1. 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.
I have no idea how to start this problem. The answer is supposed to be in lbs of CO2 but we haven't used anything but the metric system in chemistry. Any help is really appreciated!
So you're saying you want to convert from metric to US customary units? Well, don't worry, I've got you covered. Let's break it down step by step and clown around with the conversions.
First, you want to determine the mass of gasoline in those 40.00 gallons. To do that, you need to know the density of gasoline. It's given as 0.703 g·mL–1. Thank goodness it's not 0.703 clowns per gallon, or we'd be in big trouble!
To convert gallons to milliliters, just remember that there are 3785 mL in a gallon. Multiply that by 40.00 gallons and you'll find the volume of gasoline in mL.
Now that you've got the volume in mL, multiply it by the density of gasoline in g·mL–1 to find the mass in grams. I'm glad the density isn't measured in "giggles per gulp" because that would be hard to calculate!
Next, we need to convert from grams of gasoline to moles of octane. Octane has a molar mass of about 114.23 g·mol–1. Divide the mass in grams by the molar mass to find the number of moles of octane we've got.
Now, let's think about the combustion of octane. For every one mole of octane burned, it produces eight moles of carbon dioxide. That's a lot of CO2!
Finally, to convert from moles of CO2 to pounds, just multiply by the molar mass of carbon dioxide (44.01 g·mol–1) and multiply again by the conversion factor of 1 lb ≈ 453.59 g. Voila, you've got the weight of CO2 in pounds.
It's time for the grand finale! Now that you have all the ingredients, put them together and calculate the pounds of carbon dioxide produced when 40.00 gallons of gasoline are combusted. I hope you're ready for the big reveal!
By the way, I have to give a shoutout to all the alternative energy vehicles out there. Keep on rolling, you eco-warriors!
To solve this problem, you need to convert the given volume of gasoline (40.00 gallons) into grams and then determine the amount of carbon dioxide produced.
1. Convert gallons to liters:
- 1 gallon = 3.785 liters
- 40.00 gallons x 3.785 liters/gallon = 151.4 liters
2. Convert liters to milliliters:
- 1 liter = 1000 milliliters
- 151.4 liters x 1000 mL/liter = 151400 mL
3. Determine the mass of gasoline:
- Given density: 0.703 g·mL–1
- Mass = Density x Volume
- Mass = 0.703 g·mL–1 x 151400 mL
4. Convert grams to pounds:
- 1 pound = 453.592 grams
- Mass in pounds = (0.703 g/mL x 151400 mL) / 453.592 g
5. Calculate the molar mass of octane (C8H18):
- Carbon (C) molar mass = 12.01 g/mol
- Hydrogen (H) molar mass = 1.008 g/mol
- Molar mass of octane (C8H18) = (8 x 12.01 g/mol) + (18 x 1.008 g/mol)
6. Determine the moles of octane:
- Moles = Mass / Molar mass of octane
7. Determine the moles of carbon dioxide produced:
- From the balanced chemical equation of the combustion of octane, we know that 1 mole of octane produces 8 moles of carbon dioxide.
- Moles of CO2 = Moles of octane x 8
8. Calculate the mass of carbon dioxide produced:
- Mass = Moles of CO2 x Molar mass of carbon dioxide (CO2)
9. Convert grams to pounds:
- 1 pound = 453.592 grams
- Mass in pounds = (Mass of carbon dioxide produced in grams) / 453.592 g
By following these steps, you can determine the amount of carbon dioxide produced when 40.00 gallons of gasoline are combusted.
To solve this problem, we need to use several conversion factors to go from volume to mass and then to moles. Let's break it down into steps:
Step 1: Convert gallons to liters.
Since the density of gasoline is given in grams per milliliter (g/mL), we need to convert gallons to milliliters and then to liters to match the density unit.
1 gallon = 3.78541 liters (exact conversion factor).
Step 2: Convert liters to grams.
Using the density of gasoline, we can convert liters to grams using the following conversion factor:
0.703 g/mL (given in the problem).
Step 3: Convert grams to moles.
To convert grams of gasoline to moles, we need the molar mass of octane (C8H18).
The molar mass of octane is:
(12.01 g/mol + (1.01 g/mol x 8)) + (1.01 g/mol + (1.01 g/mol x 18)) = 114.22 g/mol.
Step 4: Convert moles of octane to moles of carbon dioxide (CO2).
The balanced equation for combustion of octane gives us the following mole ratio:
2 moles of octane (C8H18) produce 16 moles of CO2.
Step 5: Convert moles of CO2 to grams of CO2.
To convert moles of CO2 to grams, we need the molar mass of CO2.
The molar mass of CO2 is:
(12.01 g/mol + (1.01 g/mol x 2)) + (16.00 g/mol) = 44.01 g/mol.
Step 6: Convert grams of CO2 to pounds of CO2.
To convert grams of CO2 to pounds, we can use the conversion factor:
1 pound = 453.592 grams (exact conversion factor).
Now, let's put it all together to calculate the answer.
First, compute the volume of gasoline in liters:
40 gallons x 3.78541 liters/gallon = 151.4164 liters.
Next, calculate the mass of gasoline in grams:
151.4164 liters x 0.703 g/mL = 106.48 grams.
Then, convert grams of gasoline to moles of octane:
106.48 grams / 114.22 g/mol = 0.931 moles.
Convert moles of octane to moles of CO2:
0.931 moles x (16 moles CO2 / 2 moles octane) = 7.448 moles CO2.
Next, convert moles of CO2 to grams:
7.448 moles CO2 x 44.01 g/mol = 327.38748 grams CO2.
Finally, convert grams of CO2 to pounds:
327.38748 grams / 453.592 grams/pound = 0.721 pounds CO2.
Therefore, when 40.00 gallons of gasoline are combusted, approximately 0.721 pounds of carbon dioxide (CO2) are produced.