg CO2 for every gallon burned. If a semi truck averages 6 miles per gallon of diesel, how many liters of CO2 will it generate over a 1000 mile trip through Death Valley, where the average air temperature is 45 C and the ambient air pressure is 800 torr?

Answer 1

1000 miles x 1 gal / 6 miles = 166.67 gallons of fuels used

kg of CO₂ produced = 166.67 gal x 10.17 kg / gal = 1695 kg of CO₂ produced

moles of CO₂ produced = 1695 kg CO₂ x 1000 g / kg x 1 mole / 44.01 g = 38,514 moles CO₂ produced

Assuming CO₂ behaves as an ideal gas, we can now use the ideal gas law to calculate Liters of CO₂...

PV = nRT

P = pressure = 800 torr x 1 atm / 760 torr = 1.05 atm

V = Volume in liters = ?

n = moles = 38,514

R = gas constant = 0.0821 Latm/Kmol

T = temperature in Kelvin = 45C + 273 = 318K

Solving for V, we have...

V = nRT / P = (38,514 mol)(0.0821 Latm/Kmol)(318K) / 1.05 atm

V = 957,634 liters or 958,000 liters (rounded to 3 significant figures)