Energy content of gasoline and hydrogen comparative math question

[courtneywetts]

Homework Statement

A typical car gas tank holds 15 gallons

A) Calculate the energy content of this much gasoline
B) Calculate the chemical energy content of 15 gallons of hydrogen gas under normal conditions (12.8 MJ/m^3) and compare with the energy content of gasoline

Homework Equations

Gasoline produces 70g of CO2 per megajoule of fuel energy

need to qualify hydrogen in terms of energy and CO2 in terms of mass
(3H2 → CO2)

Burning H2 produces .475 aJ= 1.475 aJ of energy.
CO2 has molecular weight of 44 so its mass is (44) (1.66 x 10^-27) = 7.30 x 10^ 26 kg

The Attempt at a Solution

I have no idea if the above information helps at all, but I really have no idea how to start this problem

 

[nasu]

The question has nothing to do with CO2.
Look up the heat or combustion or calorific power of fuels.

 

[Chestermiller]

You need to get the heat of combustion of gasoline. Maybe you could use octane as a surrogate for gasoline, or maybe you could find out the concentrations of various hydrocarbons in typical gasoline.

 

[haruspex]

The question has nothing to do with CO2.

If the C content of the gasoline is known, the CO2 per unit energy becomes useful.
http://www.chargepoint.com/pdfs/420f05001.pdf

 

[courtneywetts]

So if carbon content per gallon of gasoline is 2421, would I then do 15 gallons x 2421 grams to get 36,315 g?

How would I go about solving part B?

 

[SteamKing]

2421 what? Units are important to correctly working out any problem.

 

[courtneywetts]

2421 what? Units are important to correctly working out any problem.

grams

 

[haruspex]

So if carbon content per gallon of gasoline is 2421, would I then do 15 gallons x 2421 grams to get 36,315 g?

Yes. What mass of CO2 will that produce?

How would I go about solving part B?

That looks much simpler. You're told the volume and the energy per volume.

 

[courtneywetts]

Yes. What mass of CO2 will that produce?

That looks much simpler. You're told the volume and the energy per volume.

I am not sure what you are saying?

Is part A correct or do I need to do more to solve the problem?

 

[haruspex]

I am not sure what you are saying?

Is part A correct or do I need to do more to solve the problem?

Part A asks for the energy content. So far you have found the carbon content (mass). You know the relationship between the energy and the CO2 mass. So what's the missing step?

 

[courtneywetts]

Part A asks for the energy content. So far you have found the carbon content (mass). You know the relationship between the energy and the CO2 mass. So what's the missing step?

I know that produces 70g of CO2. Would I use this?

 

[haruspex]

I know that produces 70g of CO2. Would I use this?

You know what produces 70 of CO2?

 

[courtneywetts]

You know what produces 70 of CO2?

I know that gasoline produces 70 g of CO2 - not sure if this is relevant though?

 

[haruspex]

I know that gasoline produces 70 g of CO2 - not sure if this is relevant though?

"70g of CO2 per megajoule of fuel energy"

so you know
1. the relationship between the mass of CO2 produced and the energy produced;
2. the relationship between the mass of a quantity of gasoline and the mass of carbon in it;
You want
3. the relationship between the mass of a quantity of gasoline and the energy produced;
What one more relationship do you need to connect 1 and 2?

 

[courtneywetts]

"70g of CO2 per megajoule of fuel energy"

so you know
1. the relationship between the mass of CO2 produced and the energy produced;
2. the relationship between the mass of a quantity of gasoline and the mass of carbon in it;
You want
3. the relationship between the mass of a quantity of gasoline and the energy produced;
What one more relationship do you need to connect 1 and 2?

I am not sure how to connect the two? Do I already have this info?

 

[haruspex]

I am not sure how to connect the two? Do I already have this info?

I'm sure you do. What mass of CO2 will be produced by burning 1kg of carbon? (Think about atomic masses.)

 

[courtneywetts]

I'm sure you do. What mass of CO2 will be produced by burning 1kg of carbon? (Think about atomic masses.)

So if the atomic mass of carbon is 12 and the atomic mass of oxygen is 16 what do I do with this?

Also I have two oxygen so would I add all of these to get 44?

The answer in the back of the book for part A is 2.2 billion J but I have no idea how this was gotten.

 

[haruspex]

So if the atomic mass of carbon is 12 and the atomic mass of oxygen is 16 what do I do with this?

Also I have two oxygen so would I add all of these to get 44?

Yes. So you have, for burning gasoline:

• 12 atomic masses C corresponds to 44 atomic masses CO2
• 70g CO2 corresponds to 1MJ energy
• 1 gallon gasoline corresponds to 36,315 g C

So how many J energy correspond to 1 gallon gasoline?

 

[courtneywetts]

Yes. So you have, for burning gasoline:

• 12 atomic masses C corresponds to 44 atomic masses CO2
• 70g CO2 corresponds to 1MJ energy
• 1 gallon gasoline corresponds to 36,315 g C

So how many J energy correspond to 1 gallon gasoline?

The answer in the back of the book is 2.2 billion J but I don't know how this was gotten. I don't know what to do with the above info

 

[haruspex]

The answer in the back of the book is 2.2 billion J but I don't know how this was gotten. I don't know what to do with the above info

Each item gives you a ratio, and they connect in a chain: ratio of gasoline volume to carbon mass; ratio of carbon mass to CO2 mass; ratio of CO2 mass to energy. Just connect them up.

 

[courtneywetts]

Each item gives you a ratio, and they connect in a chain: ratio of gasoline volume to carbon mass; ratio of carbon mass to CO2 mass; ratio of CO2 mass to energy. Just connect them up.

How would I set this up as a ratio?

 

[haruspex]

How would I set this up as a ratio?

I'm not sure why you're finding this so hard. It's really very straightforward.
If there are 20 oranges per box (a ratio of 20 oranges: 1 box) and the price is 30c per orange (a ratio of 30c:1 orange), what is the price per box (ratio of cents to boxes)? What I'm asking you to do is no harder than that, except that you have to combine three ratios instead of two.

 

[courtneywetts]

I'm not sure why you're finding this so hard. It's really very straightforward.
If there are 20 oranges per box (a ratio of 20 oranges: 1 box) and the price is 30c per orange (a ratio of 30c:1 orange), what is the price per box (ratio of cents to boxes)? What I'm asking you to do is no harder than that, except that you have to combine three ratios instead of two.

In the oranges case I would multiply 20 by .30

So for this would I multiply 44 x 70 x36,315?

 

[haruspex]

In the oranges case I would multiply 20 by .30

So for this would I multiply 44 x 70 x36,315?

No, there's a little more to it than that. You didn't take into account the 12, and sometimes you may need to divide by a ratio, not multiply by it. Have another go. Draw pictures if it helps, or take it in steps: start with 1 gallon of gasoline, calculate how many grammes of carbon it contains, then how many grammes of CO2 that will produce, then how much energy you would expect with that much CO2.

 

[courtneywetts]

No, there's a little more to it than that. You didn't take into account the 12, and sometimes you may need to divide by a ratio, not multiply by it. Have another go. Draw pictures if it helps, or take it in steps: start with 1 gallon of gasoline, calculate how many grammes of carbon it contains, then how many grammes of CO2 that will produce, then how much energy you would expect with that much CO2.

So 1 gallon of gasoline contains 36,315 g of Carbon which will produce 70 g of CO2 but then what?

 

[haruspex]

So 1 gallon of gasoline contains 36,315 g of Carbon which will produce 70 g of CO2 but then what?

12g of C produce 44g CO2, remember? So many g of CO2 will 36,315 g of Carbon produce?

 

[courtneywetts]

12g of C produce 44g CO2, remember? So many g of CO2 will 36,315 g of Carbon produce?

Would I just divide these two?

 

[haruspex]

Would I just divide these two?

12g of C produce 44g CO2.
So 1g of C produces .. how many g of CO2?
So 36,315 g of Carbon produce.. how many g of CO2.?

 

[courtneywetts]

12g of C produce 44g CO2.
So 1g of C produces .. how many g of CO2?
So 36,315 g of Carbon produce.. how many g of CO2.?

When I did this as a ratio I got 133,155 g of CO2 but that's still not the answer in the back of the book is there another step?

 

[haruspex]

When I did this as a ratio I got 133,155 g of CO2 but that's still not the answer in the back of the book is there another step?

Yes, you haven't used the final ratio: 70g CO2 corresponds to 1MJ energy.
If 1 gal gasoline releases 133,155 g of CO2, and each 70g CO2 indicates 1MJ of energy, how many MJ for the whole gallon?

 

[courtneywetts]

Yes, you haven't used the final ratio: 70g CO2 corresponds to 1MJ energy.
If 1 gal gasoline releases 133,155 g of CO2, and each 70g CO2 indicates 1MJ of energy, how many MJ for the whole gallon?

When I did this I got 1902.214 MJ. Is this right?

If so how would I go about doing part B?

 

[courtneywetts]

Wait I realized that is only for 1 gallon so I got 28530 MJ

 

[haruspex]

When I did this I got 1902.214 MJ. Is this right?
that is only for 1 gallon so I got 28530 MJ

Right!

If so how would I go about doing part B?

This is much easier. you have 15 gals at 12.8 MJ/m^3.

 

[courtneywetts]

Right!

This is much easier. you have 15 gals at 12.8 MJ/m^3.

I don't understand what this means though? Is this all the information I need?

 

[haruspex]

I don't understand what this means though? Is this all the information I need?

The only other information you need is how to convert US gallons to m³. Look it up.