Amount Of Carbon Dioxide Produced By A Vehicle Combusting Octane Fuel

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Amount Of Carbon Dioxide Produced By A Vehicle Combusting Octane Fuel

An automobile travels 225 miles at 20.5 miles/gallon. What is the amount of carbon dioxide produced if the gasoline is composed of octane (C_{8}H_{18}) whose density is 0.69 g/mL.

**The strings**:
S_{7}P_{1}A_{15} (containership-mass).

S_{7}P_{6}A_{66} (grouping/interaction- chemical)
**The math**:

Both Pj Problem are of Interest, however, Pj Problem of type *grouping/interactio* (chemical) is in focus.

Combustion of octane as follows:

2C_{8}H_{18} + 25O_{2} -------> 16CO_{2} + 18H_{2}O

Total gallons of octane combusted = 225/20.5 = 10.98 gallons = 10.98 x 3.79 liters = 41.54 Liters

density per liter = 0.69/0.001 = 690 g/L

So, mass of octane = density x volume = 690 x 41.6 = 28704 g

Molar mass of octane = 12x8 + 1x18 = 96 + 18 = 114 g

So, moles of octane combusted = 28704/114 = 251.8 moles

From balanced equation:

2 moles of C_{8}H_{18} produced 16 moles of CO_{2}

So, 251.8 moles of C_{8}H_{18} produce (251.8 x 16)/2 = 2014 moles of CO_{2}

Molar mass of CO_{2} = 12 + 32 = 44 g

So, mass of 2014 moles = 44 x 2014 = 88616 g = 88.6 kg.

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