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Below is the symbol equation for the combustion of octane with oxygen to produce carbon dioxide and water. What number is needed in the blank before O_(2) to balance the equation? C_(8)H_(18)+ldots O_(2)arrow 16CO_(2)+18H_(2)O

Question

Below is the symbol equation for the combustion of octane with oxygen to produce carbon dioxide
and water. What number is needed in the blank before O_(2) to balance the equation?
C_(8)H_(18)+ldots O_(2)arrow 16CO_(2)+18H_(2)O

Below is the symbol equation for the combustion of octane with oxygen to produce carbon dioxide and water. What number is needed in the blank before O_(2) to balance the equation? C_(8)H_(18)+ldots O_(2)arrow 16CO_(2)+18H_(2)O

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GeorgiaProfessional · Tutor for 6 years

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25

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## Step 1: <br />Firstly, inspect the unbalanced equation,<br />\[<br />\mathrm{C}_{8} \mathrm{H}_{18}+\quad \mathrm{O}_{2} \rightarrow 16 \mathrm{CO}_{2}+18 \mathrm{H}_{2} \mathrm{O}<br />\]<br /><br />## Step 2:<br />As per the Law of Conservation of Mass, the number of atoms should be same on both the reactant and product sides. The number of carbon and hydrogen atoms are the same on both sides of the equation. However, the oxygen atoms are not balanced.<br /><br />## Step 3:<br />On the right side, calculate the total number of oxygen atoms:<br />It can be obtained from two compounds, \(16\mathrm{CO}_2\) and \(18\mathrm{H}_2\mathrm{O}\).<br />In \(16\mathrm{CO}_2\), each molecule of \(\mathrm{CO}_2\) contributes 2 oxygen atoms. So a total of \(2*16=32\) atoms from \(\mathrm{CO}_2\).<br />In \(18\mathrm{H}_2\mathrm{O}\), each molecule of \(\mathrm{H}_2\mathrm{O} \) contributes 1 oxygen atoms. So a total of \(1*18=18\) atoms from \(\mathrm{H}_2\mathrm{O} \). <br />So in total, the right side of the equation has \(32 + 18 = 50\) oxygen atoms.<br /><br />## Step 4:<br />Going to the left side, remember that in a molecule of \(\mathrm{O}_2\), there are 2 oxygen atoms. Therefore, to balance the equation with \(50\) oxygen atoms on the right side, we would require \(50\div2=25\) molecules of \(\mathrm{O}_2\). <br /><br />## Step 5:<br />So, enter \(25\) as the coefficient in front of \(\mathrm{O}_2\) to balance the equation. The balanced equation is thus: \(\mathrm{C}_{8}\mathrm{H}_{18} + 25\mathrm{O}_{2} \rightarrow 16 \mathrm{CO}_2 + 18\mathrm{H}_2\mathrm{O}\).
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