Balance the chemical equation for the combustion of hexane, \(\mathrm{C}_{6} \mathrm{H}_{14}(l)\). The unbalanced equation is: \(\mathrm{C}_{6} \mathrm{H}_{14}(l)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) Answer: Balance C: \(\mathrm{C}_{6} \mathrm{H}_{14}(l)+\mathrm{O}_{2}(g) \rightarrow 6 \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) Balance H: \(\mathrm{C}_{6} \mathrm{H}_{14}(l)+\mathrm{O}_{2}(g) \rightarrow 6 \mathrm{CO}_{2}(g)+7 \mathrm{H}_{2} \mathrm{O}(g)\) Balance O: \(\mathrm{C}_{6} \mathrm{H}_{14}(l)+\frac{19}{2} \mathrm{O}_{2}(g) \rightarrow 6 \mathrm{CO}_{2}(g)+7 \mathrm{H}_{2} \mathrm{O}(g)\) Multiply through by 2 to get rid of the fractional coefficient: \(2 \mathrm{C}_{6} \mathrm{H}_{14}(l)+19 \mathrm{O}_{2}(g) \rightarrow 12 \mathrm{CO}_{2}(g)+14 \mathrm{H}_{2} \mathrm{O}(g)\)

Step by step solution

01

Balance C atoms

To balance the C atoms, we will count the number of C atoms on both sides of the equation and adjust the coefficients accordingly. There are 6 C atoms in hexane, so we will need 6 CO₂ molecules to balance the C atoms: \(\mathrm{C}_{6} \mathrm{H}_{14}(l)+\mathrm{O}_{2}(g) \rightarrow 6 \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\)

02

Balance H atoms

Next, we will balance the H atoms. There are 14 H atoms in hexane, so we need 7 H₂O molecules to balance the H atoms: \(\mathrm{C}_{6} \mathrm{H}_{14}(l)+\mathrm{O}_{2}(g) \rightarrow 6 \mathrm{CO}_{2}(g)+7 \mathrm{H}_{2} \mathrm{O}(g)\)

03

Balance O atoms

Finally, we will balance the O atoms. There are 12 O atoms in 6 CO₂ molecules and 7 O atoms in 7 H₂O molecules, giving us a total of 19 O atoms on the products' side. We need 19/2 O₂ molecules to balance the O atoms: \(\mathrm{C}_{6} \mathrm{H}_{14}(l)+\frac{19}{2} \mathrm{O}_{2}(g) \rightarrow 6 \mathrm{CO}_{2}(g)+7 \mathrm{H}_{2} \mathrm{O}(g)\)

04

Convert fractional coefficients to whole numbers

Since fractional coefficients are not proper, we must convert them into whole numbers. To do this, we will multiply the entire equation by 2: \(2 \mathrm{C}_{6} \mathrm{H}_{14}(l)+19 \mathrm{O}_{2}(g) \rightarrow 12 \mathrm{CO}_{2}(g)+14 \mathrm{H}_{2} \mathrm{O}(g)\) The balanced equation for the combustion of hexane is: \(2 \mathrm{C}_{6} \mathrm{H}_{14}(l)+19 \mathrm{O}_{2}(g) \rightarrow 12 \mathrm{CO}_{2}(g)+14 \mathrm{H}_{2} \mathrm{O}(g)\)

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