Final answer:
The coefficient of oxygen when balancing the equation C2H6 + O2 → CO2 + H2O is 7. We balance the hydrocarbons first, then adjust the oxygen molecules to ensure there are an equal number of atoms on each side of the equation.
Step-by-step explanation:
To determine the coefficient of oxygen when balancing the equation C2H6 + O2 → CO2 + H2O, one would first balance the carbon atoms and then the hydrogen atoms, which gives us a basic framework:
2C2H6 + O2 → 4CO2 + 6H2O
By doing this, we have created an equation that has an even number of carbon and hydrogen atoms on each side, but we'd need to adjust the oxygen to balance it correctly. After adding up the oxygen on the product side (4 molecules of CO2 with 2 atoms of oxygen each equals 8 oxygen atoms, and 6 molecules of H2O with 1 atom of oxygen each equals 6 oxygen atoms, totaling 14 oxygen atoms), we need to provide the same number of oxygen atoms on the reactant side. The number 14 is even and divisible by 2 (since O2 contains 2 oxygen atoms), and therefore we can use 7 O2 molecules:
2C2H6 + 7O2 → 4CO2 + 6H2O
Thus, the correct coefficient of oxygen is 7.