A diesel engine burns dodecane ($C_{12}H_{26}$) as a reference fuel. The atomic weights are: $C = 12\text{ g/mol}$, $H = 1\text{ g/mol}$, and $O = 16\text{ g/mol}$. Assuming atmospheric air contains $23.2\%$ oxygen by mass, the stoichiometric air-fuel ratio on a mass basis for complete combustion of dodecane is ________ (round off to 2 decimal places).
Answer Key:
15.01
Step-by-Step Solution & Explanation
1. Stoichiometric combustion equation:
$C_{12}H_{26} + \left(12 + \frac{26}{4}\right) O_2 \to 12 CO_2 + 13 H_2O$
$12 + 6.5 = 18.5\text{ moles of } O_2$
2. Molar mass of fuel ($C_{12}H_{26}$):
$M_{\text{fuel}} = (12 \times 12) + (26 \times 1) = 144 + 26 = 170\text{ g/mol}$
3. Mass of oxygen required per mole of fuel:
$m_{O2} = 18.5 \times 32\text{ g} = 592\text{ g}$
4. Mass of air containing this oxygen:
$m_{\text{air}} = \frac{592\text{ g}}{0.232} \approx 2551.72\text{ g}$
5. Stoichiometric Air-Fuel Ratio:
$(A/F)_{st} = \frac{2551.72\text{ g air}}{170\text{ g fuel}} \approx 15.01$