A large sport utility vehicle has a mass of 2500kg. Calculate the mass of CO2 emitted into the atmosphere upon accelerating the SUVfrom 0.0mph to 66.0 mph. Assume that the required energy comes from the combustion of octane with 30% efficiency. (Hint: Use KE= 1/2mv^2 to calculate the kinetic energy required for the acceleration.) I already converted mph to m/s by multiplying by .44704. and got 28.1635m/s. then I you have the used this equation Work=.5*2500*(28.1635)^2-.5*2500*0^2....but whats next?
To calculate the mass of CO2 emitted into the atmosphere upon accelerating the SUV, you need to first calculate the work done in accelerating the vehicle using the formula:
Work = (1/2) * m * (v^2 - u^2)
where:
m is the mass of the SUV (2500 kg)
v is the final velocity (28.1635 m/s)
u is the initial velocity (0 m/s)
From your calculations, you have already calculated the final velocity correctly.
Now, you need to calculate the initial velocity, which is 0 m/s since the SUV starts from rest.
Substituting the values into the equation:
Work = (1/2) * 2500 * (28.1635^2 - 0^2)
= (1/2) * 2500 * (792.096157225 - 0)
= 990120.19640625 J
Next, you need to calculate the energy consumed from the combustion of octane. Since the efficiency is given as 30%, you can calculate it by dividing the work done by 0.3 (30% expressed as a decimal):
Energy consumed = Work / 0.3
= 990120.19640625 J / 0.3
= 3300400.6546875 J
Now, you need to convert the energy consumed to joules (J) into kilojoules (kJ) by dividing it by 1000:
Energy consumed (kJ) = Energy consumed (J) / 1000
= 3300400.6546875 J / 1000
= 3300.4006546875 kJ
Finally, to calculate the mass of CO2 emitted, you need to consider the energy released upon combustion of octane. According to standard data, the combustion of 1 mole of octane releases approximately 5530 kJ of energy. Assuming the complete combustion of octane, you can calculate the moles of octane consumed by dividing the energy consumed by 5530 kJ/mol:
Moles of octane consumed = Energy consumed (kJ) / 5530 kJ/mol
= 3300.4006546875 kJ / 5530 kJ/mol
= 0.59545908412 mol
Since the molecular formula for octane is C8H18, you can calculate the mass of octane consumed by multiplying the moles of octane by its molar mass of 114.22 g/mol:
Mass of octane consumed = Moles of octane consumed * Molar mass of octane
= 0.59545908412 mol * 114.22 g/mol
= 67.96436877 g
Finally, considering that octane (C8H18) releases 3 molecules of CO2 for every molecule of octane combusted, you can calculate the mass of CO2 emitted by multiplying the mass of octane consumed by the molar mass of CO2 (44.01 g/mol) and the stoichiometric ratio:
Mass of CO2 emitted = Mass of octane consumed * (3 * Molar mass of CO2 / Molar mass of octane)
= 67.96436877 g * (3 * 44.01 g/mol / 114.22 g/mol)
= 95.040223007 g
Therefore, the mass of CO2 emitted into the atmosphere upon accelerating the SUV from 0.0 mph to 66.0 mph is approximately 95.04 g.