My motorcycle has a capacity of 4.5 gal of octane. If I combust all of the octane, what is the volume of CO2 generated by my motorcycle on one tank of gas? Assume that I burn all of the octane into CO2 on a warm day in June, where it is 80 degrees F outside with a barometric pressure of inHg
I thought we did this together about a week ago.
you're right, I was actually just trying to research it the search bar. Sorry
To calculate the volume of CO2 generated by your motorcycle, we need to know the stoichiometric ratio between octane and carbon dioxide (CO2) when it undergoes complete combustion. The balanced chemical equation for the combustion of octane is:
2 C8H18 + 25 O2 -> 16 CO2 + 18 H2O
From this equation, we can see that for every 2 moles of octane (C8H18) combusted, 16 moles of carbon dioxide (CO2) are produced.
To find the moles of octane in your motorcycle tank, we need to convert the volume of octane from gallons to moles. The conversion factor between volume and moles of a gas depends on the temperature, pressure, and the specific gas constant.
First, let's convert the temperature from Fahrenheit to Kelvin:
Temperature in Kelvin = (80 degrees Fahrenheit + 459.67) * (5/9)
Next, we need to convert the pressure from inches of mercury (inHg) to pascals (Pa). The conversion factor is 1 inHg = 3386.39 Pa.
Now we can calculate the number of moles. We'll use the ideal gas law:
PV = nRT
Where:
P = pressure in Pascals
V = volume in liters
n = moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature in Kelvin
Assuming your motorcycle tank pressure is atmospheric pressure (given barometric pressure), we can substitute the values and solve for moles:
n = PV / RT
The volume V can be converted from gallons to liters using the conversion factor 1 gallon = 3.78541 liters.
Once you have the moles of octane, you can multiply by the stoichiometric coefficient of CO2 (16 moles of CO2 per 2 moles of octane) to find the moles of CO2 produced.
Finally, to get the volume of CO2 in cubic meters, we multiply the moles of CO2 by the molar volume at standard temperature and pressure. The molar volume is approximately 22.4 L/mol.
Let's calculate the volume of CO2 generated by your motorcycle:
1. Convert the barometric pressure from inHg to Pa:
Barometric Pressure in Pa = Barometric Pressure in inHg * 3386.39
2. Convert the temperature from Fahrenheit to Kelvin:
Temperature in Kelvin = (80 + 459.67) * (5/9)
3. Calculate the volume of octane in moles:
Volume of octane in liters = 4.5 gal * 3.78541 L/gal
Volume of octane in moles = (Volume of octane in liters * Barometric Pressure in Pa) / (R * Temperature in Kelvin)
4. Calculate the moles of CO2 produced:
Moles of CO2 produced = (Volume of octane in moles * 16) / 2
5. Convert the moles of CO2 to volume in cubic meters:
Volume of CO2 in cubic meters = Moles of CO2 produced * 22.4 L/mol * (1 m^3 / 1000 L)
By following these steps and performing the calculations using the given values, you can find the volume of CO2 generated by your motorcycle on one tank of gas.