100 moles of oxygen
Given the chemical reaction between the hydrocarbon compound and oxygen expressed as:
[tex]2C_8H_{18}+25O_2\rightarrow18H_2O+16CO_2[/tex]Based on stoichiometry, you can see that 2 moles of the hydrocarbon compound react with 25 moles of oxygen. Therefore if 8 moles of the hydrocarbon in the equation fully react, the number of moles of oxygen needed will be expressed as:
[tex]\text{moles of O}_2=\frac{8\cancel{molesofC_8H_{\mleft\{18\mright\}}}}{2\cancel{molesofC_8H_{18}}}\times25molesofO_2[/tex]The number of moles of oxygen needed will be simplified further as:
[tex]\begin{gathered} \text{moles of O}_2=\frac{\cancel{8}^4}{\cancel{2}_{}}\times25molesofO_2 \\ \text{moles of O}_2=4\times25molesofO_2 \\ \text{moles of O}_2=100\text{moles} \end{gathered}[/tex]This shows that if 8 moles of the hydrocarbon in the equation fully react, 100 moles of oxygen would be needed.
