A diesel fuel has a chemical mass composition of $86\%$ Carbon ($C$) and $14\%$ Hydrogen ($H$). Calculate the stoichiometric (theoretical) mass of air required in $\text{kg}$ for complete combustion of $1\text{ kg}$ of this fuel. (Air contains $23\%$ Oxygen by mass)
Answer Key:
14.78
Step-by-Step Solution & Explanation
Theoretical oxygen required per kg fuel:
$O_2 = \left( \frac{32}{12} \times C \right) + (8 \times H) = \left( \frac{8}{3} \times 0.86 \right) + (8 \times 0.14)$
$O_2 = 2.2933 + 1.120 = 3.4133\text{ kg of } O_2$
Since air contains $23\%$ oxygen by mass:
$\text{Air required} = \frac{3.4133}{0.23} \approx 14.84\text{ kg}$
(Using standard 23.2% gives 14.71 kg; range 14.5 to 14.9 kg).