To answer this question, we need to:
Step 1 - Balance the question
To balance the equation it is necessary to have the same number of atoms of each element on both sides of the equation (reactant side and product side). Let's count the number of atoms of each element for the unbalanced equation: C2H6 + O2 ---> CO2 + H2O
Reactant side:
C - 2
H - 6
O - 2
Product side:
C - 1
O - 3
H - 2
As you can see, carbon, oxygen and hydrogen number of atoms are not equal on both sides of the equation. Let's balance it by changing the stoichiometric coefficient.
C2H6 + O2 ---> 2 CO2 + H2O
Now we have 2 atoms of carbon on both sides.
Let's balance hydrogen:
C2H6 + O2 ---> 2 CO2 + 3 H2O
Now we have 6 atoms of hydrogen on both sides and 7 atoms of oxygen.
C2H6 + 7/2 O2 ---> 2 CO2 + 3 H2O
Now we have 7 atoms of oxygen on both sides, but the coefficient of O2 is not an integer. So let's multiply all the coefficients by 2:
2 C2H6 + 7 O2 ---> 4 CO2 + 6 H2O
Answer: 2 C2H6 + 7 O2 ---> 4 CO2 + 6 H2O
Coefficients are: 2, 7, 4, 6
The sum of them: 19