Question

Write the balanced equation for the combustion of isooctane to produce water vapor and carbon dioxide gas.Assuming gasoline is isooctane, with a density of g/mL, what is the theoretical yield of carbon dioxide produced by the combustion of gal of gasoline (the approximate annual consumption of gasoline in the United States)?

Answer 1

Answer:

The yield is 16 moles of CO2 per 2 moles of isooctane.

The mass of CO2 is 1.15 billion tonnes

Explanation:

First we set the unbalanced equation:

$C_{8}H_{18} + O_{2} \longrightarrow CO_{2} + H_{2}O$

Now we proceed to balance the equation:

$2C_{8}H_{18} + 25O_{2} \longrightarrow 16CO_{2} + 18H_{2}O$

With the equation balanced, we see that the theoretical yield is 16 moles of CO2 per 2 moles of isooctane and we can proceed to make calculations with the following data:

$\rho _{C_{8}H_{18}}=0.69 g/mL\\Consumption: 142.86x10^{9} gal\\1gal=3785.41 mL\\M_{C_{8}H_{18}}=114.23g/mole\\M_{CO_{2}}=44.01g/mole$

Knowing the different relations between mass, density and molar mass, we have the following results:

$V_{C_{8}H_{18}}=5.41x10^{14}mL\\m_{C_{8}H_{18}}=3.73x10^{14}g\\n_{C_{8}H_{18}}=3.27x10^{12}mole\\n_{CO_{2}}=2.62x10^{13}mole\\m_{CO_{2}}=1.15x1015g\\m_{CO_{2}}=1.15x10^{9}tonnes$