Assuming gasoline is 100% isooctane, with a density of 0.692g/mL, what mass of carbon dioxide is produced by the combustion of 1.2x10^10 gal of gasoline (the approximate annual consumption of gasoline in the U.S.)?

Example problem. Just follow the steps.

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2.2 x 10^12 mole co2

oral question

To calculate the mass of carbon dioxide produced by the combustion of the given amount of gasoline, we need to follow a step-by-step approach:

Step 1: Convert gallons to liters
Since the density of gasoline is given in grams per milliliter, we need to convert gallons to liters.

1 gallon ≈ 3.78541 liters

Therefore, 1.2 x 10^10 gallons ≈ 4.54249 x 10^10 liters

Step 2: Calculate the mass of gasoline
Using the density of gasoline, we can calculate the mass of gasoline in grams.

Mass of gasoline = volume × density
Mass of gasoline = (4.54249 x 10^10 liters) × (0.692 g/mL)

Note: We need to convert 0.692 g/mL to g/L for consistency.

0.692 g/mL ≈ 0.692 g/1000 mL ≈ 0.692 g/L

Now we can calculate the mass of gasoline:

Mass of gasoline = (4.54249 x 10^10 liters) × (0.692 g/L)

Step 3: Convert mass of gasoline to moles
To determine the moles of gasoline, we need to know the molar mass of isooctane (C8H18). The molar mass of carbon (C) is 12.01 g/mol, and the molar mass of hydrogen (H) is 1.008 g/mol.

Molar mass of isooctane = (8 × molar mass of carbon) + (18 × molar mass of hydrogen)

Molar mass of isooctane = (8 × 12.01 g/mol) + (18 × 1.008 g/mol)

Now we can calculate the number of moles of gasoline:

Number of moles of gasoline = (Mass of gasoline) / (Molar mass of isooctane)

Step 4: Calculate the moles of carbon dioxide produced
The complete combustion of isooctane produces 8 moles of carbon dioxide (CO2) for every 2 moles of isooctane burned.

Using the balanced equation:

C8H18 + 12.5O2 -> 8CO2 + 9H2O

We can calculate the moles of carbon dioxide:

Moles of carbon dioxide = (Number of moles of gasoline) × (8 moles of CO2 / 2 moles of isooctane)

Step 5: Calculate the mass of carbon dioxide
To determine the mass of carbon dioxide produced, we need to multiply the moles of carbon dioxide by its molar mass.

Molar mass of carbon dioxide (CO2) = (1 × molar mass of carbon) + (2 × molar mass of oxygen)

Molar mass of carbon dioxide = (1 × 12.01 g/mol) + (2 × 16.00 g/mol)

Now we can calculate the mass of carbon dioxide:

Mass of carbon dioxide = (Moles of carbon dioxide) × (Molar mass of CO2)

Following these steps, you'll be able to calculate the mass of carbon dioxide produced by the combustion of the given amount of gasoline.