Question

A website promoting the use of alternative energy vehicles and hybrid technologies claims that, \"A typical automobile in the USA uses about 1.5 gallons of gasoline every day, producing about 25 lbs of carbon dioxide.\" To determine the truth of this statement, calculate how many pounds of carbon dioxide are produced when 1.500 gallons of gasoline are combusted. Assume that the primary ingredient in gasoline is octane, C8H18(l), which has a density of 0.703 g÷mL "1..

Answer 1

The correct answer is 27.0 lb.

First, there is a need to write the combustion reaction of C₈H₁₈ (l):

2C₈H₁₈ (l) + 25 O₂ (g) → 16 CO₂ (g) + 18 H₂O (g)

Now convert the volume of octane from gallons to ml,

1.0 gallon = 3785.41 ml

1.5 gallons × 3785.41 ml / 1.0 gallon = 5685 ml

Now using formula of density calculate the mass of octane as follows:

Density = mass / volume

Mass = density × volume

mass octane = 5685 ml × 0.703 g / ml = 3996.6 g

Then there is a need to calculate the number of moles of octane with its molar mass:

moles octane = 3996.6 g (1 mole of C₈H₁₈) / 114.23 g = 34.987 mol

2 mole of C₈H₁₈ produce 16 CO₂

34.987 mole C₈H₁₈ will produce 16CO₂ / 2 mol C₈H₁₈ × 34.987 mol C₈H₁₈ = 279.9 moles CO₂

Now there is a need to convert the moles of CO₂ into its mass with its molar mass as follows:

mass CO₂ = 279.9 moles × 44.009 g/mol = 12318 g CO₂ = 12.318 Kg

Now, 1 Kg = 2.20 lb

12.318 Kg (2.20 lb) / 1.00 Kg = 27.0 lb