Question

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

This is an incomplete question, here is a complete question.

Assuming gasoline is 89.0% isooctane, with a density of 0.692 g/mL, what is the theoretical yield (in grams) of CO₂ produced by the combustion of 1.80 × 10¹⁰ gallons of gasoline (the estimated annual consumption of gasoline in the U.S.)?

Answer : The theoretical yield of carbon dioxide is $1.453\times 10^{14}g$

Explanation :  Given,

Volume of isooctane = $1.80\times 10^{10}gallons$

First we have to convert volume into liters, we use the conversion factor:

1 gallon = 3.785 L

So, $1.80\times 10^{10}gallon\times (\frac{3.785L}{1gallon})=6.813\times 10^{10}L$

Now we have to calculate the mass of isooctane.

$\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}$

Volume of isooctane = $6.813\times 10^{10}L=6.813\times 10^{13}mL$    (Conversion factor:  1 L = 1000 mL)

Density of isooctane = 0.692 g/mL

Now put all the given values in above equation, we get:

$0.692g/mL=\frac{\text{Mass of isooctane}}{6.813\times 10^{13}mL}\\\\\text{Mass of isooctane}=(0.692g/mL\times 6.813\times 10^{13}mL)=4.714\times 10^{13}g$

Now we have to calculate the number of moles.

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$      .....(1)

Given mass of isooctane = $4.714\times 10^{13}g$

Molar mass of isooctane = 114.22 g/mol

Now put all the given values in equation 1, we get:

$\text{Moles of isooctane}=\frac{4.714\times 10^{13}g}{114.22g/mol}=4.127\times 10^{11}mol$

The chemical equation for the combustion of isooctane is:

$2C_8H_{18}+25O_2\rightarrow 16CO_2+18H_2O$

By Stoichiometry of the reaction we can say that,

As, 2 moles of isooctane produces 16 moles of carbon dioxide.

So, $4.127\times 10^{11}mol$ of isooctane will produce = $\frac{16}{2}\times 4.127\times 10^{11}mol=3.3016\times 10^{12}mol$ of carbon dioxide

Now we have to calculate the mass of carbon dioxide.

Molar mass of carbon dioxide = 44.00 g/mol

Moles of carbon dioxide = $3.3016\times 10^{12}mol$

Now put all the given values in equation 1, we get:

$3.3016\times 10^{12}mol=\frac{\text{Mass of carbon dioxide}}{44.00g/mol}\\\\\text{Mass of carbon dioxide}=(3.3016\times 10^{12}mol\times 44.00g/mol)=1.453\times 10^{14}g$

Hence, the theoretical yield of carbon dioxide is $1.453\times 10^{14}g$