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Density question/CO2 emission watch

1. I think I have the answer, but I'm not sure.

Here is the question:

Every morning I drive my son to school in the car. Each one-way trip takes about 25 minutes. My car’s fuel efficiency rating, according to the manufacturer, is about 30 miles per US gallon of gasoline. Estimate the amount (in kg) of carbon dioxide emission for each one-way trip.

It says that there is no model answer, but that a rough estimate in the same order of magnitude should be able to be found. You will have to find some information on your own, and make some assumptions.

What I did is:

Assumed 1 US gallon of gasoline weighs 6.4 pounds. Molar mass of CO2 is 44, so weight of carbon (Mr 12) would be 44/12 or roughly 3.7. Assuming the gasoline is 100% octane then Mr of octane is 114 with carbon make up at 96 so 96/114 is 84%. Assuming complete combustion; not CO or NOx then it would be 6.4 * 0.84 * 3.7 = 19.89 pounds. Divide 2.2 is 9.04 kg so 9.04 kg of CO2 emitted per US gallon. Assuming the car goes 50 mph then for 25 minutes thats 20.8 miles so 20.8/30 = 0.693*9.04 = 6.3kg of CO2 emitted in the 25 minute one way journey.

However, my professor was talking about how the units were wrong. miles should be into kilometers, which I dont understand why you would do that. And that the density of gasoline (because you need the mass) is will be required to find an answer. However I dont understand how you'd find the volume or even why the density would be needed. Is what I did the right thing?
2. (Original post by G A B R I E L)
I think I have the answer, but I'm not sure.

Here is the question:

Every morning I drive my son to school in the car. Each one-way trip takes about 25 minutes. My car’s fuel efficiency rating, according to the manufacturer, is about 30 miles per US gallon of gasoline. Estimate the amount (in kg) of carbon dioxide emission for each one-way trip.

It says that there is no model answer, but that a rough estimate in the same order of magnitude should be able to be found. You will have to find some information on your own, and make some assumptions.

What I did is:

Assumed 1 US gallon of gasoline weighs 6.4 pounds. Molar mass of CO2 is 44, so weight of carbon (Mr 12) would be 44/12 or roughly 3.7. Assuming the gasoline is 100% octane then Mr of octane is 114 with carbon make up at 96 so 96/114 is 84%. Assuming complete combustion; not CO or NOx then it would be 6.4 * 0.84 * 3.7 = 19.89 pounds. Divide 2.2 is 9.04 kg so 9.04 kg of CO2 emitted per US gallon. Assuming the car goes 50 mph then for 25 minutes thats 20.8 miles so 20.8/30 = 0.693*9.04 = 6.3kg of CO2 emitted in the 25 minute one way journey.

However, my professor was talking about how the units were wrong. miles should be into kilometers, which I dont understand why you would do that. And that the density of gasoline (because you need the mass) is will be required to find an answer. However I dont understand how you'd find the volume or even why the density would be needed. Is what I did the right thing?
You seem to have a reasonable method.

If you have the mass of 1 US gallon = 6.4 pounds = 2.909 kg
octane = C8H18 (relative mass = 114), thus moles of octane = 25.52 moles
1 mole of octane releases 8 moles of CO2
1 US gallon releases 8 x 25.2 = 204.147 moles CO2 (relative mass 44) = 8982 g = 9Kg approx per gallon

Same ball park...
3. (Original post by charco)
You seem to have a reasonable method.

If you have the mass of 1 US gallon = 6.4 pounds = 2.909 kg
octane = C8H18 (relative mass = 114), thus moles of octane = 25.52 moles
1 mole of octane releases 8 moles of CO2
1 US gallon releases 8 x 25.2 = 204.147 moles CO2 (relative mass 44) = 8982 g = 9Kg approx per gallon

Same ball park...
Alright thanks. The only reason I can think of km/h coming in is if the country/car which is used uses km/h not miles, but other than that i see no reason for there to be a conversion. Do you see any reason to use density here though?
4. (Original post by G A B R I E L)
Alright thanks. The only reason I can think of km/h coming in is if the country/car which is used uses km/h not miles, but other than that i see no reason for there to be a conversion. Do you see any reason to use density here though?
If you aready know the mass of 1 gallon of petrol then there is no need to use density. However ,to find the mass of 1 gallon you would need density as 1 gallon is a measure of volume.
5. Your prof probably wants you to convert everything into SI, but there are inaccuracies involved in every conversion so I'd not bother if you are happy working miles. I'd say that 30 mph is a more reasonable estimate of average speed so perhaps that's why your prof thinks you have got the units wrong.

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