Respuesta :
Answer : The mass of [tex]CO_2[/tex] produced form the combustion is, 16.43 kg
Explanation :
Density : It is defined as the mass contained per unit volume.
Formula used for density :
[tex]Density=\frac{Mass}{Volume}[/tex]
First we have to calculate the mass of octane.
Given :
Density of octane = 0.703 g/mL
Volume = 2.00 gallons = 7570 mL
conversion used : 1 gallon = 3785 mL
Now put all the given values in the above formula, we get:
[tex]0.703g/mL=\frac{Mass}{7570mL}[/tex]
[tex]Mass=5321.71g[/tex]
Now we have to calculate the moles of octane.
[tex]\text{Moles of octane}=\frac{\text{Mass of octane}}{\text{Molar mass of octane}}[/tex]
Molar mass of octane = 114 g/mole
[tex]\text{Moles of octane}=\frac{5321.71g}{114g/mole}=46.68mole[/tex]
Now we have to calculate the moles of [tex]CO_2[/tex].
The balanced chemical combustion reaction of octane will be:
[tex]2C_8H_{18}+25O_2\rightarrow 16CO_2+18H_2O[/tex]
From the balanced chemical reaction we conclude that:
As, 2 moles of [tex]C_8H_{18}[/tex] react to give 16 moles of [tex]CO_2[/tex]
So, 46.68 moles of [tex]C_8H_{18}[/tex] react to give [tex]\frac{46.68}{2}\times 16=373.44[/tex] moles of [tex]CO_2[/tex]
Now we have to calculate the mass of [tex]CO_2[/tex].
[tex]\text{ Mass of }CO_2=\text{ Moles of }CO_2\times \text{ Molar mass of }CO_2[/tex]
Molar mass of [tex]CO_2[/tex] = 44 g/mol
[tex]\text{ Mass of }CO_2=(373.44moles)\times (44g/mole)=16431.36g=16.43kg[/tex]
Thus, the mass of [tex]CO_2[/tex] produced form the combustion is, 16.43 kg
