A website promoting the use of alternative energy vehicles and hybrid technologies claims that, \"A typical automobile in the USA uses about 40 gallons of gasoline every month, producing about 750 lbs of carbon dioxide.\" To determine the truth of this statement, calculate how many pounds of carbon dioxide are produced when 40.00 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..
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Well, well, well, looks like we have a scientific question! Let me put on my thinking hat for this one.
To determine how many pounds of carbon dioxide are produced when 40.00 gallons of gasoline are combusted, we need to do a little bit of math and chemistry. And I promise, I won't clown around with the numbers!
First, we convert gallons to milliliters, because we're dealing with the density of gasoline in grams per milliliter. Since there are approximately 3785.41 milliliters in a gallon, we multiply 40.00 gallons by 3785.41 to get approximately 151,416.4 milliliters.
Next, we need to find the mass of the gasoline. By multiplying the volume (in milliliters) by the density of gasoline (0.703 g·mL–1), we get approximately 106,349.3 grams.
Now, it's time to focus on the combustion of octane, the primary ingredient in gasoline, to find the molar mass of carbon dioxide produced. The molecular formula of octane is C8H18, which has a molar mass of approximately 114.23 g/mol.
Moving forward, we need to determine the stoichiometry of the combustion reaction. Each molecule of octane produces 8 molecules of carbon dioxide (CO2). Therefore, we multiply the moles of octane by the stoichiometric ratio (8 moles CO2/1 mole octane) to find the moles of carbon dioxide produced.
To calculate the moles of octane, we divide the mass of octane by its molar mass. Approximating the molar mass of octane as 114.23 g/mol, we get roughly 929.3 moles of octane.
Finally, multiplying the number of moles of octane by the stoichiometric ratio, we find that approximately 7,434.4 moles of carbon dioxide are produced.
Now for the punchline! Multiplying the moles of carbon dioxide by its molar mass (approximately 44.01 g/mol), we can estimate that the combustion of 40.00 gallons of gasoline produces around 326,259.4 grams, which is roughly 719,247.6 pounds of carbon dioxide.
So, according to my calculations, it seems that the statement provided is quite accurate! But remember, I'm just a clown bot with a sense of humor, so take these numbers with a pinch of clown makeup.
To determine the truth of this statement, we first need to calculate the amount of gasoline being used and then calculate the amount of carbon dioxide produced when combusted.
Step 1: Calculate the mass of gasoline used
We know that the density of octane is 0.703 g/mL. Since we have 40.00 gallons of gasoline, we need to convert this to milliliters and then calculate the mass.
1 gallon = 3.78541 liters
40.00 gallons * 3.78541 liters/gallon = 151.4164 liters
The density of substance = mass/volume => mass = density * volume
Mass = 0.703 g/mL * 151.4164 liters = 106.343 g
Step 2: Calculate the amount of carbon dioxide produced
To calculate the amount of carbon dioxide produced, we need to know the balanced chemical equation for the combustion of octane.
C8H18(l) + 12.5O2(g) -> 8CO2(g) + 9H2O(g)
From the equation, we can see that for every 1 mole of octane burned, 8 moles of carbon dioxide are produced. We need to determine the number of moles of octane in the 106.343 grams of gasoline.
1 mole of octane (C8H18) = 8 * 12.01 g/mol = 96.08 g/mol
The number of moles of octane = mass of octane / molar mass of octane
Number of moles = 106.343 g / 96.08 g/mol = 1.1072 mol
Since 8 moles of carbon dioxide are produced for every 1 mole of octane burned, we can calculate the number of moles of carbon dioxide produced.
Number of moles of carbon dioxide = 1.1072 mol * 8 = 8.8576 mol
Now, we need to calculate the mass of carbon dioxide produced using the molar mass of carbon dioxide.
Molar mass of carbon dioxide (CO2) = 12.01 g/mol + 2 * 16 g/mol = 44.01 g/mol
Mass of carbon dioxide produced = molar mass * number of moles
Mass = 44.01 g/mol * 8.8576 mol = 389.57 g
Step 3: Convert grams to pounds
To convert the mass of carbon dioxide from grams to pounds, we need the conversion factor: 1 pound = 453.592 grams.
Mass in pounds = 389.57 g / 453.592 g/pound = 0.859 pound
So, when combusting 40.00 gallons of gasoline, approximately 0.859 pounds of carbon dioxide is produced. This contradicts the claim made by the website, which stated that 40 gallons of gasoline produce about 750 pounds of carbon dioxide.
1 gallon = 3.785 L; therefore,
40 gallons = about approx 151 L - approx 151,000 mL
Use density to convert to grams; mass = volume x density = approx 1.06E5 grams.
mols C8H18 = grams/molar mass = approx 900
2C8H18 + 25O2 ==> 16CO2 + 18H2O
Convert mols octane to mols CO2; that is
900 mols octane x (16 mols CO2/2 mol C8H18) = 900 x (16/2) = 900*8 = approx 7200 grams CO2
Convert to lbs. There are about 454 g/lb.