One gallon of octane is equivalent to 23.4 mol of octane

[grumpyasian]

Homework Statement

one gallon of octane is equivalent to 23.4 mol of octane. the density of it is .703g/mL.

Homework Equations

to travel the same distance traveled with one gallon of octane, how many moles of ethanol would you need?( assuming the car works just as well with ethanol as it does with gasoline, same efficiency of conversion of chemical energy to mechanical work.)

The Attempt at a Solution

23.2 mol C8H18(.703g C8H18/mL) (1 mol C2H6O/1 mol C8H18)

idk what to do next

 

[DDTea]

In a car, chemical energy from gasoline (or in this problem, octane) is being converted to mechanical work. Since we're assuming that both gasoline and ethanol have the same efficiency, we can simply compare the amount of energy per mole that gasoline and ethanol have. Next, you will want to calculate how many moles of ethanol are required to produce the same amount of energy as 23.4 moles of octane (that is, 1 gallon of octane). That will lead you to your answer.

 

[grumpyasian]

i still don't know what i am still missing in the process of finding the answer. do i times it by 1000mL to cancel out the mL from the density or what? I am totally lost.

 

[Borek]

You need density to convert gallon to mass and moles.

 

[DeeNos]

I would first clarify the question and make sure I understand what is being asked. It appears that the question is asking for the number of moles of ethanol needed to travel the same distance as one gallon of octane, assuming the car has the same efficiency with both fuels.

To solve this problem, we can use the information provided in the question. We know that one gallon of octane is equivalent to 23.4 mol of octane. We also know the density of octane is 0.703 g/mL. This means that one gallon of octane has a mass of 0.703 g/mL x 3.785 L/gallon = 2.661 g.

Next, we can use the molar mass of octane (114.23 g/mol) to calculate the number of moles present in 2.661 g of octane:

2.661 g C8H18 x (1 mol C8H18/114.23 g C8H18) = 0.0233 mol C8H18

Since one gallon of octane is equivalent to 23.4 mol of octane, we can set up a proportion to determine the number of moles of ethanol needed:

0.0233 mol C8H18 / 23.4 mol C8H18 = x mol C2H6O / 1 mol C2H6O

Solving for x, we get:

x = 23.4 mol C2H6O x (0.0233 mol C8H18 / 23.4 mol C8H18) = 0.0233 mol C2H6O

Therefore, to travel the same distance as one gallon of octane, we would need 0.0233 mol of ethanol.