Determining the Oxygen Requirements for Complete Combustion of a Gallon of Car-Grade Gasoline

In the context of automotive fuel combustion, understanding the required amount of pure oxygen for the complete burning of gasoline is crucial for analyzing engine efficiency and emissions. This article delves into the necessary calculations for an ideal scenario, focusing on a gallon of car-grade gasoline and presenting the mass ratio of gasoline to required oxygen.

Composition of Gasoline

Car-grade gasoline is primarily composed of hydrocarbons, with an approximate average molecular formula of C8H18, which represents octane. Despite the simplification, this formula provides a benchmark for our analysis. It is important to note that gasoline can contain a variety of different hydrocarbons, making this a representative average.

Combustion Reaction

The complete combustion of octane can be represented by the following balanced equation:

2C8H18 25O2 rightarrow; 16CO2 18H2O

This indicates that 2 moles of octane (car-grade gasoline) require 25 moles of oxygen for thorough combustion.

Density and Mass of Gasoline

The density of gasoline is approximately 0.74 kg/L. Given that 1 gallon is equal to about 3.78541 liters, the mass of 1 gallon of gasoline can be calculated as follows:

Mgasoline 0.74 kg/L × 3.78541 L ≈ 2.8 kg

Moles of Octane in Gasoline

The molar mass of octane C8H18 is approximately:

Moctane 8 × 12.01 g/mol 18 × 1.008 g/mol ≈ 114.22 g/mol

To find the number of moles of octane in 2.8 kg of gasoline, we perform the following calculation:

Noctane (2800 g / 114.22 g/mol) ≈ 24.5 moles

Moles of Oxygen Required

From the combustion reaction, the moles of oxygen required can be determined as follows:

NO2 (25/2) × Noctane (25/2) × 24.5 ≈ 153.125 moles

Mass of Oxygen Required

The molar mass of oxygen O2 is approximately 32.00 g/mol. Therefore, the mass of oxygen required is:

MO2 153.125 mol × 32.00 g/mol ≈ 4899.99 g ≈ 4.9 kg

Mass Ratio

Finally, to find the mass ratio of gasoline to oxygen, we use the calculated masses:

Ratio Mgasoline / MO2 2.8 kg / 4.9 kg ≈ 0.57

Summary

From the calculations, we find that:

Moles of Oxygen Required: Approximately 153.125 moles Mass of Oxygen Required: Approximately 4.9 kg Mass Ratio of Gasoline to Oxygen: Approximately 0.57

This means for every kilogram of gasoline, about 0.57 kg of oxygen is required for complete combustion. This understanding is fundamental for maximizing engine efficiency and minimizing emissions.

Understanding these chemical and physical relationships is crucial for engineers and automotive technicians, helping to optimize fuel use and minimize environmental impact.